Weak ferromagnetism in antiferromagnets: Fe$_{2}$O$_{3}$ and La$_{2}$CuO$_{4}$

TL;DR

This paper develops a Green's function-based method to analyze weak ferromagnetism in antiferromagnets, accounting for spin-orbit coupling, and applies it to Fe₂O₃ and La₂CuO₄, achieving results consistent with experiments.

Contribution

It introduces a novel approach combining Green's functions and perturbation theory to calculate canting angles and exchange interactions in weak ferromagnets.

Findings

Calculated canting angles agree with experimental data

Derived effective spin Hamiltonian including Dzyaloshinskii-Moriya interactions

Applied method successfully to Fe₂O₃ and La₂CuO₄

Abstract

The problem of weak ferromagnetism in antiferromagnets due to canting of magnetic moments was treated using Green's function technique. At first the eigenvalues and eigenfunctions of the electronic Hamiltonian corresponding to collinear magnetic configuration are calculated which are then used to determine first and second variations of the total energy as a function of the magnetic moments canting angle. Spin-orbit coupling is taken into account via perturbation theory. The results of calculations are used to determine an effective spin Hamiltonian. This Hamiltonian can be mapped on conventional spin Hamiltonian that allows to determine parameters of isotropic and anisotropic (Dzyaloshinskii-Moriya) exchange interactions. The method was applied to the typical antiferromagnets with weak ferromagnetism Fe$_{2}$O$_{3}$ and La$_{2}$CuO$_{4}$. The obtained directions and values of the magnetic moments canting angles are in a reasonable agreement with experimental data.