# Generalized Boundary Conditions for Spin Transfer

## TL;DR

This paper develops a comprehensive thermodynamic and microscopic framework for understanding spin-transfer torque at interfaces between normal metals and various magnetic materials, generalizing existing concepts beyond collinear cases.

## Contribution

It introduces a generalized set of spin-transfer coefficients applicable to diverse magnetic interfaces, extending the concept of spin-mixing conductance to noncollinear and complex magnetic systems.

## Key findings

- Derived microscopic scattering-matrix expressions for the generalized coefficients.
- Established a thermodynamic description focusing on dissipation and work at interfaces.
- Unified treatment of static and dynamic spin-transfer phenomena across different magnetic materials.

## Abstract

We develop a comprehensive description of static and dynamic spin-transfer torque at interfaces between a normal metal and a magnetic material. Specific examples of the latter include ferromagnets, collinear and noncollinear antiferromagnets, general ferrimagnets, and spin glasses. We study the limit of the exchange-dominated interactions, so that the full system is isotropic in spin space, apart from a possible symmetry-breaking order. A general such interface yields three coefficients (corresponding to three independent generators of rotations) generalizing the well-established notion of the spin-mixing conductance, which pertains to the collinear case. We develop a nonequilibrium thermodynamic description of the emerging interfacial spin transfer and its effect on the collective spin dynamics, while circumventing the usual discussion of spin currents and net spin dynamics. Instead, our focus is on the dissipation and work effectuated by the interface. Microscopic scattering-matrix based expressions are derived for the generalized spin-transfer coefficients.