ple set at each time that you learn from that That's correct I see but in this case this is independent that we just run you see we run MD simulations of the water or structure that we have it here and then we predict DFT or that structure that recalculate single point DFT of that structure that we get and then we see the error bar I see between Interesting and then my second question is actually the structure of the neural network you are using he mentioned graph neural network you said you are not using that are you using fit for neural networks because if you use fit for neural networks I imagine that you basically take the structure of your system and then you have to basically flatten it into like a single layer that you input but then you totally lose the knowledge of the symmetries and so how do you do that in practice You mean we use fit for neural network Are you using fit for neural network? Yeah Okay then it means that you take basically different positions of your atoms and you flatten it as a vector to put in your neural network but then you totally lose I mean you totally lose the idea of the symmetries right? But actually it's sort of like that because we transfer from the atomic structures to the local environment right and the neural network only we learn just the number that you extract of the atomic structures and energies and then include and then transfer to the machine learning models so our neural network don't learn atomic position like XYC coordinate directly but we transform the XYC coordinate to set up the local So there's a preprocessing step Okay, I see Yeah, that's correct Thanks I skip this part, sorry because maybe it's already known before sorry, but we can talk about the descriptors later Thank you very much Great, thanks again, Naunga Great pleasure And the next talk will be given by Zili from ICTP here on the phase diagram of iron in Earth's core from deep learning a signal at five minutes So okay, good afternoon My name is Zili, I'm a postdoc here working with the central schedule So today I'm going to show basically is a different topic which is about the phase diagram of pure iron in the Earth's core from deep learning So this is the outline of today's presentation So I will start to show that actually we can apply the methods from computational material science to study the problems in Earth's science Then I will move on to the today's main topic the pure iron at extreme conditions So in order to study the phase stability I develop a neural network potential for that So to study the mechanical stability of the BCC phase then I will show you the phase stability of all the possible solid iron phases So this is followed by a very short, very brief summary So Earth is a planet we live So of course we want to understand what is inside Geophilic is the method you can use to decipher the density, the compression wave velocity and the shear velocities as a function of depth And based on these continuities we can divide the Earth into different layers The crust, the mantle, the outer core and the inner core And the shear velocity for Earth's outer core is zero That means it is in the liquid state And for the other parts it is in the solid state But that is not enough We also would like to know what kind of minerals that could be present at the Earth's mantle conditions and at the Earth's inner core conditions So this could be provided by mineral phyllox And in the figure on the left-hand side is one of my favorite So they are clearly summarized What kind of minerals that could be present at the Earth's mantle conditions So probably you are more familiar with this phase the phyroperapylicis So it's a magnesium-riched FeO So because it's FeO, no It's really high-debated about this phase at low mantle conditions But from mineral phyllox we cannot know precisely what is a relative percentage of different minerals So for this we need to know the thermodynamic properties for all these minerals But in order to check our predictions we need to know the elastic properties for all these minerals Of course, Earth is not static It is dynamic So you have a subatomic zone that means very cold, very heavy materials that will sink into the Earth's deeper interior And these very light and hotter materials will rise up along this calm and boundary In order to study this dynamic process we need to use fluid dynamics For this we need to calculate the viscosity of plastic properties and the transport properties for different minerals That is the input for this fluid dynamics But nowadays I realize the isotopic fractionation is a new trend in our field So in the past, so one of the central problems for Earth science is to understand all these properties for different minerals And in the past it's very difficult But in the last 20 years lots of methods has been introduced from computational material science that really make the geologist's life easier I just want to show a few cases just to explain to you the chemical reaction when the computational material science means Earth science This is from my previous work The first case I want to show you is about the deep carbon circle This is actually my master work At that time, people are more interested in the deep carbon circle in the deep Earth's interior We know that at the Earth's surface most of the carbon is stored in this carbon in the face such as the cedarite But from our calculations based on ab initio-large dynamic simulations we found it out at high pressure and high temperature it will dissociate into this this iron-rich carbon in the face applied diamond So from our study, we found it out this diamond is everywhere in the lowman conditions We also did a test and compared the performance of different exchange quality functional In this case, we found this hybrid functional performance better than the TFT-plus-U method The second case I want to show is about the formation of the moon This is actually my PhD thesis So after the upload mission people start to realize there are lots of similarities between the moon and the Earth In order to explain these similarities the Janin-Pen model is actually developed So in this model the mass-sized object will collide with the proto-Earth So it results in the formation of the proto-lunar disk From this disk, the moon is formed But for us, we would like to know the behavior of this impactor's iron core during this Janin-Pen process So for this we use ab initio-molecular dynamic simulations to calculate the Hugon lines The Hugon lines tells us the peak conditions that could be reached during this impactor process So as long as you give me the impactor velocities I can tell you the highest pressure and temperature they can reach We also calculate the entropy along these two Hugon lines Then after we obtain all this information we develop a thermodynamic model and we find out lots of iron vapor that could be produced during this impactor process Now after my PhD work I got the opportunity to continue my work on this pure iron to stay with the central scala So this time I will be focusing more on the feasibility of this solid iron phase And of course iron is the major component of the Earth's core Every properties about this phase is very interesting For example, we would like to know its melting curve We also want to know that its thermal conductivity at the Earth core conditions And of course you can go beyond that you can experiment determine the melting curve to the super-Earth conditions because we would like to know whether there is life in the other planets Due to these very important properties lots of work has been done in the past I just give you a very brief summary of this work So suppose the most stable structure before melting is the AGSPR Now after it all performed abinitial molecular dynamic simulations up to the inner core boundary they found out that the melting temperature at the inner core outer boundary at around 330 gPa the melting temperature is about 6,000 Kelvin But the problem is that the simulations use a very relative small simulation number of iron atoms is only 150 Probably it will make a difference if we use a larger simulation cell So a following work done by Lowy et al they performed molecular dynamic simulations with the embedded atom models they found that actually the melting temperature at the inner core outer boundary is only 5,000 Kelvin So it's actually 1,000 Kelvin lower than the estimation done by Lowy et al That will make a huge difference if the melting temperature is very low And the DPD is also present in the experiment work and one will experience support the high melting temperature at the inner core outer boundary and one of the work done by from the Keke-Lawson group they found out the melting temperature is still very low So my conclusion is that the melting curve of this ATCPR remains highly debated Then after the publication on the melting curve of this ATCPR phase people started to realize that probably ATCPR is not the most stable phase before melting And indeed the work done by Keke-Lawson and Ben-Noshko they found it out actually at high pressure and temperature the ATCPR phase will transform into the BCC phase That's very interesting I mean if the BCC phase is present at the inner core conditions we have a lot of stories that have been rewriting about the geodynamo However with the rise of the computational power a large simulation has been done by Goddwell in 2015 and they found it out actually the BCC iron is even not mechanically stable it is located at the saddle point along the beam path that means you deform the BCC iron and change its C-Wassay ratio but this picture is challenged again by Ben-Noshko in 2017 and the new phenomenon is emergent they found out in this BCC iron they found out this fast diffusion because this is a liquid component it will entropically stabilize this BCC iron phase So my conclusion about stability of BCC iron so it remains highly debated and of course probably BCC iron is the most stable phase and there is only one work to support this idea as you can see in the figure on the right hand side that actually at high temperature at 6,000 Kelvin that the cheap energy of the BCC phase is lower than the AGC phase So to summarize the similar dynamic stability of the solid iron phase it remains highly debated and in our work we would like to solve all the problems in one piece of work So for this we want to we develop a new one level potential for iron and the packaging we are using is called DPMD which is developed in the robot cars group and I won't give too many details about this method because it's already a dedicated talk on this I just want to stress one more point that you can actually treat deep learning as a function with atomic positions as an input and the energy force and stress as the output and there's nowadays there's a lot of packages you can use to train the neural network potentials and they differ a little bit in the atomic descriptor and the neural network structure and in DPMD they use some embedding techniques to construct this atomic descriptor as you can see that it's all matrix operations that is very good for GPU calculations because nowadays GPU is a new trend and they also try to use a regular neural network structure which is greatly enhanced the learning performance for very deep neural network So after we train the neural network potential for iron we use an independent test data set to characterize the performance of the DPModels As you can see from figure on the left hand side the x-axis represent pressure and the y-axis represent temperature we actually characterize the performance of DPModels on energy, force and pressure over a wide range of pressure and temperature conditions and for one of this column, this column that from top to the bottom it represents a different phase such as liquid, this is FCC and ACCP and BCC phase And as we also check the performance of the DPModels with the different number of atoms just to make sure that its performance remains stable if we want to perform larger scale simulations As you can see from the upper panel that the root mean squared error of energy is less than 6 MeV per atom Think about this, we are performing simulations at 6,000 Kelvin the KBT is very large and the error on the force so in most low case is less than 0.3 MeV per angstrom so that's super accurate for the pressure in most cases the root mean squared error is less than 0.6 GPA We also did a comparison between our DPModels and the E-M potential developed by Noshiko As you can see that the root mean squared error of force predicted by E-M potentials in the most cases is larger than 1 MeV per angstrom so it's huge After we check the accuracy of these DPModels the first questions we want to solve is the mechanical stability of the BCC iron phase For this we use different techniques and the first technique we are using is to directly calculate the elastic constants I just remind you that for FCC or BCC phase there are three independent elastic constants the C11, C12 and C44 and the stability conditions requires that the C11 must be larger than C12 and C4 is also positive For this we use two different stream metrics we deform the BCC iron lattice then we run MD simulations to obtain this result the stress tensor from this based on this we can estimate the elastic constants so after we obtain the elastic constants we estimate all the pressure temperature conditions that is C11 is equal to C12 so above this BCC instability line the BCC iron phase is mechanically stable and below it is not mechanically stable We also check our predictions based on these elastic constant calculations for this we take several conditions along this instability line then we deform BCC iron along this beam path by changing in C was a ratio after we deforming this BCC iron we calculate the stress difference and from this we can calculate the work that is done to deform the BCC iron and in the figure on the right-hand side this tetragonal distortion T you can treat it as auto-parameter if it is equal to one that represents this structure is the BCC phase and if it is equal to 1.26 it corresponds to the FCC phase so based on the work that is done to deform from the BCC phase to FCC phase we can sum it up to calculate the free energy difference between the BCC phase and the FCC phase however from our calculations we found out that actually the stress difference does not change continuously as a function of the tetragonal distortion T that means we cannot there is a phase transition here we cannot use this method to estimate the free energy difference between the BCC phase and the FCC phase but we can actually integrate this stress difference like around the T equals to 0 to show that actually the BCC phase is located in a local minimum so now we finally sorted out the mechanical stability of the BCC diurent we found out that the BCC diurent is a mechanical stable at the earth in the core conditions so we move on to calculate but we would like to know whether temperature alone is enough to mechanically stabilize the BCC diurent phase so for this we use a shower I want to give more details about this method because in Darwin there is a dedicated talk on this so from a shower we can we can obtain this auxiliary form of spectrum it agrees very well with the previous studies use a very similar approach but the problem is that for this strongly harmonic system whether this auxiliary form of spectrum is meaningful is problematic so there is another method in a shower which is called position of free energy Hessian which is a second order derivative of the free energy with respect to atomic positions so as long as you find this unstable mode like here a collective motion along this imaginary mode that will decrease this free energy of the system that means in this case it is not mechanically stable we also