We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1 and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin S, for J2/J1<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0, and for 1/8<J2/J1<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary S, including S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all S. We show that for S>1, the transition remains first order, with a finite hysteresis width, but for S=1/2 and, possibly, S=1, there appears a new intermediate phase without a quasiclassical long-range order.
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We acknowledge useful conversations with C. Batista, A. Chernyshev, D. Maslov, N. Perkins, and O. Starykh. The work was supported by the NSF DMR-1523036.
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