Probing magneto-elastic phenomena through an effective spin-bath coupling model

Abstract

A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the present work, the consequences of identifying the effects of dissipation as resulting from interactions with a bath of spins are explored, in addition to elastic, degrees of freedom. The corresponding stochastic differential equations are solved numerically and the moments of the magnetization are computed. The stochastic equations implicitly define a measure on the space of spin configurations, whose moments at equal times satisfy a hierarchy of deterministic, ordinary differential equations. Closure assumptions are used to truncate the hierarchy and the same moments are computed. We focus on the advantages and problems that each approach presents, for the approach to equilibrium and, in particular, the emergence of longitudinal damping. T.Nussle

On dissipative symplectic integration with applications to gradient-based optimization

“…This crucial result relies on the fact that the Hamiltonian is a constant of motion. On the other hand, there are relatively few results on structure-preserving methods for dissipative systems, although this has been the subject of a nascent literature [26][27][28][29][30][31]. It is thus unknown if the key stability properties of symplectic integrators can be extended to dissipative cases precisely because a conserved quantity is no longer available.…”

“…In order to approximate H, write (26) in the form H = H + O(h r )-since φ h has order r-to obtain (28). Note that to ensure the contribution from (30) remains smaller than O(h r ) we have to choose t = h such that t e −r e −h 0 /h ∼ h r .…”