Nonlinear Extension of the Dynamical Linear Response of Spin: Extended Heisenberg Model

We introduce a new extended Heisenberg model that contains orbital-dependent spins together with the retarded effects of spin torque. The model is directly derived from the dynamical linear response functions on the transversal spin fluctuation. Our model allows us to address effects that are not accessible via the usual Heisenberg model. With the model, we can describe not only the relaxation effects due to the Landau damping caused by the Stoner excitations, but also the nesting effects of the Fermi surface. We discuss the possibilities of the extended Heisenberg model on the basis of high-resolution plots of the spin susceptibility for Fe.