Abstract

Bohr-van Leeuwen theorem dictates that a collection of interacting classical charged particles in an external magnetic field under thermal equilibrium is non-magnetic in nature. Indeed, the so called dipole-dipole interaction between the magnetic moments of electrons is too weak to account the observed magnetic order at high temperatures. The responsible interaction is identified by Heisenberg as the well-known Coulomb repulsion between the electrons, independent of spins is suitably strong enough to showcase the magnetism. The spin selectivity appears however from quantum mechanics via the famous Pauli Exclusion Principle. Two electrons with parallel (ferromagnetism) for antiparallel spins (antiferromagnetism) behave differently, even though the fundamental interaction is the same. The observation of weak ferromagnetic in antiferromagnetic crystals prompted Dzyaloshinskii and Moriya (DM) to propose a special type anisotropic spin interaction for the system. In this pedagogical article, we indicate the origin of such DM interaction from the relevant symmetry and indicate a simple two-spin toy model leading to an exact dispersion relation of the magnetic system.

Keywords

Magnetic Moments, Ferromagnetism, Antiferromagnetism, Dzyaloshinskii- Moriya Interaction, Dipole-dipole Interaction