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 $\ensuremath{\alpha}$-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 $\ensuremath{\alpha}$-MnS. The general question of the incorporation of biquadratic exchange terms $\ensuremath{-}j{({\mathrm{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{j})}^{2}$ into molecular-field and spin-wave theories of magnetism is discussed, and a simple spin-wave theory is developed for $\ensuremath{\alpha}$-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 $\ensuremath{\alpha}$-MnS, for which we find values ${J}_{1}=7\ifmmode^\circ\else\textdegree\fi{}$K and ${J}_{2}=12.5\ifmmode^\circ\else\textdegree\fi{}$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 ${10}^{\ensuremath{-}3}$, which is at least an order of magnitude smaller than any previous estimates made for ${\mathrm{Mn}}^{2+}$ interactions.