---
abstract: 'We report a femtosecond response in photoinduced magnetization rotation in the ferromagnetic semiconductor GaMnAs, which allows for detection of a four-state magnetic memory at the femtosecond time scale. The temporal profile of this cooperative magnetization rotation exhibits a discontinuity that reveals two distinct temporal regimes, marked by the transition from a highly non-equilibrium, carrier-mediated regime within the first 200 fs, to a thermal, lattice-heating picosecond regime.'
author:
- 'J. Wang'
- 'I. Cotoros'
- 'X. Liu'
- 'J. Chovan'
- 'J. K. Furdyna'
- 'I. E. Perakis'
- 'D. S. Chemla'
title: |
    Memory Effect in the Photoinduced Femtosecond Rotation of Magnetization\
    in the Ferromagnetic Semiconductor GaMnAs
---

![(Color online) Static magnetic memory. (a)-(b): Sweeping a slightly tilted [*B*]{} field (5$^o$ from the [*Z*]{}-axis and 33$^o$ from the [*X*]{}-axis) up (dashed line) and down (solid line) leads to consecutive 90$^o$ magnetization switchings between the [*XZ*]{} and [*YZ*]{} planes, manifesting as a “major" hysteresis loop in the Hall magneto-resistivity. (c)-(d): “Minor" hysteresis loop with [*B*]{} field sweeping in the vicinity of 0T. The magnetic memory state X$-$(0) or Y$+$(0) is parallel to one of the easy axis directions in the [*XY*]{} plane. ](Fig1f.eps)

\[dep\]

Magnetic materials displaying [*carrier-mediated*]{} ferromagnetic order offer fascinating opportunities for non-thermal, potentially [*femtosecond*]{} manipulation of magnetism. A model system of such materials is Mn-doped III-V ferromagnetic semiconductors that have received a lot of attention lately [@ohno1998]. On the one hand, their magnetic properties display a strong response to excitation with light or electrical gate and current via carrier density tuning [@Koshiharaetal97PRL; @ohnoetal2000; @wangetalPRL2007]. On the other hand, the strong coupling ($\sim$1 eV in GaMnAs) between carriers (holes) and Mn ions inherent in carrier-mediated ferromagnetism could enable a [*femtosecond*]{} cooperative magnetic response induced by photoexcited carriers. Indeed, the existence of a very early non-equilibrium, non-thermal femtosecond regime of collective spin rotation in (III,Mn)Vs has been predicted theoretically [@ChovanetalPRL2006]. In addition, a coherent driving mechanism for femtosecond spin rotation via [*virtual*]{} excitations has also been recently demonstrated in antiferro- and ferri-magnets [@coherent]. Nevertheless, all prior studies of photoexcited magnetization rotation in ferromagnetic (III,Mn)Vs showed dynamics on the few picosecond timescale, which accesses the quasi-equilibrium, quasi-thermal, lattice-heating regime [@psRotationGaMnAs]. Up to now in these materials, the main observation on the femtosecond time scale has been photoinduced demagnetization [@wangetalPRL2005; @wangetalreview2006; @wang2008; @Cywinski_PRB07].

Custom-designed (III,Mn)V hetero- and nano-structures show rich magnetic memory effects. One prominent example is GaMnAs-based four-state magnetic memory, where “giant” magneto-optical and magneto-transport effects allow for ultrasensitive magnetic memory readout [@fourstate]. However, all detection schemes demonstrated so far have been static measurements. Achieving an understanding of collective magnetic phenomena on the femtosecond time scale is critical for terahertz detection of magnetic memory and therefore essential for developing realistic “spintronic” devices and large-scale functional systems.

In this Letter, we report on photoinduced [*femtosecond*]{} collective magnetization rotation that allows for femtosecond detection of magnetic memory in GaMnAs. Our time-resolved magneto-optical Kerr effect (MOKE) technique directly reveals a photoinduced four-state magnetic hysteresis via a quasi-instantaneous magnetization rotation. We observe for the first time a distinct initial temporal regime of the magnetization rotation within the first $\sim$200 fs, during the photoexcitation and highly non-equilibrium, non-thermal carrier redistribution times. We attribute the existence of such a regime to a [*carrier-mediated*]{} effective magnetic field pulse, arising without assistance from either lattice heating or demagnetization.

