Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation

Abstract

Quantum magnetic phases near the magnetic saturation of triangular-lattice antiferromagnets with XXZ anisotropy have been attracting renewed interest since it has been suggested that a nontrivial coplanar phase, called the $\ensuremath{\pi}$-coplanar or $\mathrm{\ensuremath{\Psi}}$ phase, could be stabilized by quantum effects in a certain range of anisotropy parameter $J/{J}_{z}$ besides the well-known 0-coplanar (known also as $V)$ and umbrella phases. Recently, Sellmann et al. [Phys. Rev. B 91, 081104(R) (2015)] claimed that the $\ensuremath{\pi}$-coplanar phase is absent for $S=1/2$ from an exact-diagonalization analysis in the sector of the Hilbert space with only three down-spins (three magnons). We first reconsider and improve this analysis by taking into account several low-lying eigenvalues and the associated eigenstates as a function of $J/{J}_{z}$ and by sensibly increasing the system sizes (up to 1296 spins). A careful identification analysis shows that the lowest eigenstate is a chirally antisymmetric combination of finite-size umbrella states for $J/{J}_{z}\ensuremath{\gtrsim}2.218$ while it corresponds to a coplanar phase for $J/{J}_{z}\ensuremath{\lesssim}2.218$. However, we demonstrate that the distinction between 0-coplanar and $\ensuremath{\pi}$-coplanar phases in the latter region is fundamentally impossible from the symmetry-preserving finite-size calculations with fixed magnon number. Therefore, we also perform a cluster mean-field plus scaling analysis for small spins $S\ensuremath{\le}3/2$. The obtained results, together with the previous large-$S$ analysis, indicate that the $\ensuremath{\pi}$-coplanar phase exists for any $S$ except for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ and the existence range in $J/{J}_{z}$ is largest in the most quantum case of $S=1/2$.