Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping

TL;DR

This paper introduces a pseudo-PT symmetric Dirac equation and a new mean spin operator that better describes electron magnetization dynamics, aligning quantum theory with the phenomenological Landau-Lifshitz-Gilbert model.

Contribution

It proposes a novel pseudo-PT symmetric Dirac equation and defines a new mean spin operator that accurately models magnetization in ferromagnetic materials.

Findings

The new mean spin operator aligns with experimental magnetization measurements.

The derived equation of motion is compatible with the Landau-Lifshitz-Gilbert equation.

The approach offers a quantum foundation for magnetization dynamics.

Abstract

The pseudo-PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldy-Wouthuysen transformations. A new spin operator PT symmetric expectation value (called the mean spin operator) for an electron interacting with a time-dependent electromagnetic field is obtained. We show that spin magnetization - which is the quantity usually measured experimentally - is not described by the standard spin operator but by this new mean spin operator to properly describe magnetization dynamics in ferromagnetic materials and the corresponding equation of motion is compatible with the phenomenological model of the Landau-Lifshitz-Gilbert equation (LLG).