Classical Theory of the Ground Spin-State in Normal Tetragonal Spinels. I. Néel, Yafet-Kittel, and Collinear Antiferromagnetic Modes

Abstract

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.