consider the effects of temperature we found out the temperature will greatly stabilize the BCC diurent as you can see here at 4000 Kelvin the end point the frequency at the end point is negative but with increased temperature the unstable region shrinks towards the brilliant zone center around the gamma point however from this calculation we found it out even at 7000 Kelvin BCC diurent is not mechanically stable so there is a difference between the calculation with the shower and our elastic constant calculations that actually reflect the contributions of the self diffusion so the self diffusion will stabilize the BCC diurent at the highest temperature at 7000 Kelvin so our research highlights the roles played by self diffusion in mechanically stabilize the BCC diurent then we want to calculate the Gibbs free energy for different phases because we want to build the free diagram for this we use thermodynamic integration method to calculate the Gibbs free energy for the FCC phase for the IGCP phase and for the liquid phase basically in thermodynamic integrations you couple your system of interest with a system that has a known free energy but this method does not you cannot apply this method to the BCC phase because BCC phase has a self diffusion if you do this you will know the simulation will not converge so for this for BCC diurent we use a two phase coexistence method in this method we put the solid iron and the liquid iron in contact then we run simulations in the NVE ensemble from these simulations we can obtain the equilibrium pressure and temperature but as you can see here there is an interface that will really affect the final results but we do not have such problems because we can systematic test the effects of the number of atoms on this melting pressure and the temperature and during these simulations we constantly monitor the structure change just to increase whether there is a new phase that is present and this is a in this figure I showed the Gipsy-Frander difference calculated with the DP models and the different color represent different temperatures and this dotted line represent the liquid phase and this solid line represent the BCC phase and this dashed line represent the FCC phase and we treat the IGCP iron as a reference as you can see at 5,000 Kelvin near the melting point of the BCC of this IGCP phase the Gipsy-Frander difference between FCC and the IGCP phase is on the order of 10 MeV atoms so we now start to worry about whether the accuracy of our DP models is enough to distinguish these two phase so for this we use a free energy perturbation theory to check the accuracy of the Gipsy-Franderity of our DP models so in this method we first run simulations in the NPT ensemble then we extract several snap shots to run this density function theory calculations from these calculations we can get the energy at the DFT level then we plug in back to this formula we can calculate the Gipsy-Frander difference between the DFT potentials and the DP models and from a figure on the right-hand side you can clearly see that actually the accuracy of the Gipsy-Franderity in our DP models is quite good usually in most cases it's less than 3 MeV per atom the most interesting feature of our DP model is that its performance is really stable with respect to the number of atoms just to give you an example let's say for the IGCP phase the friend difference between the DFT model and the DP model at around 200 atoms it is 1-1 MeV per atom if we use a much larger simulation cell at 500 atoms it is still quite stable to minus 1 MeV per atom so that's really good because that may indicate that our potentials can be used for large-scale simulations and this is the major conclusion about this work that we finally sorted out the thermodynamic stability for all the solid iron phases and in this figure this blue line represents the melting curve of this PCC iron and this green line represents the melting curve of the FCC iron and this red line represents the melting curve of the AGCP iron as you can see that AGCP iron has the highest melting curves so that means AGCP iron is the only stable phase before melting there's no solid phase transition at high temperature another feature is that the melting curve of this PCC iron phase at around 4000 Kelvin if we extend this blue line to around 4000 Kelvin is actually 4 within this instability region so that's the reason we cannot perform the simulation here to determine the melting temperature of the PCC iron and the inside is a short comparison between expanding work and from our calculations we do support the melting temperature at the inner core outer boundary is very high it's around 6000 Kelvin so after we know that AGCP iron is the most stable phase we would like to know whether this phase yield a seismic velocity that is compatible with the geophysical observations for this we are calculating the shear velocities as a function of temperature and the inner core temperature is very close to the melting temperature of the AGCP iron phase as you can see that at the melting point of the AGCP iron the shear velocity is still very high comparing to the geophysical observations which is about 1 km per second high than geophysical observations so in our previous work that is a septic velocity sample that we suggest that it is probably caused by the effects of viscous green boundaries because we need to transform or translate our single crystal elastic constant to the shear velocity for polycrystals and there is another work that suggests that probably the low shear velocities is caused by the Schupannic AGCP iron alloys that means you put a lot of elements in the interstitial side of the AGCP structure but we found that actually the BCCR has a very low shear velocities that is compatible with the geophysical observations that is very easy because now we found out BCCR is not thermodynamic stable but it has very good geophysical properties and this is my summary so finally we determined the free stability for the pure iron up to Earth's inner core conditions and it remains debated about the origin of all the observed low shear velocities in the Earth's inner core and thanks for your attention Thank you for the great talk and we are open for questions You should have a very... very large energy difference Besides... Can we trust the DFT energies or there are Monte Carlo estimation of the relative error of the DFT? So what is the scale? Besides because you study the error due to the neural network Yes, yes, yes So the energy... Eventually it could be that BCCR is more stable because the DFT is not predicting the right energy So the energy we are using here is the DFT level We use free energy for being theory but the problem is that we actually did a test with the different exchange correlation function and we confirmed that our conclusion will hold the different exchange correlation function but the problem is that we still don't know the accuracy about this DFT at high temperature That remains a problem The normal quantum Monte Carlo simulations usually put the electron temperature at T equals to zero but we will not hold for this case because the electronic temperature is very important that will greatly stabilize the BCCR interface So can you help me just understand a real basic thing You have a very nice curve up there for different structures and you've shown us some stability arguments but if I look at that curve which phase is the most stable? It's ACP, yes It's ACP and how do you know that from that graph? How do you know? Because let's say let's compare the melting curve of the BCCR and the ACP at this conditions the cheapest free energy of the liquid phase is lower than the BCCR but it is still less than the cheapest free energy for the solid ACP phase So that means the ACP is the most stable phase Okay, so if you had a real melt of liquid and you cool it then you would see that structure is more stable It would be the first one Thank you When we tried to predict the Grunizen parameters from in our case we were using the Gaussian Approximation Potential for BCCR It was incredibly difficult and one needed to have absolute K-point sampling convergent to make sure all the training was consistent Is this something that you also observed or do you have any comments there? We didn't really calculate the Grunizen properties but for our machine dataset it's always larger than 200 items then we use 2x2x2 K-points to assemble the Grunizen Yeah, but we were surprised because in an equivalent system with just say one atom of iron we needed to go up to 40x40x40 sampling or equivalent dense sampling on the supercells to actually be able to get the right Grunizen parameter and the way we interpreted that was that the machine learning was getting a little bit confused by having supercells of varying size somehow still some remnants of K-point sampling but maybe GAP is more sensitive also to this Probably I guess you're working on the lower temperature one probably now the temperature here is very high so the density is very smooth Okay, I think if there are no more questions we thank Z and all the speakers I'm looking at Nicola Seriani here we are meant to start at 2 o'clock but maybe we should do 215 so everyone can enjoy ICTP culinary might and so we meet again at 215 here So I think the kind of the kind of the kind of the kind of okay so that would be the explanation so I think this problem of overthinking is general, where it means that some of the robots already have a general understanding from a sense point. You should have come to the psychic conference, but it's something wrong. We should get together. I think that we just meet, and with the use of sense, and each of us can say something about the program. You can say something about it. But maybe you can still say a few words, one minute, and then I don't know. Or maybe you can say something about the sense point, and then maybe I can say one minute about the sense point, for example. So, I think there will be, I mean, because the program is there, I don't know, other people say, we spend one minute each playing, and then everybody needs to be after the science, and then see what's going on. It's not very factual, I mean, as I am, but I'm not sure. Well, well, if that's the least, if that email is there, everybody needs to be after it. So, if I could hold a few of some power involved, if I could adapt it to my mind. Yeah. Are you trying to show it off? I don't know. I don't know. If you read something about the robot, it's very difficult. That's why I said it's difficult. Oh, OK. Am I saying wrong? Oh, yeah, well, we're going to do that. Great. That's fine. That's great. OK. Well, I will. Yeah. But, you know, it's just a model. Just a model. Yeah, just a model is fine, right, to understand what's going on. Oh, well, we could make it general. I know. I'm hoping that not everybody would otherwise be unmanageable. Yeah. But we can say that. We can say that. I still suspect that a few people will read right out of the end. A few people will not read the rest. So I guess the beautiful side of it is that maybe people will finally read it. Yeah, we can say it through. Well, I said, yes, it's here. There are only the three of us. When you're coming. And the short one, right? So we can, yeah. Maybe Friday. Yeah. Well, this is only the three of us. But between at the end of the day. So you work also on battery? Yes. Yes. Well, yes. Yes. I cannot show the only thing. I know what is going on. I cannot bring it up. It's a really tough field. No, no. Yeah, I know. Yes, yes. OK. In that case, this is a different case. I think there are many, many reasons. Expert in the repeat, probably not in the problem. We have the chair of the last session setting up. It's tough. Okay. So I'm not actually personally acting on it. Yeah, yeah, yeah. This one? Yeah. No, no, no. No, no, no, no. At the wedding? Yeah. No, no, really, thanks a lot. It's the same problem. That's exactly what it's like. I cannot read this to you. Yeah, yeah, yeah, yeah. If you were married, so you can't keep my jealousy. That's true. We have an order. Yes. And... Yeah, yeah, it's the same thing. We indicate. Yes, the whole once. Actually, we're very impressive. So we have a lot of rules. It's really... Yeah, yeah, yeah. And in principle, the formula is the numbers, and you get the number. Exactly. The number of complications. Yeah, that's the problem. Yeah, yeah, yeah. Exactly. That's what we say, though. But at the first stage, it runs. You know, they ask you... No, no, don't ask. No, thank you. So I tried my own laptop, but it didn't work. Otherwise, you can upload a video. I had some video. No, no, this is the desktop. So you can try. Yeah, can you imagine? Yes. So I knew that... I'm here. I might. So I knew my best. Yeah, make it very important. Who are they? They're the lack of one. They're the lack of one. They're the lack of one. I'll stop. I'll let you know your things. Thanks very much. Okay. I'll ask you if you can remove the badge. I'll try it. Okay. Yeah, quickly. Without spoilers. Okay, towards... Without spoilers. Without spoilers. The question answered, we want to let it continue. Yeah, so the pipeline is... Yeah, yeah, 20%. Now we can't take off the... Yeah, well... That's good. We'll be short. Yes, yes. I had another thing that... In the program there is written the wrong application. They call that one is the... Okay. Thanks. Just to upset Nicola. Yeah, I mean, I think it's my fault. It's my fault. Next to you. Yeah. Who should I ask for uploading the talk? They want to upload the talk. Okay. How are you? How are you? I'm good. I'm good. We'll be here around the... This bill. Okay. Okay. Yeah. Thank you for the questions. You have your own. Yeah. Okay, welcome back. So we have talks from two different sessions now. The first one is a session called Methods for Phonons and Thermal Transport. Oh, I forgot to introduce myself. Sorry, I'm Shobana Narasimhan from the Jawaharlal Nehru Centre for Advanced Scientific Research in Bangalore and India. So we will now have a talk on thermodynamics and dynamical properties of strongly anharmonic and quantum materials. The talk is by Lorenzo Monacelli, who is from EPFL in Lausanne. Thank you very much for the introduction. And I want to thank the organiser for giving me the opportunity of speaking in this very broad audience today. I am Lorenzo Monacelli. And I will tell you something about how to compute the thermodynamic properties in materials and dynamical properties in materials that suffer from strong anharmonicity in the ionic displacement and also have show sizeable quantum fluctuations. So we are interested in computing thermodynamic properties because it's the study of a system in equilibrium and in particular we are interested in linking what are the microscopic properties of a material that we can simulate in a computer to the mesoscopic properties that are, for example, described by temperature, volume and number of particles. And these links is done by statistical mechanics and in particular by quantity, which is fundamental in this field, which is the free energy. So if we know the free energy of the system, we can establish which is the equilibrium a specific thermodynamic condition. For example, in a canonical ensemble, the minimum free energy at fixed temperature, volume and number of particles determines what is the equilibrium. And so we can use this property to compute phase diagram. Now, from thermodynamics, the free energy is simply the internal energy minus the temperature times the entropy and this is linked to microscopic properties of the system with this equation, which is quite simple, which is just the internal energy is just the average of the Hamiltonian and the entropy can be computed with Boltzmann definition, it's just the average of the logarithm of the density matrix. Now, in