## Research Papers in Physics and Astronomy

#### Date of this Version

August 1978

#### Abstract

We consider the random anisotropy model for amorphous magnetism by making a *local*-mean-field approximation (LMFA) on arrays of spin-one particles. Hysteresis loops and the temperature (*T*) dependence of several thermodynamic quantities are presented for various values of the ratio of the strength of the exchange (*J*) to the strength of the uniaxial anisotropy (*D*). Using the LMFA limits us to systems with a small number (*N*) of spins, of which we explicitly consider *N*=64, 216, and 1000. We assume periodic boundary conditions on a system with *N*^{1/3} spins along an edge, nearest-neighbor coupling of constant strength, and six nearest neighbors (as for a simple cubic lattice). For *J*>0 the free energy of spin-glass-like states is higher than that of corresponding states with remanent magnetization. The dependence of the coercive field (*B*_{c}) on *J* and *D* is discussed and the apparent discrepancy of Chi and Alben vis à vis Callen, Liu, and Cullen concerning the behavior of *B*_{c} for large *D* is clarified. A calculation of the temperature dependence of *B*_{c} is presented which is reminiscent of experimental results. This random anisotropy is found to give rise to a second peak in the specific heat for suitable values of *D*/*J*. The magnetic susceptibility (χ_{T}) is calculated for both positive and negative J and shows positive and negative paramagnetic Curie-Weiss temperatures, respectively. The slopes of the χ_{T}^{-1} (*T*) curves for *T* well above the critical temperature (*T*_{c}) have values that are roughly equal to 3/2, the value appropriate to *D*=0 and *S*=1. The local order parameter *q* is used to identify *T*_{c}, which correlates well with the critical temperature identified from other thermodynamic quantities. The presence of the random anisotropy is found to reduce *T*_{c} by up to about 25%. The results of several temperature-dependent calculations are summarized in a phase diagram and regions of paramagnetic, random ferromagnetic, and random antiferromagnetic (or spin-glass-like) behavior are identified.

## Comments

Published by American Physical Society.

Phys. Rev. B18, 1377 (1978). http://prb.aps.org. Copyright © 1978 American Physical Society. Permission to use.