The main sample studied was grown by low-temperature molecular beam epitaxy (MBE), and consisted of a 73-nm Ga$_{0.925}$Mn$_{0.075}$As layer on a 10 nm GaAs buffer layer and a semi-insulating GaAs \[100\] substrate. The Curie temperature and hole density were 77 K and $3 \times 10^{20}$ cm$^{-3}$, respectively. As shown in Fig. 1, our structure exhibits a four-state magnetic memory functionality. By sweeping an external magnetic field B aligned nearly perpendicularly to the sample normal, with small components in both the [*X*]{} and [*Y*]{} directions in the sample plane, one can sequentially access four magnetic states, X$+\rightarrow$Y$-\rightarrow$X$-\rightarrow$Y$+$, via abrupt 90$^o$ magnetization ($\mathbf{M}$) switchings between the [*XZ*]{} and [*YZ*]{} planes \[Fig. 1(a)\]. In these magnetic states, $\mathbf{M}$ aligns along a direction arising as a combination of the external B field and the anisotropy fields, which point along the in-plane easy axes \[100\] and \[010\]. The multistep magnetic switchings manifest themselves as abrupt jumps in the four-state hysteresis in the Hall magneto-resistivity $\rho _{Hall}$ \[Fig. 1(b)\] (planar Hall effect [@fourstate]). The continuous slopes of $\rho _{Hall}$ indicate a coherent out-of-plane $\mathbf{M}$ rotation during the perpendicular magnetization reversal (anomalous Hall effect [@ohno1998]). Fig. 1(c)-(d) show the B scans in the vicinity of 0T, with the field turning points between the coercivity fields, i.e., $B_{c1}<\left|B\right|<B_{c2}$. This leads to a “minor” hysteresis loop, accessesing two magnetic memory states at $B=$0T: X$-$(0) and Y$+$(0).

We now turn to the transient magnetic phenonmena. We performed time-resolved MOKE spectroscopy [@wangetalreview2006] using 100 fs laser pulses. The linearly polarized ($\sim$12 degree from the crystal axis \[100\]) UV pump beam was chosen at 3.1 eV, with peak fluence $\sim$ 10$\mu$J/cm$^2$. A NIR beam at 1.55 eV, kept nearly perpendicular to the sample ($\sim$ 0.65 degree from the normal), was used as probe. The signal measured in this polar geometry reflects the out-of-plane magnetization component, M$_z$.

![(Color) Photoinduced femtosecond four-state magnetic hysteresis. (a) B field scans of $\triangle \theta _{k}$ at 5K for time delays $\triangle t=$ -1 ps, 600 fs, and 3.3 ps. The traces are vertically offset for clarity. Inset (left): temporal profiles of normalized Kerr ($\theta _{k}$) and ellipticity ($\eta _{k}$) angle changes at 1.0T; Inset (right): static magnetization curve at 5K ($\sim$4 mrad), measured in the same experimental condition (but without the pump pulse). (b) Temporal profiles of photoinduced $\triangle \theta _{k}$ for the four magnetic states. Shaded area: pump–probe cross–correlation.[]{data-label="mag-dep"}](Fig2f.eps)

