Abstract
The magnon spectrum of GdCl3, a two-sublattice ferromagnet in which the dipolar interactions are comparable with the two dominant exchange interactions, is investigated analytically and numerically. The spin-wave energies are found by deriving a generalization of the Holstein-Primakoff result, valid for a system of two equivalent sublattices with arbitrary symmetric interactions between all pairs of spins. The dipole-dipole interactions are treated exactly, by using the Ewald technique to evaluate certain k-dependent lattice sums and their derivatives at k = 0. In the long-wavelength region a formula is obtained for the quadratic approximation to the spectrum, which shows a complicated angular dependence, and this is used to calculate the form of the exponential magnetization curve at very low temperatures. The full dispersion relations are then obtained numerically, without renormalization, using the two possible sets of values for the exchange constants J1 and J2 derived from high-temperature experiments. For set A (J1 = 0.073 °K, J2 = 0.007 °K) the curves for different values of θk cross one another, and the `optical' mode energies are unusually low; for the more likely set B (J1 = -0.025 °K, J2 = 0.040 °K) the spinwave band becomes wider as k increases, and its lower edge is almost flat for an appreciable range of wave numbers. By integrating numerically over the Brillouin zone the zero-point spin defect is shown to be small, and the magnetization and specific heat are found as functions of temperature.
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