# Magnetic force theory combined with quasi-particle self-consistent GW method

## TL;DR

This paper combines magnetic force linear response theory with the quasiparticle self-consistent GW method to better understand magnetic interactions, revealing GW effects on bandwidth, interaction strength, and orbital coupling in magnetic materials.

## Contribution

It introduces a straightforward way to incorporate GW self-energy effects into magnetic force calculations, enabling detailed analysis of magnetic interactions beyond total energy differences.

## Key findings

- GW self-energy slightly reduces $d$ bandwidth in ferromagnetic $3d$ elements.
- GW enhances magnetic interactions while maintaining long-range features.
- QSGW significantly reduces interaction strengths in antiferromagnetic transition-metal monoxides.

## Abstract

We report a successful combination of magnetic force linear response theory with quasiparticle self-consistent GW method. The self-consistently determined wavefunctions and eigenvalues can just be used for the conventional magnetic force calculations. While its formulation is straightforward, this combination provides a way to investigate the effect of GW self-energy on the magnetic interactions which can hardly be quantified due to the limitation of current GW methodology in calculating the total energy difference in between different magnetic phases. In ferromagnetic $3d$ elements, GW self-energy slightly reduces the $d$ bandwidth and enhances the interactions while the same long-range feature is maintained. In antiferromagnetic transition-metal monoxides, QSGW significantly reduces the interaction strengths by enlarging the gap. Orbital-dependent magnetic force calculations show that the coupling between $e_g$ and the nominally-empty $4s$ orbital is noticeably large in MnO which is reminiscent of the discussion for cuprates regarding the role of Cu-$4s$ state. This combination of magnetic force theory with quasiparticle self-consistent GW can be a useful tool to study various magnetic materials.