this equation here, in principle there are both ionic degrees of freedom and electronic degrees of freedom, but for thermodynamic room temperature or temperature which are lower than thousands of Kelvin, the electronic degrees of freedom are not so important, at least directly, because the temperature is not sufficiently high to excite electronic transitions. Therefore, in most cases, we can do a very good approximation, which is the Born-Oppen-Eimer approximation, which consists in integrating out the electronic degrees of freedom and treating the system as it is always in the ground state of electrons and therefore the degrees of freedom that I'm describing here are ionic degrees of freedom, so are ions, and these density matrix actually describe the ionic positions and this Hamiltonian here is the Born-Oppen-Eimer Hamiltonian, which can be computed at any level of theory, densifactional theory, more sophisticated one like quantum Monte Carlo or even machine learning potentials. Now, the free energy is very important because it not only allows us to describe which is the equilibrium of a system, so the phase diagram of a system, but also its thermodynamic properties through the derivatives of the free energy, so the derivative of the free energy with respect to volume gives us the pressure, for example, and this allows us to compute for thermal expansion of a material and if we do other derivatives, we can compute thermodynamic observables like the bulk modulus, the specific heat, the heat capacity and the thermal expansion and so we can completely characterize a system of its equilibrium properties by just knowing the free energy and its derivatives, so it's very important quantity. Unfortunately, it's also extremely challenging to compute free energy from a simulation and the reason is that these average here cannot be done by a simple sample of the potential energy like we are used to compute observables and the reason is that this logarithm has an important contribution from region of the phase space which have a very low probability of occurring in a simulation and in the equilibrium condition. Therefore, we cannot compute this integral using standard approaches. However, there are methods have been developed to compute free energy and one of the most effective method is thermodynamic integration and in this method, what we actually do we define an auxiliary Hamiltonian from which we know how to compute the free energy because it's analytical. For example, it could be an harmonic oscillator and then we parameterize a Hamiltonian with a parameter lambda so that this Hamiltonian is equal to the auxiliary Hamiltonian when lambda is equal to zero and is equal to the exact Hamiltonian when lambda is equal to one. And then we can integrate between lambda that goes from zero to one and get the exact free energy. So this equation here is exact and it's a way of computing the free energy and the cool thing about this equation is that actually this derivative of the free energy can be computed using standard sampling techniques because this object here is actually unobservable that can be computed with standard approach and this is just the difference between the exact potential for example the one we get from density functional theory and the auxiliary one that define our auxiliary Hamiltonian. Now, this is, as I told you, a feasible approach so there have been already many calculations using exploiting this approach but it can be extremely expensive anyway and in particular this is true if our system suffers for sizable quantum fluctuation because then sampling this object here for many values of lambda between zero and one becomes challenging because molecular dynamics for example is not any more a good way of doing this sample we need to rely on more sophisticated approach like path integral and doing this with many values of lambda could be challenging. It is not impossible. Some cases have been achieved but it is still computationally extremely expensive so we wonder is there a way of starting from this exact expression to get an approximated one which is more feasible computationally and the first thing we can think of doing is actually to assume that this value here inside the integral is a constant and then we can take out from the integral and we approximate the energy in this way. Now this is accounting for an harmonicity because this term here is correcting our Hamiltonian accounting for all an harmonicity and we can prove something which is very important for this approximation here is that this approximate symbol here is actually lower equal so we can prove that the exact free energy is always below the free energy we obtain with this approximation and this is very interesting because while this is already a quite good approximation for the free energy depending on the starting Hamiltonian auxiliary Hamiltonian we can do more. We can now say that among all possible trial Hamiltonian that we can use the one that give us the lowest free energy as a final value of this equation will be the best one because we know that the exact free energy will be always lower than this value and this will allow us to formulate a variational principle in which we can say okay, now we can choose among all possible Hamiltonian the one that give us the minimum value of the free energy and indeed we cannot choose all possible Hamiltonians but only Hamiltonians for which we know how to compute the free energy and these are for example harmonic Hamiltonian and that's how we define the self-consistent harmonic approximation in which this Hamiltonian is chosen as the most general harmonic Hamiltonian and optimizing this Hamiltonian just means optimizing the parameters which are this auxiliary force constant matrix and the average centroid position the centroid position of the atoms in the system and by optimizing this we can compute the free energy and the cool thing about that is that we don't need to evaluate to do any kind of molecular dynamics here because we know how to sample this Hamiltonian analytically and then we need to fluctuation very quickly so we don't need to thermalize anything we just need to extract we need to perform the minimization but we need just to extract randomly distributed atomic configuration and compute this average here and this is extremely efficient and can be done at the initial quite easily and I will show you an application in which we did this with Nicola Marzari very interesting which is the case for the halide perovskite which are a very important family of systems for application in perovskite solar cells which is the fastest growing solar technology nowadays and the very cool thing is that one of these perovskite halides reached the power conversion efficiency of 25.2% which is competitive with silicon which has been achieved after 60 years of optimization while this is pretty young candidate the problem of these candidates is that they contain lead which is toxic and so we need to find a substitution to lead which can be feasible and this perovskite here with tin is one of the most promising eco-friendly solution but while its performance are competitive with the one of lead it has a major drawback which is that it is unstable if we expose this system to the air and what happens actually is that it tends to oxidize and it tends to it decomposes in a different phase which is not perovskite it is a yellow phase which then further oxidize and transform and degrade the performance so if we can prevent this perovskite to transform in this yellow phase it will be extremely useful and the problem with this perovskite is that we don't know the real phase diagram and the reason is that this is a phase rich material which have the old perovskite polymorphs from cubic, tetragonal and all to wrong because different temperatures if the system is synthesized under inert atmosphere but if we take this system and we expose to the air it rapidly change the structure into this yellow phase which can be then restore the cubic structure by rising the temperature above 425 Kelvin so this is a quite complex phase diagram and it's not clear which one of these two phases is actually more stable so is the air simply pushing this perovskite structure toward the real ground state which is the yellow phase or rather it's just a surface effect of some kind of impurities that generate at the surface and so a more complex effect and to answer the question the only way we can do with calculation is computing the free energy of the two phases and compare them and this is the result interesting result to get so I'm comparing the free energy of the yellow phase here in orange with the free energy of the perovskite structure and what we observe that in the working condition which are between 300 and 350 Kelvin we observe that actually the cubic phase of the perovskite and all the perovskite structure are more stable than the yellow phase so it seems that the perovskite structure is more stable and so this formation of the yellow phase is not an intrinsic effect but it's due to surface and impurities and other more complex effect but that can be treated with better engineering of the system and we can also go beyond and if you wonder about the accuracy of this free energy I'll show the next slide in which we thanks to the derivative of the free energy we can compute, characterize the thermodynamic properties of the system and for example here we relaxed the volume including all an harmonicity of finite temperature thanks to the fact that we can compute the pressure to the derivative of the free energy and we computed the thermal expansion which is in very good agreement with experiment and also the transition between here you see this angle here that the difference between an orthorhombic cell when theta is different from 90 degrees to a rhomboidal cell when theta becomes 90 degrees and as you can see the system is transit the experimental transition temperature is 360 so if you look at this line this point here is 350 Kelvin so it's very good agreement with experiment and also the transition between the rhomboidal structure and the cubic structure occurs when the A and C meter becomes the same and as you can see here this occurs at 450 Kelvin in our simulation while the experimental transition temperature is found to be 440 Kelvin so again a remarkable good agreement which seems that this method is very powerful and very predictive so this is another example that we recently that has been recently accepted in natural physics and this work is done in collaboration with Marsula which we present tomorrow and so probably we give you more details about this on the phase diagram of hydrogen of high pressure hydrogen here we are at 0 Kelvin so all the anharmonicity is given by the quantum fluctuation of the H2 molecules and you can see here the difference between the static phase diagram so the enthalpy you get from a standard DFT calculation and what you get if you add on the top of the static enthalpy we get 0.0 energy which was the state of art before this work and then we can add the total contribution of the free energy using this self-consistent harmonic approximation and as you can see it's the phase diagram changes completely and in this last term here we observe a first molecular to molecular transition between phase 3 and phase 6 of hydrogen and then we observe the atomization at 577 Kelvin and this is very important because the atomic phase of hydrogen is predicted to be a room temperature superconductor so it's very interesting and the interesting thing about this work is that before the so we reproduce this transition temperature which has been observed by an experiment to another molecular phase and we did the calculation also for deuterium to try to predict what is the isotope effect and we obtain a shift for this transition of 32 gPa and after we publish on archive this work almost contemporary work by Paul Hubert measure this isotope effect to be 35 so we were both of us not aware of one of the other work and we got a very good agreement with the experiment so I hope this can convince you that this method has really a very important predictive even in very difficult system like this one so but these are thermodynamics so this is to characterize thermodynamics but sometimes we want to do more and we want to study the phonons however there is a caveat on all these methods both the that even similar methods like self-consistent phonon temperature dependent energy landscaping and this similar methods as these have is that one is tempted to take these phonons defined by the harmonic auxiliary Hamiltonian and define phonons through them but unfortunately this is not correct because this Hamiltonian is just an auxiliary quantity to describe the thermodynamics of the system to compute the phonons we need to ask ourselves what a phonon really is and a phonon is an excitation of the lattice so unfortunately a phonon is a dynamical quantity intrinsically speaking while this theory is a static quantity because it's based on free energy however there is a case in which the excitation of the lattice can have a zero energy so it can be described by static theory and it is when we have second order phase transition in which the displacive phase transition in which we have a lattice excitation whose energy goes to zero and trigger a symmetry lowering of the system and this can be computed with the static response function which is related to the Hessian matrix of the free energy which is not the same thing as the auxiliary force constant and therefore we can compute the Hessian matrix and let's take for example the example of the perovskite I showed you before this is the CSSNI3 perovskite in the harmonic phonon dispersion in the cubic phase you can see we have imaginary phonons in this region which means this phase is unstable at zero kelvin which is common for many materials and then if we do the simulation of the Hessian matrix at 250 kelvin we see a strong renormalization of all the bands and as we increase the temperature this soft mode starts increasing up to 450 kelvin when finally it becomes stable and therefore say that the transition temperature is of this kind and occurs between 400 and 450 which again is in extremely good agreement with the experiment in which this occurs at 440 kelvin and however the phonons we get, the band structure I show you is good only to compute second order phase transition, again those are not the real phonons of the system the phonons are dynamical quantity they must be computed with a dynamical theory which is the we can compute them as the poles of the dynamical spectral function obtained by the green function of the lattice and to do this in the study case in the case of frequency equals zero the inverse of the green function coincide with the free energy Hessian so the theory matches we need a dynamic theory to compute phonons and this can be done with the time-dependent self-consistent harmonic approximation in which instead of optimizing the free energy we find a dynamical equation that makes the action constant so that kill the derivative of the action and we get this self-consistent equation which is very close to self-consistent time-dependent or time-dependent density functional which is our theory and if we take the linear response of this equation we can get the green function and this can be done, for example the details of these are done in this paper here in which we show the implementation of a Lancho's algorithm which is similar also to what is done in time-dependent DFT to achieve this and actually I can show you the results again I can write the cubic phase of the CSN i3 and in this case we see this is the spectral function and you can see how this system actually is really an harmonic this is not the logarithm of the spectral function, this is the