Spin-lattice relaxation beyond Gilbert damping

Abstract

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.

Angular momentum conservation and phonon spin in magnetic insulators

“…A Hamiltonian of the form of Eq. (2) has been used recently to compute the relaxation of a classical spin system [38]. Ultimately, the origin of the Hamiltonian (2) lies in the spin-orbit coupling of the electrons: The anisotropic contribution (2b) arises from the dynamical crystal field that affects the electronic orbitals and thereby the spin states, whereas the position dependence of the exchange contribution (2a) is due to the dependence of the electronic hopping integrals on the interatomic distances.…”

Refined electron-spin transport model for single-element ferromagnetic systems: Application to nickel nanocontacts

“…In fact, even the coefficient of the simpler anisotropy correction used in Ref. [5] exhibits uncertainty of up to an order of magnitude compared to the available experimental results. Consequently, in analogy with Ref.…”

“…The above model of ferromagnetic exchange is isotropic and hence does not conserve the angular momentum of the combined lattice and spin system [4,5]. Furthermore, it is well known that magnetic anisotropy, whose origin can be traced to SOC, cannot be ignored in low-dimensional systems such as ferromagnetic nancontacts [19,55].…”

“…The modeling of dynamic and thermal effects on spins in ferromagnetic systems is a challenging problem [1,2], since the inclusion of spin-orbit coupling (SOC) becomes essential at the atomic scale [3][4][5]. If, furthermore, the goal is to account for electronic transport in these systems, the task becomes even more complicated.…”

“…It consists of an atomistic multiphysics approach that combines spin-lattice dynamics (SLD) and DFT electronic transport calculations in a unique way. We include the magnetic anisotropy corrections in our SLD calculations in order to be able to model accurately the magnetoelastic effects in low-dimensional ferromagnetic structures [4,5]. Combined with the SLD model, we use a post-self-consistent-field ab initio methodology to calculate electronic transport that takes * wd2@alu.ua.es into account the effect of the SOC [21,23] as well as the contribution from noncollinearity (NC) in the spins [24,25].…”