Classical Theory of Spin Configurations in the Cubic Spinel

Abstract

It recently has been pointed out that the Yafet-Kittel triangular spin configurations do not minimize the classical Heisenberg exchange energy in the cubic spinel. A perturbation calculation for determining the ground configuration is described in the present paper. We consider only nearest neighbor A-B and B-Binteractions (JAB and JBB), one spin magnitude SA for the A sites, and one SB for the B sites. The method consists of first determining the largest value, y0, of y = JBBSB/JABSA, for which the Néel configuration is stable with respect to sufficiently small spin deviations. One then looks for solutions of the extremum equations as power series in y−y0(≥0), such that the spin deviations from the Néel configuration are small when y−y0 is small. The detailed calculations lead to the following conclusions: 1. Equilibrium configurations exist which have, simultaneously, nonzero angles between spins on the A sites and between those on the B sites. 2. The ground state in the cubic spinel will probably be a long-range-ordered canted-spin arrangement,for at least some finite range of y−y0. The significance of these conclusions in connection with experiments on MnCr2O4 and Mn3O4, and with Anderson's remarks concerning spin configurations in spinels, is discussed.