Phases of a Triangular-Lattice Antiferromagnet Near Saturation

Abstract

We consider 2D Heisenberg antiferromagnets on a triangular lattice with spatially anisotropic interactions in a high magnetic field close to the saturation. We show that this system possess rich phase diagram in field/anisotropy plane due to competition between classical and quantum orders: an incommensurate noncoplanar spiral state, which is favored classically, and a commensurate co-planar state, which is stabilized by quantum fluctuations. We show that the transformation between these two states is highly non-trivial and involves two intermediate phases -the phase with co-planar incommensurate spin order and the one with non-coplanar double-Q spiral order. The transition between the two co-planar states is of commensurateincommensurate type, not accompanied by softening of spin-wave excitations. We show that a different sequence of transitions holds in triangular antiferromagnets with exchange anisotropy, such as Ba3CoSb2O9.Introduction. The field of frustrated quantum magnetism witnessed a remarkable revival of interest in the last few years due to rapid progress in synthesis of new materials and in understanding previously unknown states of matter. The two main lines of research in the field are searches for spin-liquid phases and for new ordered phases with highly non-trivial spin structures [1]. For the latter, the most promising system is a 2D Heisenberg antiferromagnet on a triangular lattice in a finite magnetic field, as this system is known to possess an "accidental" classical degeneracy: every classical spin configuration with a triad of neighboring spins satisfying S r + S r+δ1 + S r+δ2 = h/(3J), where J is the exchange interaction, belongs to the ground state manifold.An infinite degeneracy, however, holds only for an ideal Heisenberg system with isotropic nearest-neighbor interaction. Real systems have either spatial anisotropy of exchange interactions, as in Cs 2 CuCl 4 [2, 3] and Cs 2 CuBr 4 [4-6] for which the interaction J on horizontal bonds is larger than J on diagonal bonds (see insert in Fig. 1), or exchange anisotropy in spin space, as in Ba 3 CoSb 2 O 9 , for which J z < J ⊥ = J (an easy plane anisotropy) [7][8][9]. An anisotropy of either type breaks accidental degeneracy already at a classical level and for fields h = hẑ slightly below the saturation field h sat selects a non-coplanar cone state with

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

“…For large spin values S ≫ 1, Starykh et al [30] have estimated (J/J z ) c1 and (J/J z ) c2 based on the dilute Bosegas expansion formalism, in which magnetic states in the vicinity of the saturation are described as BoseEinstein condensations (BECs) of dilute magnons via the Holstein-Primakoff transformation [32,33]. The values of (J/J z ) c1 and (J/J z ) c2 were determined at leading order in 1/S as…”

“…has recently received increasing attention since the latest theoretical studies [29,30] indicated the possibility for the emergence of a new magnetic phase, named the π-coplanar or Ψ phase for J > J z > 0.…”

Quasi-two-dimensional Bose-Einstein condensation of lattice bosons in the spin- 12 XXZ ferromagnet K2CuF4

“…This canted ferromagnetic state exactly corresponds to the Bose -Einstein condensed state of the lattice bosons. Bose-gas description of spin model was extended to Heisenberg antiferromagnets in high magnetic fields, and the phase transitions between fully polarized and antiferromagnetic ordered states or the spin structures of the ordered states were discussed from the BEC point of view [35][36][37].…”

Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy

“…Finally, it is interesting to note that a double-Q conical state, like the one described by Eq. (3), has been obtained below the saturation field of a spatially anisotropic TL model [28].…”