Quantum effects expressed by the energy shift ΔE from the Néel energy ${\mathit{E}}^{\mathrm{N}\mathrm{é}\mathrm{el}}$ and the spin reduction ΔS for zero-point fluctuations of magnons are investigated theoretically for the triangular antiferromagnets (TLAF) on the xy plane with the one-ion-type axial anisotropy -‖D‖(${\mathit{S}}^{\mathit{z}}$${)}^2$. We use a method of constructing the canonical transformation without knowledge of the analytical expression called the Bogoliubov transformation. As a result, boson-type excitations are obtained numerically. Here, characteristic properties are discussed in comparison with those for TLAF with the plane-type anisotropy +‖D‖(${\mathit{S}}^{\mathit{z}}$${)}^2$, for which the canonical transformation can be given in analytical form. Furthermore, the calculation is performed to reveal quantum effects in a six-sublattice structure, which is formed in layered TLAF with the interlayer antiferromagnetic exchange interaction. The behavior of calculated ΔE and ΔS is discussed in the context of magnetic properties of ${\mathrm{VBr}}_2$, ${\mathrm{VCl}}_2$, ${\mathrm{CsNiBr}}_3$, and ${\mathrm{CsMnI}}_3$.

• Received 30 December 1994

DOI:https://doi.org/10.1103/PhysRevB.52.3400