Spin waves in EuS

Abstract

The ferromagnetic compounds of Eu2+ have recently been studied as nearly ideal examples of the Heisenberg model with considerable success. Measurements of the zero-field specific heat and magnetization of powdered EuS in the liquid-helium temperature region have recently been reported. The data were separately analyzed in terms of simple spin-wave theory to give rather indefinite results, especially for the second-neighbor exchange. But together these data provide an unprecedented opportunity to test the Heisenberg model. It is necessary to analyze the data using the complete spin-wave theory as derived by Holstein and Primakoff, including the effect of magnetic dipolar coupling in producing a variation with propagation vector of the spin-wave energy and, hence, spin-wave moment. It is also essential that the finite size of the Brillouin zone be taken into account. By numerical calculation values of the exchange integrals between first neighbors (J1) and second neighbors (J2) as well as an average field H acting in the domains (presumably due to anisotropy and dipolar fields) were sought which would simultaneously produce good fits to both the specific heat and magnetization. It was found that J1/kB=0.20°±0.01°K, J2/k B=-0.08°∓0.02°K, and H=4±2 kOe. By combining the Rushbrooke and Wood value for the transition temperature Tc when J2=0 with the molecular field result for the dependence of T c on J2 we may calculate from the above values T c=15.8°±0.6°K. The paramagnetic Curie point is calculated to be 20.1°±0.8°K. These are in good agreement with measured values. The origin of the large field H is not known, but it is consistent with the fields required to saturate powdered EuS. © 1964 The American Institute of Physics.