Physical condition and spin-resolved exchange correlation kernels in an inhomogeneous many electron system

TL;DR

This paper investigates the spin symmetry relations of exchange-correlation kernels in inhomogeneous many-electron systems, deriving conditions for their physical consistency and applying them to spintronics-relevant magnetic systems.

Contribution

It derives and examines the physical conditions for spin symmetry relations of exchange-correlation kernels in inhomogeneous electron systems with arbitrary spin polarization.

Findings

Derived the spin symmetry relation for exchange-correlation kernels.

Established conditions for physical consistency in ferromagnetic and nonmagnetic systems.

Applied the conditions to spintronics-relevant magnetic systems.

Abstract

We first exploit the spin symmetry relation $f^{\rm xc}_{s\bar s} (\zeta)=f^{\rm xc}_{\bar s s}(-\zeta)$ for the exact exchange correlation kernel $f^{\rm xc}_{s\bar s}(\zeta)$ in an inhomogeneous many electron system with arbitrary spin polarization $\zeta$. The physical condition required to satisfy the specific symmetry relation $f^{\rm xc}_{s\bar s}(\zeta) = f^{\rm xc}_{\bar s s}(\zeta)$ is derived and examined for simple ferromagnetic-nonmagnetic structure by taking the electrochemical potential into account. The condition is then applied to several composite systems useful in spintronics applications such as the magnetic system with net spin polarization.