Sensitivity of Curie Temperature to Crystal-Field Anisotropy. II. FeF2

Abstract

Fe${\mathrm{F}}_2$ is a simple two-sublattice antiferromagnet and has a rutile crystal structure. Its large anisotropy can be represented to a good approximation by single-ion crystal-field terms of the type discussed in Paper I. The purpose of the present paper is, firstly, to analyze relevant high- and low-temperature experimental data in order to estimate as accurately as possible the important exchange and anisotropy parameters for Fe${\mathrm{F}}_2$ and, secondly, to use this information to test the various theories for transition temperature which were the subject of Paper I. An adequate spin Hamiltonian for Fe${\mathrm{F}}_2$ can be written as $\mathcal{H}=\Sigma \stackrel{}{\mathrm{nn}}{J}_1{\mathbf{S}}_i·{\mathbf{S}}_j+\Sigma \stackrel{}{\mathrm{nnn}}{J}_2{\mathbf{S}}_i·{\mathbf{S}}_j-\Sigma \stackrel{}{i}DS_{\mathrm{iz}}^{}{}_{}{}^2,$ where ${\Sigma }_{\mathrm{nn}} \left({\Sigma }_{\mathrm{nnn}}\right)$ is over all pairs of nearest (next-nearest) neighbor spins $S_i$ and $S_j$, and where ${\Sigma }_i$ is over all spins in the system. From an analysis of nuclear-resonance and magnetic-susceptibility data we find $D=6.5\mathrm{}\pm 0.3$ ${\mathrm{cm}}^{-1\mathrm{}}$, $J_2=3.85\mathrm{}\pm 0.2$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $\frac{J_1}{J_2}=0.1\mathrm{}\pm 0.25$. The resulting ratio $\frac{D}{J_2}=1.7\mathrm{}\pm 0.2$ takes Fe${\mathrm{F}}_2$ outside the small anisotropy range for which the theory of Paper I was primarily developed. Even so, use of the above parameter values in that theory results in a theoretical estimate for the Néel temperature which is in error by only some 12% for Fe${\mathrm{F}}_2$. This estimate is considerably more accurate than those obtained by use of molecular-field theory or by earlier Green's-function approximations.