Weak Ferromagnetism in Antiferromagnets: α- Fe2 O3 and La2 Cu O4

Abstract

The problem of weak ferromagnetism in antiferromagnets due to canting of magnetic moments is 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 the first and the 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 the conventional spin Hamiltonian that allows one to determine parameters of isotropic and anisotropic (Dzyaloshinskii-Moriya) exchange interactions. The method is applied to the typical antiferromagnets with weak ferromagnetism α- Fe2 O3 and La2 Cu O4. The obtained values of the magnetic moments canting angles are in good agreement with previous theoretical results and are in reasonable agreement with experimental data. © 2005 The American Physical Society.