Compatible microstructures in magnetic materials

Abstract

A mathematical relationship between magnetic material constants is proposed for which highly reversible microstructures form during phase transformations. The microstructures formed during paramagnetic-to-ferromagnetic phase transformation are systematically studied, and specific combinations of material constants---namely, magnetocrystalline anisotropy ${\ensuremath{\kappa}}_{1},{\ensuremath{\kappa}}_{2}$ and magnetostriction ${\ensuremath{\lambda}}_{100},{\ensuremath{\lambda}}_{111}$---for which stress-free interfaces with divergence-free magnetization can form are identified. The microstructural analysis shows that magnetic materials with ${\ensuremath{\kappa}}_{1}\ensuremath{\le}0$, ${\ensuremath{\kappa}}_{2}\ensuremath{\ge}\frac{9|{\ensuremath{\kappa}}_{1}|}{4}$, and ${\ensuremath{\lambda}}_{111}=\ensuremath{-}\frac{{\ensuremath{\lambda}}_{100}}{3}$ form exactly compatible and divergence-free phase boundaries. Furthermore, the analysis shows that, consistent with experimental observation, magnetic alloys that undergo cubic-to-monoclinic-II transformation have multiple solutions satisfying the high-reversibility condition and are suitable candidates for alloy development. Broadly, the results could guide the design of magnetic materials with low fatigue and hysteresis for energy applications.