Three-dimensional ordering in bct antiferromagnets due to quantum disorder

Abstract

Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearest-neighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting (in a mean-field sense) antiferromagnetic planes which together form a body-centered-tetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order ${\mathit{J}}_{\mathrm{\perp }}^2$/(${\mathit{J}}^2$S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate ${\mathit{J}}_{\mathrm{\perp }}$, the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign ${\mathrm{\sigma }}_{\mathit{i}}$ (i=1,2,...M) to the staggered moment of the planes. Our result for the zero-point energy (for M≳2) up to the sixth order in j=${\mathit{J}}_{\mathrm{\perp }}$/J is E({${\mathrm{\sigma }}_{\mathit{i}}$}) =${\mathit{E}}_1$+${\mathit{CE}}_{\mathit{G}}$(${\mathit{j}}^6$/S)[-2${\mathrm{\sigma }}_1$ ${\mathrm{\sigma }}_3$-2${\mathrm{\sigma }}_{\mathit{M}\mathrm{-}2}$ ${\mathrm{\sigma }}_{\mathit{M}}$+2∑i =1M-2${\mathrm{\sigma }}_{\mathit{i}}$ ${\mathrm{\sigma }}_{\mathit{i}+2\mathrm{}}$-3∑i=1M-3${\mathrm{\sigma }}_{\mathit{i}}$ ${\mathrm{\sigma }}_{\mathit{i}+}$ ${\mathrm{\sigma }}_{\mathit{i}+2\mathrm{}}$ ${\mathrm{\sigma }}_{\mathit{i}+3\mathrm{}}$], where C≳0 and ${\mathit{E}}_1$ are constants independent of the σ’s, and ${\mathit{E}}_{\mathit{G}}$ is the classical ground-state energy. (Here sums from i to j when ji are interpreted to be zero.)