Fig. 2(a) shows the B field scan traces of the photoinduced change, $\Delta\theta_K$, in the Kerr rotation angle at three time delays, $\triangle t=$ -1 ps, 600 fs, and 3.3 ps. The magnetic origin of this femtosecond MOKE response [@KoopmansetAl00PRL] was confirmed by control measurements showing a complete overlap of the pump–induced rotation ($\theta _{k}$) and ellipticity ($\eta _{k}$) changes \[left inset, Fig. 2(a)\]. $\Delta\theta_K$ is negligible at $\triangle t=$-1 ps. However, a mere $\triangle t=$600 fs after photoexcitation, a clear photoinduced four-state magnetic hysteresis is observed in the magnetic field dependence of $\Delta\theta_K$ (and therefore $\Delta M_z$), with four abrupt switchings at $\left|B_{c1}\right|=$0.074T and $\left|B_{c1}\right|=$0.33T due to the magnetic memory effects. As marked by the arrows in Fig. 2(a), the four magnetic states X$+$, X$-$, Y$-$, Y$+$ for $\left|B\right|=$0.2T give different photoinduced $\Delta\theta_K$. It is critical to note that the steady-state MOKE curve, i.e. $\theta_K$ without pump field, doesn’t show any sign of magnetic switching or memory behavior \[right inset, Fig. 2(a)\]; these arise from the pump photoexcitation. The B field scans also show a saturation behavior at $\left|B\right|>$0.6T, to be discussed later. We note that the photo–induced hysteresis loops at $\triangle t=$3.3 ps and 600 fs sustain similar shapes, with only slightly larger amplitudes at 3.3 ps. This observation confirms that the dynamic magnetic processes responsible for the abrupt switchings occur on a femtosecond time scale. Fig. 2(b) shows the photoinduced $\Delta\theta_K$ dynamics for the four initial states X$+$, X$-$, Y$-$, and Y$+$. An extremely fast $\Delta\theta_K$ develops within 200 fs, with magnitude and sign that distinctly differ, depending on the initially prepared state, consistent with Fig.2 (a). The substantial difference in $\Delta\theta_K$ under the same B field - for instance between the X+ and Y+ states - shows that the magnetic dynamics is not due to simple demagnetization [@BeaurepaireetalPRL96; @wangetalPRL2005; @wangetalreview2006].

The photoinduced dynamics of the zero–B field memory states \[Fig. 1(c)\] elucidates the salient features of the femtosecond magnetic processes. Fig. 3(a) shows the temporal profiles of the photo-induced $\Delta\theta_K$ for X$-$(0) and Y$+$(0) initial states. Since the initial magnetization vector lies within the sample plane, $\Delta \theta _{k}$ in the first 200 fs reveals an out–of–plane spin rotation, with negligible contribution from demagnetization. More intriguingly, the $\mathbf{M}$ in X$-$ and Y$+$ initial states rotates to different [*Z*]{}-axis directions, as illustrated in Fig. 3(b). This leads to opposite signs of the photoinduced signals and is responsible for the four-state magnetic switchings. Furthermore, the observation of an initial discontinuity in the temporal profiles of the $\mathbf{M}$ tilt reveals [*two distinct temporal regimes*]{}, marked in Fig. 3(a): a substantial magnetization rotation concludes after the first 200 fs and is followed by a [*much slower*]{} rotation change afterwards (over 100’s of ps).

![(Color online) (a) Photo-induced $\Delta \theta _{k}$ for two in-plane magnetic memory states, shown together with the pump-probe cross-correlation (shaded). The opposite, out–of–plane $\mathbf{M}$ rotations for the X$-$(0) and Y$+$(0) are illustrated in (b).[]{data-label="power"}](Fig3f.eps)

We now discuss the origin of the observed femtosecond magnetization rotation. In the previously held picture of light–induced magnetization rotation in ferromagnets, the photoexcitation alters the anisotropy fields via quasi-equilibrium mechanisms, such as heating of the lattice (magneto-crystalline anisotropy) or heating of the spins (shape anisotropy) [@heating]. Since the in-plane magnetic memory states of Fig. 1(c) have negligible shape anisotropy, a significant B field within the standard picture can only occur on a time scale of several picoseconds via the lattice heating mechanism. However, it has been shown theoretically [@ChovanetalPRL2006; @ChovanetalPRB2008] that the Mn spin in GaMnAs can respond quasi-instantaneously to a femtosecond effective magnetic field pulse generated by hole spins via nonlinear optical processes assisted by interactions. This light–induced B field pulse may be thought of as a femtosecond modification of the magnetic anisotropy fields. In the realistic system, one needs to also treat microscopically the transient magnetic anisotropy changes, due to the complex valence bands and highly non–thermal hole populations in the femtosecond regime, which drastically affect the photoexcited carrier spin. Due to the [*hole-mediated*]{} effective exchange interaction between Mn spins, the anisotropy fields in GaMnAs result from the coupling of several valence bands by the [*spin-orbit interaction*]{} and depend on the transient hole distribution and coherences between different bands [@ChovanetalPRB2008]. In the static case, recent experimental [@anisotropy-exp] and theoretical [@anisotropy-the] investigations have shown that increasing the hole density significantly reduces the cubic anisotropy (K$_c$) along the \[100\] direction, while enhancing the uniaxial anisotropy (K$_u$) along \[1-10\]. One therefore expects that the photoexcited hole population turns on an effective magnetic field pulse ($\Delta B_{c}$) along the \[1-10\] direction \[Fig. 4(a)\]. This photo-triggered $\Delta B_{c}$ then exerts a spin torque on the $\mathbf M$ vector, $\Delta \overrightarrow B_{c}\times 
\overrightarrow { M}$, and pulls it away from the sample plane. The directions of these spin torques for the X$-$(0) and Y$+$(0) states are opposite, leading to different $\mathbf M$ rotation paths \[Fig. 3\]. Since this mechanism is mediated by the the non–thermal holes, the appearance of $\Delta B_{c}$ is quasi-instantaneous, limited only by the pulse duration of $\sim$100 fs [@ChovanetalPRB2008]. This femtosecond magnetic anisotropy contribution from the non–thermal photoexcited carriers should be contrasted to the quasi–thermal contribution, arising from, e.g., the transient lattice temperature elevation on the picosecond time scale [@psRotationGaMnAs].

