where D and E are parameters that determine the magnetic anisotropy, and S ^ ^ x , S ^ ^ y , S ^ ^ z are spin matrices of dimension 2 S + 1 . It is customary to take z as the easy axis so that D<0 and |D|>> E. For E=0, this Hamiltonian commutes with S ^ ^ z , so that we can write the eigenvalues as E ( S z ) = D S z 2 , where S z takes the 2S+1 values in the list (S, S-1,...., -S)