Selection of the ground state of the kagome-lattice $XXZ$ antiferromagnet by quantum fluctuations is investigated by combining nonlinear spin-wave and real-space perturbation theories. The two methods unanimously favor $\mathbf{q}=0$ over $\sqrt{3}\times \sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\le \mathrm{\Delta }\lesssim 0.72$. Both approaches are also in accord on the magnitude of the quantum order-by-disorder effect generated by topologically nontrivial, looplike spin-flip processes. A tentative $S\text{−}\mathrm{\Delta }$ phase diagram of the model is proposed.

• Received 22 September 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.237202