Ordering in ferromagnets with random anisotropy.

Abstract

We summarize and extend our study (using real-space response and correlation functions) of the properties of a continuous-symmetry ferromagnet with random anisotropy, distinguishing between the cases of weak and strong random anisotropy. For the weak-anisotropy case we find three different magnetic regimes, according to the strength of the external magnetic field H. In zero H, the net magnetization is zero, although the ferromagnetic correlation length (FCL) is large. We call a ferromagnet in this first regime a correlated spin glass (CSG). It has a very large magnetic susceptibility, and hence a relatively small coherent anisotropy converts it into a nearly typical ferromagnetic domain structure. Also, a relatively small magnetic field nearly aligns the CSG, producing the second regime, which we call a ferromagnet with wandering axis (FWA). The FWA is a slightly noncollinear structure in which the tipping of the magnetization with respect to the field varies over the system. The tipping angle is correlated over a (field-dependent) correlation length which is smaller than the FCL of the CSG. As the field increases the correlation length in the FWA decreases, until the third regime is reached, wherein the tipping angles (which are smaller than in the FWA) are completely uncorrelated from site to site. We obtain the magnetization or susceptibility (as appropriate) for each of these three regimes. We also show that the temperature dependence of the (single-ion) random anisotropy strength can provide a plausible explanation for certain classes of reentrant phenomena and susceptibility cusps observed in magnetization studies. Neutron scattering studies appear to be consistent with the predicted ${H}^{\mathrm{\ensuremath{-}}1/2}$ dependence of the FCL in the FWA regime, and display the expected rise of the FCL in the CSG regime as the random anisotropy strength decreases with increasing temperature.