High-Temperature Susceptibility of Heisenberg Ferromagnets Having First- and Second-Neighbor Interactions

Abstract

Exact power-series expansion of the high-temperature magnetic susceptibility of the nearest-neighbor Heisenberg ferromagnets have been provided by Rushbrooke and Wood. This paper describes the derivation of high-temperature susceptibility series for Heisenberg ferromagnets having both first-and second-neighbor exchange. The calculation is accomplished by extending the general diagrammatic technique developed by Rushbrooke and Wood to include the second-neighbor interaction. All mixed coefficients for terms through the fourth power of the inverse temperature have been computed for arbitrary spin and general lattice structure. The series expansions have been applied to the susceptibility of gadolinium in order to determine the quality of information which can be obtained from experimental data. It is found that the susceptibility is not quite sensitive enough to be able to specify the values of both the first- and second-neighbor exchange constants. It is shown, however, that the theory is capable of providing one definite relationship between the values of the two constants. The determination of unique values for the constants then requires the analysis of additional experimental data. The value of the Curie constant is uniquely specified.