Spin Dynamics with Inertia in Metallic Ferromagnets

TL;DR

This paper investigates the inertia of spin in metallic ferromagnets, deriving a concrete expression for spin inertia, analyzing its dynamical behavior, and exploring its effects on spin waves, domain walls, and responses to time-dependent magnetic fields.

Contribution

It provides a specific formula for spin inertia in metallic ferromagnets and analyzes its impact on spin dynamics and magnetic structures.

Findings

Derived a formula for spin inertia $m_s$ in metallic ferromagnets.

Analyzed spin dynamics with inertia using spinning top and sphere models.

Explored effects of inertia on spin waves, domain walls, and magnetic field responses.

Abstract

Non-adiabatic contribution of environmental degrees of freedom yields effective inertia of spin in effective spin dynamics. In this paper, we study several aspects of the inertia of spin in metallic ferromagnets. (i) a concrete expression of the spin inertia $m_s$: $m_s=\hbar S_c/(2g_{\rm sd})$, where $S_c$ is the spin polarization of conduction electrons and $g_{\rm sd}$ is the $sd$ coupling constant. (ii) dynamical behavior of spin with inertia, discussed from viewpoints of a spinning top and of a particle on a sphere. (iii) behavior of spin waves and domain walls in the presence of inertia, and behavior of spin with inertia in the case of a time-dependent magnetic field.