Thermodynamic Properties of Impure Heisenberg Antiferromagnets

The local thermodynamic properties of Heisenberg antiferromagnets with dilute substitutional impurities are studied by Green's-function techniques within the random-phase approximation (RPA). A body-centered two-sublattice model, with a single exchange constant and a single-ion staggered-anisotropy field, is used. A representative set of impurity exchange and spin magnitudes is chosen for quantitative study. The spectral distribution of spin excitations, including localized mode contributions, the zero-point spin deviation, and the temperature dependence of the magnetization are examined for the impurity and its first four shells of neighbors. Within the limitations of the single-exchange model (and of the RPA) a comparison is made with resonance and optical experiments on Zn, Fe, and Ni impurities in Mn${\mathrm{F}}_2$. Good agreement was found in the first two cases, but no successful fit to the Ni data was possible, perhaps reflecting the importance of the substantial additional exchange with near neighbors in this case.