Spin-lattice relaxation beyond Gilbert damping

A combined dynamics for the spin and lattice degrees of freedom is proposed. For that we couple a Heisenberg spin Hamiltonian via a distance dependent exchange integral and an anisotropic correction to the lattice, where the latter is formed by a harmonic potential. With these extensions the transfer of energy as well as angular momentum between lattice and spins is possible. We test this model successfully by reproducing the Einstein-De Haas effect for a free cluster. On the other hand we find severe differences of the temperature dependent demagnetization dynamics of the new approach as compared to the well-established magnetization dynamics covered by Gilbert damping.