Classical Theory of the Ground Spin-State in Cubic Spinels

Abstract

An investigation of the classical Heisenberg exchange energy has led to the discovery of a new spin configuration, called a ferrimagnetic spiral. The explicit construction of this state is accomplished by application of Lyons-Kaplan generalization of the Luttinger-Tisza method (GLT). For all $B\ensuremath{-}B$ interactions which are sufficiently large to destabilize the N\'eel (collinear) configuration, this spiral has lower energy than all previously proposed spin configurations including those of N\'eel and Yafet-Kittel. Furthermore, this ferrimagnetic spiral is found to be stable against arbitrary small deviations of the spin vectors over a range of interactions that is contiguous with the N\'eel range. It is also shown, by further application of the GLT method, to have the lowest energy over an additional large class of spin configurations. In view of these results, it is likely that the ferrimagnetic spiral is the ground state over its range of local stability.The complete class of configurations possessing "equal relative angles" (i.e., invariance of the angles between spins under lattice translations) is elucidated for the first time. It is shown that the ferrimagnetic spiral has the lowest energy over this class of configurations for a range of interactions which includes the range of stability, and extends beyond it. It follows that for interactions in the latter range, the relative angles in the ground state must not possess translational invariance, in contradiction to earlier hypotheses.The neutron diffraction pattern resulting from general magnetic spirals is discussed. The striking agreement between our theoretical results and the complex pattern found by Corliss and Hastings for manganese chromite supports the theory. In addition, the spin configuration at the Curie point, in the molecular field approximation, is shown to be in accord with the observed temperature dependence in manganese chromite.