Next we turn to the origin of the discontinuity that reveals the [*two temporal regimes*]{} in the collective magnetization rotation \[Fig. 3\]. The quick termination of the initial magnetization tilt implies that the effective $\Delta B_{c}$ pulse induced by the photoexcitation decays within the first hundreds of femtoseconds. The photoexcitation of a large (as compared to the ground state anisotropy field) $\Delta B_{c}$ requires an extensive [*non-thermal*]{} distribution of transient holes in [*the high momentum states*]{} of the valence band [@anisotropy-the]. This is due to the large spin anisotropy of these hole states, empty in the unexcited sample, via their strong spin-orbit interaction. In our experiment, immediately following photoexcitation at 3.1 eV, a large density of transient holes distribute themselves over almost half of the Brillouin zone along the L\[111\] direction. The Mn–hole spin exchange interaction is also believed to be enhanced along \[111\] due to strong p-d orbital hybridization [@BurchPRB2004]. Consequently, these photoexcited holes contribute strongly to the magnetic anisotropy fields. The following rapid relaxation and thermalization of the high momentum holes, due to carrier-carrier and carrier-phonon scattering, reduce $\Delta B_{c}$ within a few hundred femtoseconds. The subsequent picosecond magnetization rotation process arises from the change in magnetic anisotropy induced by the lattice temperature elevation. Our results reveal a complex scenario of collective spin rotation, marked by the transition from a non-equilibrium, carrier-mediated regime ($<$200 fs) to a thermal, lattice-heating regime on the ps time scale.

![(Color online) (a) Schematics of the photoexcited carrier–induced anisotropy field $\Delta B_{c}$. (b) Simulations of $\Delta M_{z}/M_0$ for the two magnetic memory states. Parameters used in the calculation are $K_{c}=1.198\cdot 10^{-2}meV$, $K_{u}=0.373\cdot 10^{-2}meV$, $K_{3}=0.746\cdot 10^{-2}meV$, $T_{1}=330$fs and $3\% $ of photoexcited carriers. (c) Schematics of the photoinduced M$_{z}$ for the X$-$, X$+$, Y$-$ and Y$+$ states at $\left|B\right|=$0.2T. []{data-label="temperature"}](Fig4f.eps)

We modelled the transient anisotropy phenomenologically by deriving $\Delta B_{c}$ from the magnetic free energy, $$E_{anis}=-{K_{c}\over S^{4}}
S_{x}^{2}S_{y}^{2}+{K_{u}\over S^{2}}
S_{x}^{2}+{K_{3}\over S^{2}}
S_{z}^{2},$$ describing cubic (K$_c$) and uniaxial (K$_u$) contributions, and added a time–dependent modification of $K_{c}/K_{u}$ due to the strongly anisotropic photoexcited hole states [@ChovanetalPRB2008]. The corresponding contribution to the Mn spin equation of motion is $\partial
_{t}{\bf S}={\bf S}\times {\bf H}_{anis}$, where ${\bf H}_{anis}=-
{\partial E_{anis}\over 
\partial {\bf S}}$. The light–induced change in the magnitude of $K_{c}/K_{u}$ increases during the pulse and then decreases with the energy relaxation time (T$_1$) of the high–momentum photoexcited holes. The results of our calculation are shown in Fig. 4(b), which gives a similar time dependence of the normalized $\Delta M_{z}$, with magnitude $\sim$ 0.4$\%$ of the total magnetization M$_0$ ($\sim$4 mrad at 5K), which compares well with the experiment.