spectral function and so it's really broadband and as you can see all the phonons here mix one to each other so in many cases it's not even is what and they overlap and this is very important and relevant if you are studying thermal transport for example and there is a poster this afternoon by Giovanni Caldarelli which we talk more about this and I think also the talk tomorrow by Michele Simoncelli if you are interested we can also plot the same quantity, the spectral function resolved mode by mode to have an idea on understanding what is happening and how, why this spectral function is so broad and you can see a lot of satellite peaks and this is very very interesting by itself but we can also use the same technique to actually compute Raman spectrum infrared spectrum which has dynamic quantity and here I am showing the hydrogen Raman spectrum of the phase 3 at 250 gPa and the comparison between the harmonic approximation the auxiliary frequency you get from the self-consistent harmonic approximation and the full time-dependent self-consistent harmonic approximation result compared with the experiments and as you can see if you don't fully account these dynamical properties and it's an important shift it is completely non-negligible almost 50% of the energy which is relevant if, as in this case Raman spectrum is used to determine which structures correspond to which phase because hydrogen at this high pressure is very difficult to probe with other techniques and this work has been done by Antonio Siciliano who will present a poster tomorrow to go and see his work directly. So these are my conclusions so I hope I convince you that the self-consistent harmonic approximation is a very good way of computing free energy and its derivatives and to calculate phase diagrams and low-thermodynamic properties and this presentation comes with a big warning for any of you that are working on phonons that if you use this approximation be careful that the agent value you get from these auxiliary Hamiltonian are not the real phonons but they must be corrected and the real phonons can be computed with a time-dependent extension of the theory. So the code to do this is all open source is available at this website www.ssca.eu and we are organizing currently a school about the code between 26 and 30 of June at San Sebastian so more details are available on the website and the full program will be uploaded in a few weeks hopefully and I want to thank all the collaborators that make this work possible Francesco Mauri, Michele Casula Nicola Marzari, Antonio Siciliano and Giovanni Caldarelli and thank you very much for the attention. Thank you for a very interesting talk questions. Thank you for your talk it's really interesting how would you estimate the error bar for your energy from the SHA and compared to the thermodynamic integration method. Thank you. So this is a very nice question actually in this case the error bar is present but it's not visible so it's present in the problem because the dots are bigger so you can see a bit there here the error bar and we have two kinds of errors so this is a stochastic method which is sampling this average to a stochastic approach so we have a trivial error bar which is given by the fact that we have a finite number of configurations and this is trivial to estimate and this is provided by the code that the output has an error and this is what is brought here then there is a second error which is more difficult to estimate which is what is actually the error of the approximation and I mean the point is that what you can do is to try to not describe just one quantity after one simulation you get a full thermodynamic description you can compare with other quantities and then see if some of these quantities are known experimentally how they compare like in this case so we have other phase transitions that we know where they are and so if there is a very good agreement then it's very likely that a good approximation a curiosity when the temperature goes to zero your free energy goes to zero you have a residual quantistic you have all the quantistic effects so it depends on the so in this case this is a free energy difference so it can but you have all quantum effects so here I have not shown this but if you go to very low temperature you see in this material the quantum effects at this temperature are not so relevant but for example in the case of hydrogen they are I mean this is all quantum here the effects are all quantum effects and you have I mean if you do for example thermal expansion you see that up to the by temperature the volume remain almost constant and then goes up and all the thermodynamic properties reflects this Any more questions? Can I have the speaker again? So we now switch topics to spins and magnetism and the first talk will be by Antimo Marazzo of the University of Trieste and the title is Digital 2D Spintronics with electric dipoles from spin FETs to ferroelectric topological insulators Can you hear me? Yeah. So thanks for the interaction let me just thank all the organizers for inviting me here today it's really a true honor and a great pleasure what I would like to talk about is actually two different projects the first one will be about modeling a novel 2D materials with strong Rashper spinobic coupling for spin field effect transistors while the second one will be about this ferroelectric topological insulators but these two projects as you will see they have actually a lot in common and they are in a sense two different ways control of the electron spin to manipulate spin currents in a digital way so we will just see that we need to care about the sign of a gate voltage so everything is either black or white 0 or 1, yes or no and with this digital control we can realize kind of spin electronics or probably should say spin orbitronics devices made of 2D materials and the way we are going to do this in both cases will be exploiting hopefully in a smart way in a very very strong electric dipoles so spin tronics has been around for a while the field is a little bit gigantic so today we will be concerned with two basic concepts that you see here the first one will be the spin field effect transistor as it has been put forward by Dat and Das more than 30 years ago and the other one is the concept of topological insulators so the spin field effect transistor is actually a very simple concept you have you have a spin current that is injected through this ferromagnetic contact here and that goes into a two-dimensional electron gas which is in presence of rush-pass spin orbit coupling now in order to have spin orbit coupling in an electron gas you need to break inversion symmetry the way you do this is through an external out-of-plane electric field which is driven by this gate voltage here so with this gate voltage you control the amount of rush-pass spin orbit coupling you have because of rush-pass spin orbit coupling the spin in the electron gas process so there is a precision here in the channel and then at the end you put another ferromagnetic contact and then depending on the relative alignment between the spins you can have different output signals and all of this can happen because electron gas with rush-pass interaction has this very nice bend structure here with the rich spin textures the spins winding around the center of the valley and in principle you control the rate of procession with the gate voltage so this seems very interesting but still we don't have a data-da spin-fet in our pocket after 30 years and in fact it might be actually a little bit naive proposal and there are many problems associated with realizing this device the one that I think is one of the most important I think is that you in principle would need very large electric fields to basically control this rush to have relative short channels and a device that you can consider to be sufficiently small you would need exceedingly large electric fields and to me the situation changed radically about 10 years ago when people like Arthur Freeman, Alex Zunger Zhang, Liu and Luo realized that actually what was essential to make a progress in this was there just in front of us but we were blind to it, we couldn't see it and in fact they called this effect the hidden spin polarization and I'll try to explain you this mechanism which is astonishingly simple and yet rather important so as I said to have rush for spin-over coupling you need to break inversion symmetry and people used to think that that meant breaking the global inversion symmetry in terms of the space group but they realized that actually spin-over coupling is a local effect it's an atomic almost effect so you only need to break inversion symmetry in terms of the point group so you can have a situation where you have a centrosymmetric material with strong dipole fields that compensate each other and these two components lead to doubly degenerate bands that have opposite spin polarization so you can have strong rush bands but they are doubly degenerate and the polarization sort of cancel each other and these two states are localized on one of these two separate sectors that you see here forming the inversion partners and in their work Zunger, Freemann and others not only propose this idea but they also made a list of materials and this is one of their materials it's made of lantanium, oxygen, bismuth and surfer and you see that it has a strong strong rush split band structure both in the conduction and valence band and it's doubly degenerate so we have opposite spins I think they use the green and orange color that are one, you know, they compensate each other and about the same time they propose this actually they also realize that you can use this effect this kind of materials to substantially improve the original proposal about that and that and you see it here now you have this strong rush split band structure but you cannot use it unless you break really now the space the global inversion symmetry and you do this now with a gate voltage again but a different advantage with the original proposal by that and thus, now the strength of the rush person coupling is entirely given by the internal intrinsic electric field that is in the material which in this case is very strong because essentially this material is made of by portions that are bound together by ionic bonding and now with this external field you just break the degeneracy between these two rush band you see there is a split splitting in energy and you can select which one of these hidden spin polarization you want to use when you dope the material in this field effect transistor so now here I try to show this in more general terms we take again this simplified model by that and thus but now our 2D material which is this type 2 rush for materials using the nomenclature by Zunger it has a strong rush between the coupling and we just use this gate voltage to split the degeneracy and decide whether we should have a positive gate voltage because one of the two spin textures goes up in energy and if it's negative the voltage goes down in energy so we can select which one we want to use so we want these centrosymmetry materials we want them to have local dipoles and of course we want strong spinoid coupling and so what we did was actually to try to search for other materials like this so we screened our database of easily exfoliable two dimensional materials and our best shot was this this candidate here it's made of Luthetium and oxygen it comes from an experimental pattern compound so it's a structure that's supposed to exist what we calculated with simulations is first that it's easily exfoliable it has a binding energy that is actually slightly lower than the one of graphene so we really think this should be easy to isolate as monolayers and it has a very strong rush effect just to give you a feeling how strong this number is if you want to convert this into a simple with a simple minded calculation into a how much distance it takes for this selection to flip the spin by 90 degrees it would be over the order of let's say one nanometer just to give you a feeling and this is the lowest conduction band you see there is a strong rush splitting this is valley number one and I'm talking about and why is there such a strong rush effect well you see here this is the potential profile there is a strong drop from the outer region to the internal region of the material and here there is basically a strong dipole there is another one here and they compensate each other and in fact overall the structure is centrosymmetric and so this as explained by Zunger and Freeman this valley is doubly degenerate of course and this minima are localized one is on the lower part of the material and the other one is in the upper part and now of course what we do is we put an electric field in the simulation so we put an autoplaying electric field and as expected what you see is that we break this and there is a splitting in energy between the two rush broadband but for the first time in the literature what we did was actually to dope the material to do real simulations with real electrons added and this was possible thanks to the methodological work done by T-Bosoye in his PhD thesis with Matteo Calandra and Francesco Mauri where he implemented the whole DFT and the FPT framework in a fill the fat double gate stuff so not only now we put an electric field but we also put electrons we dope the material and what we observe that the splitting which is the fundamental quantity we want to optimize here this energy splitting is actually reduced so it's lower than what would be otherwise without considering the doping and this was not explained at the time so we try to understand a bit why this happens and to do that of course we did first principle simulations but we also did a very simple electrostatic model that you see here where we have the top gate, the bottom gate that are represented as charge planes and then we have the material that is also represented as charge planes separated two planes separated by a dielectric constant now we have this band splitting S which is proportional to the internal electric field and it's made of two contributions this field it's the screen external field due to the gates and a sort of internal field due to the just charge planes in the materials because these two Rushwood bands as I said correspond to states that are localized in different sectors of the material so once you start to dope it the electrons don't go everywhere but they just go on one of the two sides basically and in fact this is what happens when you study the splitting versus this gauge charge difference which basically this external electric field this is done with dense function theory in the field effect setup but if you study that also as a function of doping you really see that the doping kills a bit the effect and it's even more clear when you consider the slope of this quantity there are two different regions clearly separated here so it's actually easy to understand this in terms of the model so if the doping is low and the electric field is sufficiently high as I said you just populate one of these two Rushwood branches and so you have a strong contribution coming from a charging balance you just put in charges on one side but then at some point you start to add electrons add electrons you start to touch also the other Rushwood branch which is higher in energy and this effect is not there anymore so you add charge basically on both sides and then you get to this other regime we call it low susceptibility regime and so this of course was useful to us to understand a bit the physics here but it's actually also useful to derive optimal operating conditions for this kind of devices because now you can do the reverse process you can put constraints on splitting to be larger in room