Neutron - diffraction studies show that the magnetic structure of $\beta -\mathrm{M}\mathrm{n}\mathrm{S}$ is either (a) type-III antiferromagnetic or (b) a complex noncollinear structure associated with a wave vector $\overrightarrow{\mathrm{k}}=\left(\frac{2\pi }{a}\right)(\frac{1}{2},1,0)$. We use group-theoretical methods and renormalization-group techniques to discuss the critical behavior associated with the transition to the magnetic structure (b). It is shown that this transition is described by an anisotropic $n=6\mathrm{}$ component vector model which possesses a stable fixed point. The compound $\beta -\mathrm{M}\mathrm{n}\mathrm{S}$ is predicted to belong to the same universality class as ${\mathrm{K}}_2$Ir${\mathrm{Cl}}_6$, Tb${\mathrm{D}}_2$, Nd, and Mn${\mathrm{S}}_2$. This is in marked contrast to the transition to structure (a) which has previously been predicted, on the basis of the Landau theory, to be of first order.

• Received 20 June 1977

DOI:https://doi.org/10.1103/PhysRevB.17.4477