An appreciable number of magnetic materials with the spinel structure exhibit tetragonal symmetry, rather than cubic, in their x-ray diffraction patterns. Because of the distortion, five different nearest-neighbor exchange interactions are possible, so that four ratios ($t, u, v, \mathrm{and} w$) amongst these interactions are required for the characterization of such a material. In this paper, we use the generalized Luttinger-Tisza method (GLT) to determine rigorously the ranges of values of the above ratios (regions in $t, u, v, w$ parameter space) for which the familiar Néel, Yafet-Kittel, and collinear antiferromagnetic spin configurations (k=0 modes) are the ground states of the classical Heisenberg exhange energy. We also determine the characteristic $k$ vectors of the spin deviations which destabilize the k=0 modes along the boundary surfaces of their ground-state regions. Such information is important as a first step towards a more complete investigation of ground-state spin configurations in tetragonal spinels.

We find the above ground-state regions to be significantly smaller than would be predicted on the basis of a sublattice model. Consequently, knowledge of the actual spin configuration can place important restrictions upon the relative strengths of exchange interactions, as in the case of copper chromite. In addition, we find that the destabilizing $k$ vector is not always parallel to a symmetry direction, even for nearly-cubic spinels.

In this paper, we also use the molecular-field approximation to investigate the relative stabilities of the k=0 mode in the neighborhood of the highest magnetic transition temperature (${\mathrm{T}}_c$). We find that the only possible ferrimagnetic configuration at $T_c$ is of the Néel type, and for moderate degrees of distortion, its stability region is much larger at $T_c$ than in the ground state. This result implies that at least two magnetic transitions must occur in any spinel with a magnetic noncollinear ground state.

• Received 23 April 1962

DOI:https://doi.org/10.1103/PhysRev.127.1983