temperature I want this my Fermi level to be in this position you can put a number of constraints and then you can derive what are the optimal values that you need to use to operate the device so to basically set the gate voltages so this was what I wanted to tell you about this work we did on spin field effect transistors and I will actually switch gear a bit but still continue to talk about spin field effect transistors as you will see but now we will not discuss things in terms of a volatile effect so we will try to move to a more non-volatile approach which is interesting for a number of reasons we will not do too much anymore computation discovery as I've shown you up to now but I will try to move to over the material design effort where we engineer an artificial heterostructures to have the desired functionality and still it will always be about this so now we will talk about the second work with it on ferroelectric van der Waals topological insulators so topological insulators are there are many kinds of them these days the first one to be realized in experiments and actually one of the first ones to be original proposed in theory is the so-called quantum spinom insulator and this is a topological phase that occurs in two-dimensional systems with time reversal symmetry so they are non-magnetic systems as described by this Z2 topological invariant is the invariant is trivial you just get that normal two-dimensional semiconductor and if it's non-trivial what you get is this topological phase with helical edge states you see them here crossing the bulky and these edge states are actually spin momentum lock you see you have opposite spins going basically towards opposite directions now these materials are interesting for applications because the properties here for instance the electron transport that occurs at the edges is low dissipation or we expect it to be low dissipation because time reversal symmetry forbids elastic best scattering and then as I said these edge states are spin momentum lock which is of course something very interesting if you want to make a spin tronic device and all these effects are robust because they are protected by the topology of the bulk electronic wave function meaning that if you now start to consider disorder, impurity it doesn't change and of course since the very early days of the field people try to come up with devices you could make out of these properties out of these materials the simplest device is always you always think about the field effects resistors and indeed people try to propose this very simple device here and just showing one of the many examples you could find the theoretical literature here on the right-hand side the experimental counterpart the idea is very simple you take these 2D materials they are topological you put them under an outer plane electric field and then if the field is sufficiently strong you basically close the gap and reopen it in the trivial phase and so you can switch on and off the presence of these edge states that are potentially low dissipation and spin momentum lock but the the feature of this is that it is volatile but what we want is actually to have a similar effect but to be non-volatile and if you want something non-volatile well you typically think about ferroelectrics so we wanted a ferroelectric material that is a bit special because we want the polarization direction to be coupled to the topological invariant so for one direction it is topological for the other direction it is trivial and if you think for a second or for more than a second this is actually very unlikely to occur in a single bulk material or if not impossible to occur so the question was can we actually make a non-volatile topological field effect transistor and I think the question is yes and today I will talk about our own work on the subject that goes back to PhD thesis some years ago and then some later follow-ups but I really want to mention that there have been also other independent related efforts all around the globe that kind of elaborated on similar ideas and more recently I see appearing more and more works on this so what we showed you are gaining momentum for now it is only among theories and simulation specialists but I try to convince you that the ingredients are so basic are so simple in general that I am confident that at some point in the near future the experimentalists will start to pick up on this now I said we wanted to have a ferroelectric TI but it was not really that it didn't work that way it was the other way around we went inspired to try to have something like that where we screened for novel quantum insulators with high throughput computational methods and among the few candidates we found at the time the worst performing really the worst we got was this material here made of indium sulfur and zinc that was terrible it had a small bending version almost no indirect gap but it had a nice feature that it was essentially made by two separate monolayers so it was a single 2D material exfoliable from other layers but still it was made of two sectors one is indium sulfide and the other is zinc sulfide and what is interesting is that this material if you consider that as a stand alone material is actually a ferroelectric so we started to ask ourselves questions like what does it happen to the band structure if I now switch to polarization would it change, I mean if it is just indium sulfide of course it doesn't change but now it's a different there is an interface with another material we started to think about this and at the end of this thinking we actually came up with a revised version or a visited version of the famous bending version mechanism so for those of you who have never seen this so the bending version is what is basically driving a most apological phase so it's actually very simple there is two bands they typically have different orbital character it can be let's say an S-like band and a P-like band for a number of reasons one is the bending or maybe just crystal field in materials that can be inverted and now if there is pinnobby coupling what happens is that this degeneracy point are not there so there is a band gap so the overall the system is a semiconductor and it has this very peculiar band structures around the Fermi level what we did was actually now to assign this two bands not to a single material but to two different mono layers one is this mono layer this one a layer the other to this other mono layer and now we put this two mono layer next to the other and this is basically a kind of curve thanks to van der Waals interaction they would just stay together and now if there is pinnobby coupling well you might actually open a gap and have this kind of inverted structures that might lead to apological phase so this is interesting I think but you can do more than that because now you can play with the nature of these two mono layers and for instance you can now take a mono layer to be a ferroelectric so you consider the interface between a ferroelectric insulator and a trivial insulator and now because this is a ferroelectric with an out of plane polarization depending on the side that you look at you might have let's say different vacuum levels so actually what is different is that the band alignment between these two mono layers so in one case if you consider one side you might have a band inversion so you can have bands crossing each other or in the other case you can have just a trivial semiconductor and this realized exactly what we were trying to achieve you see in one case for one polarization direction the system is trivial in the other case the system is topological so it has this non-volatility we looked for but of course we started with this ternary compound that was not good at all because it was terrible quantum insulator so what we wanted to do was to optimize this and so we took as our reference ferroelectric induced selenium which is very well studied among the most famous I think two-dimensional ferroelectric that has the conduction band bottom at gamma and we looked for a partner for this and we screened materials databases not only our own one on the materials club but also the one by DTU that you find online and we tried to find a semiconductor that was compatible and had the top of the valence band at the gamma point and he had to add the correct band alignment to show both trivial and topological phase depending on the polarization direction we show you the simple condition for this in the next slide for the moment I just show you the result of this screening and I will not explain the details of this but just to tell you that these are all partners possible partners the ones that have the solid bar in this window here are very likely to show this effect and the message is this is not rare because in the end we are starting from trivial semiconductors I mean they don't have to be topological they come topological when you put them together and so this is there are many candidates and what I will show is what me and Marco Gibertini decided was best for us to show this effect as an example it was good for simulations but definitely I think there are better combinations out there that waited to be found and especially from the point of view of experimental work but so what we decided there was an optimal couple it was indium selenide and copper iodine actually because copper iodine is lattice matched so simulations are easier to do but also because they are both easily exploitable so we propose something that should sort of make sense to do in experiments you see the two band structures here and the condition that I mentioned before is that the conduction band of the selenide and the valence band of the other material needs to be closer the difference needs to be lower than half the potential drop due to this ferroelectric polarization but of course things are slightly first of all it works so when you do the real interface you simulate it with the FD it works you have in one case a 50 millilectron volt bandgap a quantum insulator which is ferroelectric in the other case a trivial ferroelectric but things are more complex than what you would expect by just looking at the two monolayers isolated far apart so in the trivial phase you get the bandgaps lower than what you would expect because there is a strong interlayer function and in the topological phase the polarization is slightly lower so now you get a material and a structure where not only you have different polarization direction with different topology but you have different magnitude in the polarization strength and this is going towards the end we wanted to understand a little bit why this happens because spinobicoupling is again as I said typically a local effect but here the two bands sit on two different monolayers we started things like the bandgap versus the interlayer distance you see it increases a lot if you push together the two material we started we built a simple later coaster type bonding model inspired by a maximalized function of Newtonian to describe things in simple terms around the Fermi level and you see again the bandgap increases strongly with the interlayer coupling term that is present so what we understood at the end is that yes the gap is driven by spinorbit but it's mediated by the interlay coupling by the hybridization between the two monolayers and if you look at the numbers you see here that the gaps converge saturate at some point to a value that is proportional to the strength of spinobicoupling these mechanisms is such that the strength of spinobicoupling is almost entirely or it can be entirely transferred to the bandgap it's a very efficient way to open a bandgap so you can imagine materials where spinobicoupling is stronger because there are more heavier chemical elements and you might find bandgaps that are even larger than the ones that are shown and 50 mL is more for a semiconductor but it's actually not so bad for a topological insulator and finally all of what I've shown is resilient to the twisting angle so we rotated we twisted the two materials and the band structure is the same so the effect does not depend on the alignment or on any kind of architect it's just about the band alignment between two materials you need to have proper band alignment between a ferroelectric and a semiconductor so this is what I wanted to say for today and let me just acknowledge all the people who were involved with this you see here Ron Zang, Tibosoie, Nicola Marzari, Mathieu Festrate and Marco Givertini all these two institutions who supported our work and also praise who gave us basically the fuel to run all the simulations you've seen and before I stop two advertisements, the first one is two posters the first one is by Marco here all this work we did together on this ferroelectric topological insulators but also other work he did on a similar topic and then there is another poster by Roberto Favata PhD student here in Trieste about how to calculate actually Z2 invariance when you have large supercells and disorder systems and finally with Maria Peressi we might have still a two year poster position if you're interested in first principle modelling of 2D materials and intertombing potential based on neural networks if you're interested really drop me an email or just talk to me but you need to do it today because we are the position is being closed and with this I thank you for your attention okay, thank you very much question thank you for your nice talk I have a question concerning rush by effect I want to know if graphene can also be considered as a material that present this effect because it's benga present this semi-metal beaver and or if there is a need to drop it in order to slightly open the gap and then be considered as presenting a rush by effect do you refer to the first way the first way let's say this one here something like this actually you can't really use graphene to do this because you really need this special symmetry you really need this type to do rush by material so you need to have something symmetric and that would be okay for graphene but you need to have this strong dipoles you see this this pin layer locking fat it's really based on this so you need to have this kind of much structures you cannot do this in graphene you can do other spin orbitronic devices but they're not based on this idea yeah, nice talk so I was wondering exactly on the same thing the bands showing the raishpa are they iodine derived are they? from iodine are they from iodine? iodine, ah, yeah so this is a good question so you had this L-U-O-I-O well, yeah, they are located on iodine yes, so this part of here are iodine this is lutexium, the green one and the red one is oxygen, yeah so they are located there so yeah my question actually was is there a role of the so I guess they are the p orbitals of iodine well, yeah I mean I don't remember all the denser states what my question more precise is is there any role of orbital degeneracy of the p's I don't know what was the crystal symmetry well, I mean in a sense, yes, it's all about the side symmetries you know, you need to have the local the correct side symmetries to show a rush of effects so you can, for instance, what you could do is you can screen materials without doing explicit calculation but just looking at the side groups and thinking about what are the right side groups because the reason I am asking it because recently there have been papers which actually show that if there is an orbital degeneracy so then actually there is these crossings are more like anti-crossing and the rush effect can be very severely enhanced okay, no, that might be very interesting we did say the, you know, the hard way, so we just actually look for the strongest actually what we did was, we didn't look for this type 2 we really look with Rong Zhang who did