Nambu mechanics for stochastic magnetization dynamics

Abstract

The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved quantities. We particularly study how the damping terms of dissipative Nambu mechanics affect the consistent interaction of magnetic systems with stochastic reservoirs and derive a master equation for the magnetization. The proposals are supported by numerical studies using symplectic integrators that preserve the topological structure of Nambu equations. These results are compared to computations performed by direct sampling of the stochastic equations and by using closure assumptions for the moment equations, deduced from the master equation.

Coupling magneto-elastic Lagrangians to spin transfer torque sources

“…Moreover, additional baths, whether thermal, quantum or due to disorder, can be readily taken int ac-count at this level of modeling, since eqs. (9a) and (9b) may be modified consistently, along the lines of 28 . The details will be presented in forthcoming work.…”

Emerging magnetic nutation

“…The equation of motion of a classical or quantum magnetic moment, in the presence of this external field, is of first order in the dynamical variables and describes precession [4]. This equation implies, in particular, some nontrivial conservation laws: the norm of the magnetic moment is conserved and, for a constant external field, so is the component along it [3,5].…”

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

“…While there have been many attempts in the literature [6,7], a general, coherent, picture is, still lacking. One objective of the present study is to pursue the approach set out in [8] and provide more tangible evidence of how longitudinal damping can emerge and be related to transverse damping.…”