Fig. 1: Ground state of easy-plane triangular-lattice antiferromangets.

a Schematic ground-state phase diagram in the space of the magnetic field H scaled by the saturated field strength H_s, the reciprocal of spin quantum number S, and easy-plane anisotropy ⊥H. The phase boundaries on the plane of no anisotropy (on the back face) are obtained by the 1/S expansion method with the “cutting-at-1/3” procedure¹⁸ (solid lines) and coupled-cluster method¹⁹ (red dots). Those on the planes of S = 1/2 and H/H_s → 1 (on the right and top faces, respectively) are sketches based on the predictions of ref. ²⁰ and refs. ^21,22,23, respectively. The approximate locations of some relevant materials^{69,70,71,72,73} are indicated by the filled circles. b-e Illustrations of the sublattice spin moments in each phase appearing in a.