the screening we really look for the largest rush of splitter we could find and it happened that the largest splitter we could find corresponded to a material that was centrosymmetric so it was really a certain deep due so to say okay, thanks for the nice talk you might have mentioned it and I just missed it but what functional did you use? okay, so whatever you have seen up to let's say, up to here is DFT in standard PBE and GGA yeah, we have done a DFT plus U calculation to check that the F-electrons don't really interfere for this part of the talk in the next part of the talk we actually have done also, I mean the equation is just DFT and of course no local function to get the equilibrium structures for the trostructures but we also done just give me a second, yeah we also check what happens if you consider hybrid functional the situation is actually complex for this trostructure in one line if you do things with hybrid functional you still see this, in the sense that a topological trostructure in one case and not in the other with GW we couldn't do the full trostructure, we could not afford it we did just the the isolated monolayers and there actually GW would not predict to have topological the problem with this is that if you want to study trostructures, you don't really want to use things like G0 to 0 because you lose all this all the charge transfer all of that would remain at the DFT level because it's just one shot so we prefer actually to do hybrid functions here because at least you consider all this charge transfer all these self-consistence effects thank you I forgot to move to last I thank you for the nice talk so my question is when you were talking about the twist angle and robustness to twist angle if I understand correctly you kind of got a few snapshots of one that were computationally tractable which probably don't have very long moire length scales I was wondering if there's a way to show it's tractable at like I mean I know that's a good point in this specific case we think there is no problem because they are lattice matched so the idea is that if they are lattice matched there shouldn't be any real moire of course if you rotate things anything can happen but I would say I don't expect any moire physics to occur here but in general if you consider a general structure of course there can be moire and that can change a lot I mean topological superconducting it changes the entire physics but what is nice about this is that the bending version is at gamma as in this case by the way we actually think that even if there is some moire I mean of course it depends on the numbers but I would be confident that even with some moire modulation some moire patterns the fact should probably be there so it should be at least I think more robust than the moire strength thank you I think in the interest of time we'll conclude this session thank you Antimo both speakers for sticking to time and we'll now break for tea and we'll come back at 3.40 thank you I need to switch this off ok so welcome back to the last session of this afternoon before the posters obviously my name is Ralf Gebauer I'm here from ICTP and I will chair this session and we continue with the topic we have already started meaning magnetism and spins and all this and we are very happy now to have Sophie Weber from ETH in Zurich and she will talk about surface magnetization in antiferromagnets from symmetry considerations and first principle calculations thank you very much for having me so today I'll be presenting some of our most recent results from DFT on surface magnetization in antiferromagnets so since I'll be talking about antiferromagnets or AFMs for the next 25 minutes I'll first remind you from a big picture level some reasons why they're interesting or at least for our purposes why we care so in the field spin electronics traditionally fair magnets were the material of choice and this isn't surprising because they have a bulk magnetization that can be measured by direct methods in a lab and manipulated with external magnetic fields however more recently AFMs have emerged as an alternate material in spin electronics even though by definition they have a vanishing bulk magnetization they still have a bit like quantity in the sector or staggered magnetization which can be serviced a bit like quantity to store information and can be manipulated and read out indirectly for example by anisotropic magneto-resistance if we want to go back even farther for many decades an AFMs have been a key component in the read heads of magnetic recording devices where a phenomenon called exchange bias is leveraged whereby the exchange coupling between an AFM interface with a fair magnet fixes the direction of the magnetization of the fair magnet so AFMs are already useful the presence of surface magnetization enhances this utility so as I said before AFMs have zero bulk magnetization however this does not preclude the possibility of four bulk AFMs with certain symmetries which I'll get into what I mean by that later it is possible to have a finite magnetic dipole moment per unit area on the surface which I'll call surface magnetization because it's easier to say and this is easy to see for the 001 surface of chromium which is a prototypical AFM which I'll be focusing on for the first part of this talk so you can see just by virtue of cleaving the surface and introducing a vacuum you get this layer of chromium spins and one of the cool things about surface magnetization is that it is a directly detectable probe of the AFM domain state because it's the direction of the surface magnetization is directly connected to the bulk underlying AFM domain so in this case if your moment is up it corresponds to a bulk AFM domain with nail vector plus one if it's down you have a bulk AFM domain with nail vector minus one so now you don't have to rely on indirect methods to detect the state of your AFM domain and this surface magnetization is actually a quantity that can be measured in experiments the most common method is nitrogen scanning vacancy magnetometry it shows up in DFT if you do a slab calculation or a slab geometry of chromium in the 001 direction you get this spin polarized state and another application is thought to be an exchange bias which I talked about before so this was an experiment by the Bennett group where they switched the direction of surface magnetization in 001 chromium and when they did this the direction of the exchange bias field shifted or switched signs so it's not fully understood but surface magnetization is believed to be connected to exchange bias now, magnetoelectric materials are a subset of AFMs which are particularly relevant of surface magnetization just if anyone needs a reminder for materials which have the linear EME effect they must have broken inversion and time reversal symmetries in their bulk and as a consequence of this if you apply an electric field you induce a bulk magnetization in the compound conversely if you apply a bulk magnetic field you induce an electric polarization and the proportionality is governed by this linear response tensor alpha now it turns out that the symmetries required for non-zero linear EME response are intimately related to these symmetries that are required for non-zero surface magnetization and we can see this from kind of a qualitative picture by considering that an electric field and a unit vector normal perpendicular to a surface are both at their core just polar vectors so in the presence of either of these polar vectors we can expect the symmetry the bulk symmetry to be reduced in the same manner so this has the consequence that if you have a surface whose normal is parallel to an electric field we expect the surface to acquire the same magnetization components as the bulk if the electric field were applied in that direction another reason to focus on EME AFMs is that the direction of the surface magnetization can be controlled and manipulated by a magneto-electric annealing so there is this term in the free energy of when you're EMEs that's proportional to the product of electric and magnetic fields times alpha instance alpha switch is signed for opposite AFM domains that means that by applying either anti-parallel or parallel magnetic and electric fields you can preferentially select the state of the AFM bulk domain and as a consequence the direction of the surface magnetization and this is in contrast to non-ME AFMs where you usually need a prohibitively large magnetic field to switch surface magnetization so in the cartoon picture I showed looking at the 001 surface of chromia it was relatively straightforward to believe me when I said that there was a non-zero dipole moment pre-init area because you just saw a layer of magnetic spare magnetic spins however in more subtle cases where the reduction of symmetry by the surface actually leads to a finite surface magnetization even when in the ground state it appears to be magnetically compensated so for example in the case of minus 1 to 0 chromia which is perpendicular to the 001 surface if you look at the chromia atoms here it appears that they're going left right left right such that this surface should have a magnetization of zero however and I'll go into it more it turns up that the symmetry of the surface is such that in induced spare magnetization is allowed once you create the surface and this occurs by a canting of the surface moments and this is also possible in non-ME AFMs and centrosymmetric materials for example iron dipolaride for a long time people were confused about this material because it has a very large exchange bias when you interface the 110 surface with some ferromagnet and if we look at the 110 surface the in-plane iron moments look to be magnetically compensated so there's no surface magnetization however again because the reduction of symmetry at the surface causes these sublattices to become an equivalent the magnitudes of the moments can change such that you actually get a net surface magnetization so that's an introduction to this topic in case you are not so familiar with it and this is the outline for the rest of the talk I'll first give straightforward group theory formalism which allows you to identify bulk AFMs and their particular surface terminations which allow for a finite equilibrium surface magnetization and this has been developed in these previous papers here so we're really just expanding on it a bit then I'll focus on chromia for the first part of the remainder of the talk we'll look at the uncompensated 001 surface magnetization and its temperature dependence as well as inducing magnetization on the minus 120 surface and then we'll also quickly go into cases of surface magnetization in non-ME AFMs so here's the procedure so we're just going to focus on colinear AFMs for this entire talk so at first we have some AFM with a bulk magnetic space group let's call G and it contains the point group operations R which may or may not contain time reversal and the spatial translations now let's consider a Miller plane with a normal vector perpendicular to this plane and this is our surface of interest to see whether the surface has we expect an equilibrium magnetization on it so what we do is find the surface magnetic subgroup and the way that that's defined is you consider all of the operations of the bulk space group G which basically leave your surface normal in invariant modulo translations which are parallel to the surface which I tried to depict in this cartoon and we exclude symmetries which involve translations perpendicular to the surface because our translational symmetry is broken in that direction so once you have that subgroup then we just consider the point group associated with that so just the point group operations are in and we just check we can look up and build out whether this group is compatible with fair magnetism there are 31 of these groups that if you act all of the operations on magnetization pseudo factor at least one component is left invariant and if the subgroup is compatible it has an equilibrium surface magnetization if not it has no equilibrium surface magnetization so let's work through some examples so we'll go back to the case of chromia which is magneto electric material with a lot of interest in applications because it has relatively high nail temperature of 300 Kelvin so it has a bulk magnetic space group with broken inversion and time reversal symmetries and the moments are polarized along the 001 direction now if we look at if we want to consider the 001 surface we consider the operations which leave this surface normal invariant and if you work through all of that I won't go through the details you get this magnetic point group 3 and if we look at what these 3 operations, these 3 fold rotations about 001 and the identity due to the magnetization components the only thing that you have to pay attention to is that the MZ component is the only Cartesian component which doesn't switch sign under any of the operations so this means that this surface is fair magnetically compatible and the fair magnetization the fair magnetism has to occur along the 001 direction or the direction of ground state spin polarization and indeed there have been multiple experimental verifications of this roughness robust surface magnetization in 001 chromia for the case of the magneto-electric AFMs there also exists a convenient bulk descriptor which we can use in order to give a quantitative estimate of the surface magnetization in terms of more magnetons per unit area and this comes from higher terms in a multiple expansion of the interaction energy if you have a magnetization density mu of r interacting with a magnetic field and you do a multiple expansion the first term is your normal magnetic dipole and then the second order term which involves the derivative of the magnetic field and a spatial component the coefficient of this is called the magneto-electric multiple and because it breaks both in version and time reversal symmetries it's non-zero and AFMs and there's a concept you may be more familiar with is in the modern theory of polarization there is a elegant connection between the bulk electric polarization and the amount of charge on a surface which is perpendicular to polarization and if you indeed look at the units of volume normalized polarization it's charge per unit area analogously if we look at the units of multipleization normalized to the unit cell it's four magnetons per nanometer squared so analogously we can say that this multipleization tensor corresponds to the amount of surface magnetization we expect on a surface normal parallel to I the spatial component and magnetic dipole parallel to J so the reason one of the reasons my advisor, Nicola first got interested in this was that there's a surprising discrepancy between estimates of the 0, 0, 1 chromia surface magnetization using nitrogen vacancy magnetometry and what is expected based on this multipleization expectation where I forgot to mention this, we just rather than the central form we just if the magnetization is fairly localized you can approximate it with this point assuming that the you just have point magnetic dipoles centered at the atomic sites and you sum over the magnetic unit cell so this is what we're using so anyways what you get with theory does not agree with experiment but when we got to thinking more about this we realized this is not so surprising you can from a mean field argument you can say that the temperature at which a given magnetic moment orders is roughly proportional to its effective Heisenberg coupling which you can define just by summing over all of the nearest neighbor Heisenberg's for a given sub lattice so if you look in the bulk based on our, so there's five nearest neighbors in chromia that are relevant and based on our DFT calculations this bulk