Magnetic characteristics of three-dimensional impurity clusters in paramagnetic garnets

A study has been made on the effects of biquadratic exchange interaction and distortions on the behavior of x^-1(T), the reciprocal of the magnetic susceptibility, and the spin specific heat c(T) for impurity three-dimensional clusters. It is found that even biquadratic exchange small by comparison with the Heisenberg value (j/J₀ = 0.05) produces considerable changes (up to 30%) in the magnitude and temperature dependence of x^-1(T) in the region kT ≃ J₀. An increase in the biquadratic exchange parameter j reduces the peak in c(T) and shifts it to lower temperatures. The specific course of X^-1(T) at intermediate temperatures, kT ≃ J₀, and of c(T) at low temperatures enables one to detect these clusters and to distinguish the contributions from impurity pairs and triplets, as well as to estimate the non-Heisenberg exchange interactions.