Uniaxially compressed magnets

Abstract

The response of a compressible magnet to uniaxial stress is studied. Due to the coupling between magnetic and elastic degrees of freedom, the magnetic phase transition becomes first order, accompanied by discontinuities in the transverse and longitudinal strains. The magnitude of discontinuities is controlled by crossover exponents, while the ratio of the jumps in the two directions is related to the anisotropy of the magnet. For an isotropic system the effective Poisson's ratio ($\overline{\sigma }$) close to the transition approaches the universal value $\overline{\sigma }=-1\mathrm{}$. For positive Poisson's ratios $\sigma$, there can be a reentrant transition with increasing pressure. In the limiting case $\sigma =\frac{1}{\mathrm{}(d-1\mathrm{})\mathrm{}}$, the transition remains second order at zero pressure. In two dimensions Onsager's solution is used to obtain exact phase diagrams.