effective J is around 40 mE volts if we look at the electrostatically stable surface of zero zero one chromia you see that a bunch of the nearest neighbors are just cut off so by virtue of the termination the effective J even if we don't consider surface relaxation is 2 mE volts so more than a factor of 8 smaller so it stands to reason that at room temperature around which the experiments are being carried out the magnetization of the surface sub lattice is going to be essentially paramagnetic even if the bulk nail vector is ordered and this is what we get based on Monte Carlo simulation so this is an agreement so but we can still rescue this quantitative estimate using this multipleization bulk quantity as long as we just use a different basis so as I said before if you to calculate it using this point dipole approximation we if this if we use the unit cell corresponding to the electrostatically stable surface we get 12 4 magnetons per nanometer squared give or take however remember we just said that the magnetization of the top most chromia doesn't actually contribute at the experimental measurements so a more appropriate basis in order to capture these surface magnetization is basis we get by taking this moment and translating it down by one C lattice vector and if we recalculate using this we get a value of around 2.4 magnetons per nanometer squared and this is actually in quite good agreement with estimates from nitrogen vacancy magnetometry okay so that was the sort of intuitive cases of surface magnetization so let's go to the slightly more subtle cases so I'll stay with chromia for now and we'll go to a surface that is perpendicular to the 001 direction so the minus 2 bar 0 has a surface normal which is parallel to a 2 fold axis and again in the ground state polarization with the moments all directed along 001 this surface is magnetically compensated however if we look at the magnetic point group of the minus 1 2 0 surface which is the point group 2 which is just a 2 fold rotation the magnetization component which is left invariant is the one which is parallel to minus 1 2 y which is the surface normal so that means that fair magnetism is allowed on the surface and it has to occur by a canting of the moments along the surface normal so this is all well and good from a symmetry perspective but in addition to symmetry arguments it would be good to see whether we could expect this to actually occur in a real material so to that end we did DFT calculations these are constrained magnetic calculations in VASP using a slab of minus 1 2 0 chromia so what we do is we fix the direction of the 2 center chromia layers along the ground state 001 direction and then we can't the moments of the 2 surfaces with the canting angle with respect to 001 axis and even from a zoomed out picture you can see already that this energetic parabola is asymmetric with respect to 0 and if we zoom in the energy scale is really really tiny but based on multiple tests that I can talk about if you're interested and we think that this energy lowering is real so what this means is that this surface in DFT is stabilized energetically for a non-zero canting or induced surface magnetization of about 0.254 magnitons per nanometer squared okay so in the last few minutes I'll briefly talk about extensions of this surface magnetization idea beyond ME AFMs so I talked about this group theory formalism before which allows us to identify surfaces that are compatible with ferromagnetism meaning they can have an induced surface magnetization however something I swept under the rug is there's a subtlety between cases which are roughness or robust meaning even in the case of surface roughness or atomic steps the sign and magnitude of the surface magnetization stays constant or roughness sensitive cases where you only get surface magnetization for an atomically pristine layer and the way you can check which one you have is so once you have your surface magnetic point group you go back and check whether in the bulk magnetic space group the higher symmetry bulk magnetic space group whether there are any operations that take the combined vectors so the surface normal and the magnetic pseudo vector and translate the surface normal perpendicular to the surface and switch the direction of the magnetization vector if you do that means that you have surfaces that occur on atomic steps that are symmetry connected or energetically degenerate but they have opposite magnetization so it will average to zero for a macroscopic area if you don't have operations like this so in the operation which translates your surface normal to an atomic step keeps the direction of magnetization then like the case of zeroes or one chromia you really have a roughness robust surface magnetization which is more useful for device purposes so an easy example of this more trivial case is the rock salt nickel oxide so if you look at the 111 surface just looking at it you can tell me that there are ferromagnetic layers of spins polarized in plane however in the bulk magnetic space group which is the type 4 anti-ferromagnet so it has time reversal in its symmetry you have a symmetry which is time reversal multiplied by a translation along the 111 direction so that's just the operation that takes this moment to this moment so what that means is that these two surfaces which are symmetrically equivalent but have opposite signs of magnetization will exist in the material in the presence of roughness so 111 nickel oxide would not have a roughness robust surface magnetization ok and finally I'll go to the centrosymmetric case and I'll go back to iron-difluoride in addition to its interest as a exchange bias material it's also gotten some attention recently as a candidate ultramagnet one of these AFMs which has been splitting along certain directions of case space so it has a couple of cool features but anyways we can do this formalism again and this both magnetic space group has inversion symmetry but broken time reversal symmetry and if you look on the 111 surface again the moments are polarized in plane and pointed along opposite directions and it looks to be completely magnetically compensated and if you go through the magnetic point group formalism it's 2 prime and M prime it goes through all these operations the one that I've underlined the MY component stays invariant and in the basis of this point group Y is parallel to 001 so this surface is again paramagnetically compatible and the component is allowed along the 001 bulk direction so this is in contrast to chromia where the paramagnetism was induced by a canting away from the bulk ground state direction in this case the iron moments have to stay aligned collinearly in the 001 direction and the only way that you can get a finite paramagnetism on the surface is by the magnitude of the moments becoming an equivalent so we want to check this again in DFT so these are not constrained calculations these are just self consistent calculations neglecting spin orbit coupling we don't need it we're not checking canting we're just looking at moments magnitudes so this is a slab of 110 iron diphyloride and all we do is look at the projected magnetic, site projected magnetic moment as a function of layer for iron diphyloride and we look at the two in equivalent iron sublattices center and corner refer to the positions of the sublattice in the volcano itself and they're not the same the key takeaway is if you if you sum up the sublattice moments to get the total magnetization per layer in the center of the slab it's roughly zero whereas for both surface layers you get a non-negligible magnetization of about .014 magnitons so it's very small but it's there alright so that comes to the end of my talk in summary we've presented a group theory formalism which allows you to distinguish identify AFMs with surface magnetization and distinguish between these different cases induced uncompensated roughness robustness sensitive we've talked about the cases 0s or 1 chromia and how in that in the case of AFMs you can describe or estimate the quantitative value of surface magnetization by a bulk multiple as long as you account for temperature dependence and use the right basis and we've also shown through DFT calculations that in agreement with symmetry expectations the creation of a vacuum terminated surface means that if it's that you get a stabilization if you induce a non-zero magnetization on these surfaces and overall I guess the key takeaway point is that this surface magnetization is probably more ubiquitous than I think a lot of people realize even though it's a concept that has been studied for a long time it's kind of on the back burner and I hope this influences people to study it more I'll just acknowledge my first and foremost my advisor Nicholas Baldwin at ETH Andrea Urru who is also at the conference and Shine Ticabelle who contributed with discussions and calculations and also the materials theory group at ETH Thank you Thank you very much Sophie for this nice talk about surfaces, symmetries, magnetizations Thank you for the very nice interesting talk. I had one question about the terminations of chromium surfaces. Yes. Especially you have shown in case of disorder that there's a different termination of the surface I'm wondering if you consider if there are why this specific one. You're talking about this Yes. Yeah sorry I didn't explain this properly the experimental termination of chromium is known to be the one on the left-hand side so this I mean there are some controversies about the possibility of some disorder but for sure with electrostatic arguments this is the electrostatically stable surface and this surface does not occur naturally. The point is that when you calculate this multiplication what you do is you take you choose a bulk unit cell where if you take this bulk unit cell and tile it periodically when you cut it off at some point it sort of defines your surface so it's basically the basis that defines the surface termination so you have to choose this bulk unit cell and you choose that according to the surface termination and if you use this bulk unit cell which corresponds to the actual termination you get a magnetic you get a magnetization that is much larger than what is found in experiment but so this is only just a theoretical construct so this is all I'm saying is that this is the bulk unit cell that is more appropriate to calculate the experimental surface magnetization at room temperature because at room temperature this magnetic moment is disordered or essentially paramagnetic but the calculation is done for a bulk or for a slab then the calculation is done for a slab okay, other questions thanks for the interesting talk I have a question regarding to when you construct the different magnetic equations for the surface state like you have this especially when there's the like some of them they are counted I was just wondering how did you consider if there are spring spring correlations or when you do calculate the energy would you allow for relaxation of these spin states because you're talking about the this slide here? yeah, for this one so you're asking whether I just relax rather than doing constrained calculations relax the material and see whether I get what I get basically? yeah, I think especially for this one I'm just curious about when these spins they are pointing to different directions and then how do you consider the property that would have different size or a different effect between that size because the orientation of the spins they are different and how at this effect taking into consideration sorry, I'm not quite sure I understand your question so this, yeah, so for sure you're right the energy changes as a result of I mean you get counting and you get this yeah, I mean you get Sealo-Oshinsky-Moria interactions and such because the spins in the center are still pointed towards 001 but I guess we didn't worry about sort of the different spin correlations that were affecting the energy change all we wanted to see is whether the energy lowered if we induced a magnetization on the surface so just wanted to make sure so all these spin directions they are fixed, right, during your calculation they are fixed, right, yeah thank you anyone else has some question no? Okay, so thank you very much again okay, so this is set up, okay, so the next talk again about magnetism is by Anita Halder from Trinity Ecology Dublin and the topic is tuning the magnetic anisotropy at metal molecular interfaces, so please so good afternoon everyone, I'm Anita Halder I'm a post-op in Trinity College Dublin the title of my talk is tuning the magnetic anisotropy at metal molecular interface let's start with thanking my advisors in Trinity College Dr. Andrea Ducati and Professor Stefano Sanvito I also want to thank my collaborators Shumantho and Professor Devidoregan sorry also I want to thank the organizers here to give me the chance to present my work let's start with defining magnetocrystalline anisotropy so it's basically described as the dependence of the energy of a magnetic system along some certain direction that is the preference along some certain magnetization axis so this is basically a pure relativistic effect and coming from spin orbit coupling this certain axis is called the easy axis the easy axis can be in plane or out of plane that is the perpendicular to the plane and the perpendicular magnetic anisotropy is key ingredient in technological applications for example in permanent magnetism memory devices and the design, fabrication and characterization of outer perpendicular anisotropy have drawn lots of attention of scientific community if you think about the memory devices the recording density has been increased several order of magnitude compared to the first time when it was launched and the efficiency you can to increase that kind of efficiency the two requirements are one is you need high saturation magnetization you need strong out of plane anisotropy and actually you can define kind of hard magnet, semi hard magnet or soft magnet depending upon the value of its K1 and saturation magnetization now you can see from this plot that most of these magnets are transition metal and rare earth intermetallics the transition metal part is giving you the high saturation magnetization where the rare earth part is responsible for high anisotropy and there is some time grown in thin films to enhance the perpendicular anisotropy but with the flame thickness it is seen that there is a significant separation in the out of plane anisotropy so is there any alternative to tune that perpendicular anisotropy what is about metal molecule interface organic molecules they are already quite popular in spin tronics for 3D transition metals if you consider their thin films mostly the surface surface property dominates and so if the 3D transition metal in its bulk form if you consider its magnetic anisotropy there is almost no anisotropy or even if there it is very small now if you consider a surface due to reduced symmetry there is enhancement of perpendicular anisotropy now what is about if you are putting some molecule on top of the surface actually indeed this works and in last few years there are lots of investigation around this reduction I just want to highlight few of them this PRL paper they actually talked about cobalt C60 they deposited cobalt C60 on top of HCP sorry they deposited molecule C60 on top of HCP cobalt and they found enhancement out of plane anisotropy the same group they also extended their study they did it for another molecule and they also reported enhancement in perpendicular anisotropy then this paper if you follow they made a hydro structure of cobalt and graphene and there is massive enhancement of the perpendicular anisotropy has been reported also this paper similarly they reported this two