Antiferromagnetism in the Face-Centered Cubic Lattice. III.α-MnS

Abstract

Alpha MnS is a face-centered cubic antiferromagnet which exhibits the same ferromagnetic-layer spin arrangement which is found in MnO. The ${\mathrm{Mn}}^{55}$ zero-field nuclear magnetic resonance (NMR) has been observed in the antiferromagnetic state of $\alpha$-MnS and, from the temperature dependence of the resonance frequency, information is derived regarding the spin deviation as a function of temperature. The so-called anomalous temperature dependence of sublattice magnetization which has been reported for MnO is found to be essentially absent in $\alpha$-MnS. The general question of the incorporation of biquadratic exchange terms $-j{\left({\mathrm{S}}_i·{\mathrm{S}}_j\right)}^2$ into molecular-field and spin-wave theories of magnetism is discussed, and a simple spin-wave theory is developed for $\alpha$-MnS which includes both bilinear and biquadratic exchange interactions between nearest and next-nearest neighbors ($J_1, j_1; J_2, j_2$) as well as both isotropic and anisotropic magnetostrictive terms. The spin deviation is found to be an extremely sensitive function of $j_1$ and of distortion (anisotropic magnetostriction), but is relatively insensitive to $j_2$ and isotropic magnetostriction. The bilinear exchange interactions are estimated by using Lines' Green's-function theory to describe the paramagnetic properties of $\alpha$-MnS, for which we find values $J_1=7\mathrm{}°$K and $J_2=12.5\mathrm{}°$K. Comparison of theory with experiment for the temperature dependence of spin deviation allows an upper limit to be placed upon the magnitude of $j_1$. The ratio $\frac{j_1}{J_1}$ is found to be less than ${10}^{-3\mathrm{}}$, which is at least an order of magnitude smaller than any previous estimates made for ${\mathrm{Mn}}^{2+}$ interactions.