Specific Heat of Two-Dimensional Heisenberg Antiferromagnets: K2MnF4 and K2NiF4

Abstract

The specific heat capacities of the quasi-Heisenberg antiferromagnets ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ have been measured by means of ac calorimetric methods and, through a comparison with the isostructural compound ${\mathrm{K}}_2$Mg${\mathrm{F}}_4$, the magnetic contributions extracted. The magnetic components lie on a universal curve when plotted in units of $R\ln \mathrm{}(2S+1)\mathrm{}$ against the reduced temperature $\frac{T}{T_c^{\mathrm{}\left(2\right)\mathrm{}}}$, where $T_c^{\mathrm{}\left(2\right)\mathrm{}}$ is the respective ordering temperature. It is found that the entropy change of $R\ln \mathrm{}(2S+1)\mathrm{}$ is spread over the range $0.4\le \frac{T}{T_c^{\mathrm{}\left(2\right)\mathrm{}}}\le 4$ with a peak in the specific heat at $\sim 1.5T_c^{\mathrm{}\left(2\right)\mathrm{}}$. Smaller peaks are observed at the transition points and are attributed to the crossover to anisotropic behavior. Models for the two-dimensional Heisenberg magnet are discussed and a suggestion by Kuramoto is explored which produces good agreement with experiment and a transition temperature which is proportional to the critical exponent $\eta$.