Magnetic hysteresis in two model spin systems

Abstract

A systematic study of hysteresis in model continuum and lattice spin systems is undertaken by constructing a statistical-mechanical theory wherein spatial fluctuations of the order parameter are incorporated. The theory is used to study the shapes and areas of the hysteresis loops as functions of the amplitude (H₀) and frequency (Ω) of the magnetic field. The response of the spin systems to a pulsed magnetic field is also studied. The continuum model that we study is a three-dimensional (Ψ²)² model with O(N) symmetry in the large-N limit. The dynamics of this model are specified by a Langevin equation. We find that the area A of the hysteresis loop scales as A-H₀^0.66Ω^0.33 for low values of the amplitude and frequency of the magnetic field. The hysteretic response of a two-dimensional, nearest-neighbor, ferromagnetic Ising model is studied by a Monte Carlo simulation on 10×10, 20×20, and 50×50 lattices. The framework that we develop is compared with other theories of hysteresis. The relevance of these results to hysteresis in real magnets is discussed.