Quantum-mechanical states of dipolar crystals with two magnetic ions per unit cell.

Abstract

This paper deals with the quantum-mechanical states of dipolar crystals with two equivalent magnetic ions per unit cell, with or without the presence of an external homogeneous magnetic field. The method used is an extension of the Niemeijer-Meijer method which is based on the classical Luttinger-Tisza approach. The approximation used is that the expectation values of the spin operators, and the spin correlations, are periodic with respect to lattice translations along one crystallographic direction and double lattice translations along the other crystallographic directions. Thus, the problem is reduced to finding the minima of an effective Hamiltonian in the space of wave functions describing a cluster of eight magnetic ions. The eight-spin-wave functions are constructed by using the theory of irreducible representations of the translation and inversion group. The method developed here is applied for the calculation of the ground state of dypsprosium trichloride hexahydrate, the results of which appear in the following companion paper.