High-temperature expansions for magnetic lattices with arbitrary interactions: Application to GdCl3

A diagram technique is developed for calculating high-temperature expansion coefficients for magnetic systems with arbitrary symmetric tensor interactions between all pairs of spins. General results are obtained for the first three coefficients in the susceptibility and magnetic specific heat series, in terms of various lattice sums involving the long-range parts of the interactions. The case where both Heisenberg exchange and dipole interactions are present is considered in detail, and the results are applied to GdCl 3 , a ferromagnetic insulator ordering at 2.2 °K. Two possible sets of values for the two main exchange constants J 1 and J 2 are found by comparison with experiment: either J 1 = 0.073 ± 0.004 °K, J 2 = 0.007 ± 0 003 °K or J 1 = -0.025 ± 0.006 °K, J 2 = 0.040 ± 0.002 °K, where a positive sign denotes a ferromagnetic interaction. It is not possible to decide between these on the basis of the limited bulk measurements so far made, though resonance measurements on dilute salts favour the second possibility.