Theoretical study on quantum effects in triangular antiferromagnets with axial anisotropy using the numerically constructed Bogoliubov transformation for magnons

Abstract

Quantum effects expressed by the energy shift \ensuremath{\Delta}E from the N\'eel energy ${\mathit{E}}^{\mathrm{N}\mathrm{\'e}\mathrm{el}}$ and the spin reduction \ensuremath{\Delta}S 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 -\ensuremath{\Vert}D\ensuremath{\Vert}(${\mathit{S}}^{\mathit{z}}$${)}^{2}$. We use a method of constructing the canonical transformation without knowledge of the analytical expression called the Bogoliubov transformation. As a result, boson-type excitations are obtained numerically. Here, characteristic properties are discussed in comparison with those for TLAF with the plane-type anisotropy +\ensuremath{\Vert}D\ensuremath{\Vert}(${\mathit{S}}^{\mathit{z}}$${)}^{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 \ensuremath{\Delta}E and \ensuremath{\Delta}S is discussed in the context of magnetic properties of ${\mathrm{VBr}}_{2}$, ${\mathrm{VCl}}_{2}$, ${\mathrm{CsNiBr}}_{3}$, and ${\mathrm{CsMnI}}_{3}$.