Quadrupole Interaction in Crystals

Abstract

The quadrupole array for the lowest energy of quadrupole interaction in crystals is obtained by generalizing Luttinger and Tisza's theory of dipole interaction. The theory is presented for the two kinds of problems: the simplest case of quadrupole pertaining to a doubly degenerate orbital eg and the other general cases both for the cubic crystals. In the former case, the quadrupole interaction is written in terms of fictitious spins, whence we can get the solution of lowest energy classically, serving to obtain some informations of the orbital ordering in compounds with Mn3+, Cu2+ and Cr2+. In the latter cases, the five components of the quadrupole are totally effective, leading to a rather complicated problem. The classical solution is, however, easily obtained, though somewhat complicated. The quadrupole array of lowest energy in face-centered cubic lattice proves to be realized in molecular crystals N2, N2O, CO2 and CO, which is accompanied with large quadrupole but without or with small dipole moment.