Anisotropic Exchange between Chromium Ions

Abstract

The exchange interactions between chromium ions in Cr2O3 are studied theoretically using a recent formulation of anisotropic exchange interactions. There is a direct exchange interaction between a Cr3+ ion and its nearest and next nearest neighbors, which is much larger than other indirect interactions in the system. We assume that the neighboring ions are never excited from their orbital singlet 4A2 ground states, and we characterise the exchange interaction by three parameters for each type of neighbor. The full exchange Hamiltonian for this system is presented, and to display the relation between the exchange splittings in different excited manifolds, the problem is solved for the 2E and 4A2 states of the Cr3+ ion at the origin in an octahedral field approximation. The completeproblem, including spin-orbit interaction and the trigonal distortion of the crystal field, does not give explicit algebraic solutions, but could be solved numerically. This analysis shows how the exchange parameters measured in different states of the system are related, provided one assumes that the radial integrals involved are constant between states.