molecule C60 and ALQ3 deposited on cobalt layers and there are many more actually the same thing they made some hydro structure with graphene cobalt and heavy metal and also the magnetic heartening that is you can strengthen the magnetic exchange interaction by putting non-magnetic organic molecule so what is the scope of this work so till the date the studies are mostly based on the qualitative understanding between DFT and experimental findings but to understand the correlation between interfacial magnetocrystalline anisotropy and molecule metahybridization a detailed analysis is required so that can be done with the systematic investigation on model system so in this study to fill up this gap what we did we studied the modification of magnetocrystalline anisotropy of HCC cobalt thin flames by putting different non-magnetic molecules we used a simple simple model to understand the basic physics and then also we quantitatively from first principle DFT calculation we calculated the modification for different prototype typical systems with that I came to my results at first I will start with a very simple system let's take the simplest molecule probably ben sorry benzene now I considered 5 layers of cobalt HCC cobalt and I put a benzene molecule on top of it and then I relax the system I constrain the last 2 layers and this is the geometry as you can see and then the first thing I wanted to see what is the change in electronic structure if you put molecule on top of cobalt surface so the black one here in the density of state the black one is for the bare cobalt as you can see that the majority spin channel is completely occupied for all of them but the minority spin channel is partially occupied now if you put molecule on top of it this orbital the dj squared orbital is modified quite a lot specially you can see there is a formation of bonding bonding anti-bonding state between c, p, z and cobalt dj squared orbital the anti-bonding states are mostly here and they are spending over wide range of energy and they are mostly dj squared character and the bonding state are over here and they are mostly cobalt p, z character next we calculated the anisotropy energy to calculate the anisotropy energy we took the energy difference between total energy total band energy difference between 2 different direction and then we found that for FCC cobalt bulk if you consider bulk there is no anisotropy now if you make some slab we considered 5 layers it shows negative anisotropy that is in-plane anisotropy and then upon molecular adsorption the anisotropy is drastically reduces to minus 0.6 from almost minus 5.5 and in the next step I removed I removed the benzene molecule from here and I didn't optimize the structure this is some kind of a distorted cobalt slab and I calculated the anisotropy again and I found it became again in-plane very similar to bare cobalt so that tells me that the drastic reduce in the anisotropy is basically due to molecule metal hybridization and the atomic displacement of the of the top like the top layer has a very minor influence next we calculated the layer-wise anisotropy and that can be obtained from that delta E SoC delta E SoC you can calculate delta E SoC from the SoC matrix element and if you sum over orbital you will get the atom-wise value and then you have to take the difference between two different directions and that is proportional to your anisotropy of a particular atom so if you see this plot the red one is for bare cobalt and you can see that for all the layers for all the atoms it has like negative anisotropy so that is why in total and for bare cobalt also it prefers in plane now if you put a benzene molecule on top of it the atoms which are particularly connected to the molecule they are showing an out of plane component and some of the atoms in the second layer also I indicated here they are also showing out of plane anisotropy so they are actually cancelling the in plane anisotropy of the inner layers and as a whole the total anisotropy is very close to zero for benzene cobalt interface next also we plotted the transition matrix element between different d orbitals and if you see for bare cobalt the strongest negative anisotropy is coming from dyz and dz square orbital and if you put cobalt benzene atom on top of it that quantity is going to zero now to understand the basic physics we model it in a very simple way from second order perturbation theory we can write magnetochrystalline anisotropy like this where psi o and psi u are corresponding to occupied and unoccupied orbital and then you can actually they are promoting in plane or out of plane anisotropy you can calculate it analytically we consider our d orbitals like the energy levels of the d orbitals in that way just I want to mention that since our majority spin channel always always like filled up so we didn't consider it in our simple model crystal field split it in that way which is very similar to whatever what the result we obtain from the f t calculation these two levels are degenerate again these two levels are degenerate we consider it in our model and then if you calculate the total anisotropy it is something like that and the negative sign shows that already from our simple model it shows in plane anisotropy which is coming from our d f t calculation as well now when you are putting benzene on top of cobalt what is happening due to hybridization there is bonding and anti bonding states are forming now the anti bonding states I mean now the difference between from this orbital to this new anti bonding states are delta prime now if you calculate the emca it becomes this now depending upon this value of delta prime it can be positive or negative now if your metal molecule hybridization is not that strong it's very weak then it will be like the total quantity will be negative it will be in plane but if you have a very strong hybridization there is a chance of switching from in plane to out of plane anisotropy next we kind of relate our calculated orbital moments with a simple model called Bruno model what is Bruno model so Bruno model basically relate the orbital moment with anisotropy with total anisotropy so the easy axis of magnetization coincide with the direction of maximum orbital moment and this is exactly what we got from our d f t calculation so if you consider the red dots here these are for bare cobalt and for bare cobalt you can see that the in plane orbital moment is greater than out of plane orbital moment and that's why it prefers in plane anisotropy now upon benzene adsorption the atoms particularly which are attached to the molecule they showed a sharp drop for in plane orbital moment and that's why they prefers out of plane anisotropy then we also compared the anisotropy obtained from Bruno's model and whatever we obtained from our d f t calculation and it shows a good agreement though there is some quality quantitative difference between bare cobalt but for benzene cobalt system the agreement is quite good next after understanding the basic physics of metal molecular hybridization and how it is affecting the total anisotropy we would like to study how the chemical reactivity of the molecule affecting the total anisotropy so we have considered a different molecule which is more reactive than benzene so it has a larger hybridization and that is reflected in the total density of state if you see here the formation of bonding and anti-bonding states is more distinct so we should expect more effect in total anisotropy so next we calculated the total anisotropy and I found that for cot cobalt interface there is actually switching from in plane to out of plane so this is because because of the strong hybridization the delta prime I was mentioning in my simple model the delta prime is such that the total total anisotropy becomes positive and if you plot the layer wise anisotropy you will find the very similar thing to benzene but here the magnitude of these four atoms which are connected with the cot molecule has more value like is much more than the benzene then I also plotted the like the transition matrix between between different d orbitals and I found that this transition element between d by z and d z squared which was negative here and which became very small or zero for benzene cobalt system for in contrast to that here it became positive so totally I mean it's giving positive anisotropy next I also studied how the molecular coverage affecting the anisotropy of the slab so for that reason I considered different molecules with increasing surface area and I found the trend is very clear here and especially if you consider the surface layer anisotropy of the stop surface then you will find that there is an in plane to out of plane switching next I also studied the dependence of anisotropy of the cobalt slab thickness for that I considered different layers of cobalt slab starting from 3 to 10 though their magnitudes are oscillating are different for different number of layers the trend is very similar for all of them for all of them for bare cobalt it has negative anisotropy you are putting some molecule there is some separation of in plane anisotropy this is for one representative case the layer wise anisotropy for 8 number of layers and this is very similar to the result I have shown you for 5 layers now I also studied for another facet of cobalt HCP and for HCP in contrast to FCC bare cobalt slab has already positive anisotropy so when you are putting molecule it is basically when you are putting some molecule you are basically adding adding the positive anisotropy so it is basically enhancing the out of plane anisotropy but the physics whatever I described it is coming from metal molecular hydrophilicization then finally I I did some calculation for 2 metal molecular interface which are experimentally observed the first one is C60 cobalt system so for C60 cobalt system I considered 4 different type of configuration and I found this one is the lowest one and you can see from this layer wise plot that again the atoms which are connected to the molecule this atom they are giving like out of plane out of plane component of the anisotropy but with with the I mean varying magnitude and that magnitude depends upon the strength of hybridization so just to show I mean I considered 2 different atoms one is with highest anisotropy and another is this one and if you see the density of state for this atom it shows clearly the formation of anti-bonding and bonding state where is for this atom this is I mean the hybridization is comparatively very weak that is why it is very close to bare cobalt system and next I did it for another system as I told for LQ3 and cobalt and experiment from experimental result it has been reported that it favors out of plane anisotropy and as you can see here here also the atoms to the molecule they are showing perpendicular anisotropy and I have chosen 3 different atom just to show their hybridization kind of hybridization with the metal with the molecule and the strongest one is with the highest anisotropy with that I came to my conclusion so I studied the modification of magnetic anisotropy of the thin cobalt films upon the adsorption of molecules and the main physical phenomena responsible for the modification is cobalt digit square and carbon PZ hybridization we used a simple model based on second order perturbation theory to identify the electronic transition promoting in plane or out of plane transition and then we also showed that the suppression of the in plane anisotropy depends upon the choice of the molecule and as I showed that it can switch from in plane for that for COT molecule and then there is a possibility to engineer out of plane anisotropy by increasing the molecular coverage so we are preparing the manuscript I think it should be in online within one or two weeks and these are my I want to thank for the funding agencies and computational resources and thanks for your attention thank you very much for this nice talk yes ladies thank you thank you for your nice talk I have a question you previously mentioned that you have constrained some bottomless layer of your cobalt I just want to know if you have applied a dipole collection in order to obtain a correct absorption energy and also another question is as cobalt as 3D orbital I just want to know if you have used the DFT plus you and which value of you have used so for the first question I applied the dipole correction but then I also calculated the anisotropy but I found almost there is no change so I did it for one system and then I just followed without any correction for other systems and what was the second question DFT plus you cobalt is more directly correlated so for these calculations are GGA I didn't use any U plus U correction okay I think Antimoid so thank you for a very nice talk so my question is about the orbiter moments some point you mentioned this Bruno model you show this plot where there is an orbiter moment and then you have to charge each atom right yeah this one so you are calculating a local orbit and the question is then how do you do that because this is from the DFT right so it's the DFT calculation which is behind the orbit I mean I did switch on the spin orbit interaction and that will give you the orbital moment for the orbitalization how do you define the fact that it's associated with that specific atom specific atom probably I didn't get your question so there is an orbiter and then an atom index so I imagine this is each point is associated with specific atom but I mean when you are switching on the spin orbit interaction you will get the orbital moment power atom like for each and every atom like the way you get also the spin magnetic moment so if you switch on the spin orbit interaction you will get also the orbital moment for each and every atom and then that I just considered thanks ok further questions no well I f1 myself so when you put these kind of closed shell molecules like benzene molecules C60 on the metal surface then the strength of the interaction will depend very strongly on the level of theory you are using if you include van der Waals or not and all these kind of things which will then as a follow up change very much how strongly distorted your surface atoms and so on have you looked at the influence of these things on your results I didn't look at the influence of this thing but I found for especially for HCP cobalt there is strong effect of surface distortion but for FCC cobalt I mean there is almost nothing I mean if you see this plot yeah this one like I put the molecule and the surface atoms got distorted because of the bonding then I removed the molecule and I didn't optimize the structure and I calculated the total anisotropy and it is very similar to the bear cobalt so it shows that the main reduction is coming from the metal molecule hybridization yes and then it would be interesting to see how strongly this depends on the surface molecule distance which you have that I did actually that I did I don't have the result here but that I did I just shifted the molecule like from surface to this will depend very strongly as I said on yeah I mean this goes from chemical absorption to physical absorption you mean like but I mean different functions will give you very different distance okay I didn't check for different functions okay no further questions okay so thank you very much again okay so we will now switch gear and move from spins and magnetism to quantum computing okay but this is not your slides we are seeing it should be how strange are you sure you have connected it okay I can reconnect it help us on the way and he will answer the question about what quantum computers can do for material science and kind of I very much hope that the answer will not be that all DFT people okay so please well thanks for the introduction and I wou