Finally, Fig. 4(c) illustrates the femtosecond detection of the four-state magnetic memory shown in Fig. 2. By incorporating both the photo-induced rotation (red arrows) and the demagnetization (green arrows) effects, we can visualize the different M$_z$ changes for the four magnetic states, consistent with our observation. Demagnetization results in the high field saturation behaviour observed in Fig. 2(a). For $\left|B\right|>0.60T$, $\mathbf M$ is aligned mostly along the sample normal. Then the photo-induced signals arise from the decrease in the $\mathbf M$ amplitude, which is more or less constant with respect to the field.

In conclusion, we report on the femtosecond magnetic response of photoinduced magnetization rotation in GaMnAs, which allows for femtosecond detection of four-state magnetic memory. Our observations unequivocally identify a [*non-thermal, carrier-mediated*]{} mechanism of magnetization rotation, relevant only in the [*femtosecond*]{} regime, without assistance of either lattice heating or demagnetization. This femtosecond cooperative magnetic phenomenon may represent an as-yet-undiscovered universal principle in all carrier-mediated ferromagnetic materials - a class of rapidly emerging “multi-functional" materials with significant potential for future applications, e.g., the oxides with promise of far above room temperature Curie temperature.

This work was supported by the Office of Basic Energy Sciences of the US Department of Energy under Contract No. DE-AC02-05CH11231, by the National Science Foundation DMR-0603752, and by the EU STREP program HYSWITCH.

[10]{} bibnamefont \#1[\#1]{}bibfnamefont \#1[\#1]{}url \#1[`#1`]{}urlprefix\[2\][\#2]{} \[2\]\[\][[\#2](#2)]{}

H. Ohno, Science [**281**]{}, 951 (1998).

., ****, ().

H. Ohno [*et al*]{}., Nature [**408**]{}, 944 (2000). ., ****, ().

., ****, (); ****, ().

A. V. Kimel [*et al*]{}., Nature [**435**]{}, 655 (2005); F. Hansteen [*et al*]{}, Phys. Rev. Lett. 95, 047402 (2005).

J. Qi, [*et al*]{}., App. Phys. Lett. [**91**]{}, 112506 (2007); D. M. Wang [*et al*]{}., Phys. Rev. B [**75**]{}, 233308 (2007); Y. Hashimoto [*et al*]{}., Phys. Rev. Lett. [**100**]{}, 067202 (2008)

., ****, ().

., ****, ().

J. Wang [*et al*]{}., arXiv:0804.0451 (2008).

L. Cywi[ń]{}ski [*et al*]{}., ****, ().

H. Tang [*et al*]{}., Phys. Rev. Lett. [**90**]{}, 107201 (2003). ., ****, ().

E. Beaurepaire [*et al*]{}., Phys. Rev. Lett. [**76**]{}, 4250 (1996).

M. V. Kampen [*et al*]{}, Phys. Rev. Lett. [**88**]{}, 227201 (2002); M. Vomir [*et al*]{}, Phys. Rev. Lett. 94, 237601 (2005).

J. Chovan and I. E. Perakis, Phys. Rev. B. 77, 085321 (2008); and unpublished.

X. Liu [*et al*]{}., Phys. Rev. B. 71, 035307 (2005); K. Hamaya [*et al*]{}., Phys. Rev. B 74, 045201 (2006)

T. Dietl [*et al*]{}., Phys. Rev. B. 63, 195205 (2001); M. Abolfath [*et al*]{}., Phys. Rev. B 63, 055418 (2001)

K. S. Burch [*et al*]{}., Phys. Rev. B 70, 205208 (2004)
