Concentration inhomogeneities in random magnets. II. Effects on critical-phenomena studies.

Abstract

The effects that concentration inhomogeneities in two-component magnetic systems have on the critical behavior at the second-order phase transition ${T}_{N}$ are explicitly determined. Use is made of the technique developed in the preceding paper (I) to first properly characterize the concentration variation x(r) as a function of position r in a prototype diluted Ising antiferromagnet, ${\mathrm{Fe}}_{\mathrm{x}}$${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{F}}_{2}$. Then, with the known dependence of ${T}_{N}$(x) on x, simulations are made of the magnetic specific-heat anomaly and the quasielastic-neutron-scattering line profile as a function of reduced temperature for the random-exchange Ising-model system. The simulations reproduce experimental measurements on systems with predetermined linear concentration gradients. Errors in crossover and critical exponents in studies by others of the phase transition region in random magnets are shown to result from neglect or improper treatment of concentration gradient effects on critical behavior. It is argued that different distribution functions for concentration gradients, with the same variance, will lead to different effective critical behavior; hence knowing the latter is not sufficient in predicting the former. This is exemplified in an analysis of a neutron-scattering experiment whose critical behavior cannot be fitted by any choice of assumed linear gradient.