Non-hermitian off-diagonal magnetic response of Dirac fermions

TL;DR

This paper investigates the unique off-diagonal magnetic response of Dirac fermions under non-hermitian magnetic fields, revealing novel spin polarization effects and classical analogies in magnetization dynamics.

Contribution

It introduces the concept of non-hermitian magnetic fields affecting Dirac fermions, highlighting off-diagonal responses and classical drift analogies in spin dynamics.

Findings

Non-hermitian magnetic fields induce off-diagonal spin responses.

Imaginary magnetic fields perpendicular to mass cause finite magnetization.

Classical analogy with particles in crossed electric and magnetic fields.

Abstract

We perform a comparative study for the magnetization dynamics within linear response theory of one and two dimensional massive Dirac electrons, after switching on either a real (hermitian) or an imaginary (non-hermitian) magnetic field. While hermitian dc magnetic fields polarize the spins in the direction of the external magnetic field, non-hermitian magnetic fields induce only off diagonal response. An imaginary dc magnetic field perpendicular to the mass term induces finite magnetization in the third direction only according to the right hand rule. This can be understood by analyzing the non-hermitian equation of motion of the spin, which becomes analogous to a classical particle in crossed electric and magnetic fields. Therein, the spin expectation value, the mass term and imaginary magnetic field play the role of the classical momentum, magnetic and electric field, respectively. The latter two create a drift velocity perpendicular to them, which gives rise to the off-diagonal component of the dc spin susceptibility, similarly to how the Hall effect develops in the classical description.