Generalization of the Luttinger-Tisza method: Application to the case of highly anisotropic dipole-dipole interactions

Abstract

A previous generation of the Luttinger-Tisza method is further extended to cover the case of highly anisotropic dipole-dipole interactions (${g}_{\mathrm{zz}}\ensuremath{\ne}0$, ${g}_{\mathrm{xx}}={g}_{\mathrm{yy}}\ensuremath{\approx}0$) for ${2}^{m}(m\ensuremath{\ge}2)$ ions per unit cell. It is found that the Luttinger-Tisza method using permutation groups is applicable provided the ions occupy special positions; the resulting configurations are such that all ionic spins related to each other by ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}^{2}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}={l}^{\ensuremath{'}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}+{m}^{\ensuremath{'}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{b}}+{n}^{\ensuremath{'}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}})$ translations point in the same direction. In addition, attention is drawn to certain other cases of magnetic configurations which can be treated by the Luttinger-Tisza method; in these cases all ionic spins which are related to each other by $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}$ translations, point in the same direction.