Spin-wave results for theXXZtriangular antiferromagnet with next-nearest-neighbor couplings

We present results for the sublattice magnetization and the related phase diagram of the XXZ triangular antiferromagnet with next-nearest-neighbor couplings (${\mathit{J}}_{1\mathrm{-}}$ ${\mathit{J}}_2$ model) using the conventional O(1/S) spin-wave theory. On this level, the three-sublattice Ne´el order survives in the entire range from the XY to the Heisenberg limits for sufficiently small frustrations ${\mathit{J}}_2$/${\mathit{J}}_1$. Quantum fluctuations can destroy the long-range Ne´el order only for S=1/2 and in a narrow range near the Heisenberg limit. The sublattice magnetization, as a function of the Ising exchange anisotropy, sharply falls down close to the same limit.