Spintronics meets nonadiabatic molecular dynamics: Geometric spin torque and damping on noncollinear classical magnetism due to electronic open quantum system

TL;DR

This paper investigates the interplay of spintronics and nonadiabatic molecular dynamics by analyzing a quantum-classical hybrid system, revealing a geometric spin torque and damping effects in noncollinear magnetism due to electronic open quantum systems.

Contribution

It introduces an exact method to analyze the nonequilibrium electronic density matrix in a hybrid quantum-classical spin system, highlighting a current-independent geometric torque absent in traditional models.

Findings

Geometric torque dominates in the adiabatic regime.

Dissipative Fermi surface contribution causes spin damping.

Geometric torque acts as a field-like and damping-like component, unaccounted for in standard micromagnetics.

Abstract

We analyze a quantum-classical hybrid system of steadily precessing slow classical localized magnetic moments, forming a head-to-head domain wall, embedded into an open quantum system of fast nonequilibrium electrons. The electrons reside within a metallic wire connected to macroscopic reservoirs. The model captures the essence of dynamical noncollinear and noncoplanar magnetic textures in spintronics, while making it possible to obtain the exact time-dependent nonequilibrium density matrix of electronic system and split it into four contributions. The Fermi surface contribution generates dissipative (or damping-like in spintronics terminology) spin torque on the moments, and one of the two Fermi sea contributions generates geometric torque dominating in the adiabatic regime. When the coupling to the reservoirs is reduced, the geometric torque is the only nonzero contribution. Locally it has both nondissipative (or field-like in spintronics terminology) and damping-like components, but with the sum of latter being zero, which act as the counterparts of geometric magnetism force and electronic friction in nonadiabatic molecular dynamics. Such current-independent geometric torque is absent from widely used micromagnetics or atomistic spin dynamics modeling of magnetization dynamics based on the Landau-Lifshitz-Gilbert equation, where previous analysis of Fermi surface-type torque has severely underestimated its magnitude.