Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

Abstract

Recent experiments on the anisotropic spin-1/2 triangular antiferromagnet Cs 2 CuBr 4 have revealed a remarkably rich phase diagram in applied magnetic fields, consisting of an unexpectedly large number of ordered phases. Motivated by this finding, we study the role of three ingredients-spatial anisotropy, Dzyaloshinskii-Moriya interactions, and quantum fluctuations-on the magnetization process of a triangular antiferromagnet, coming from the semiclassical limit. The richness of the problem stems from two key facts: (1) the classical isotropic model with a magnetic field exhibits a large accidental ground-state degeneracy and (2) these three ingredients compete with one another and split this degeneracy in opposing ways. Using a variety of complementary approaches, including extensive Monte Carlo numerics, spin-wave theory, and an analysis of Bose-Einstein condensation of magnons at high fields, we find that their interplay gives rise to a complex phase diagram consisting of numerous incommensurate and commensurate phases. Our results shed light on the observed phase diagram for Cs 2 CuBr 4 and suggest a number of future theoretical and experimental directions that will be useful for obtaining a complete understanding of this material's interesting phenomenology.

Quantum phase diagram of theS=12triangular-lattice antiferromagnetBa3CoSb2O9

“…The computational cost can be greatly reduced by approximating this polynomial form based on a few guiding principles. 21 As has been pointed out in several previous studies, 7,21,25 a negative biquadratic coupling can mimic the effect of quantum fluctuations since they both favor collinear spin configurations. Thus, we propose the simple expression…”

“…A similar approach was introduced in Ref. 21, with the only difference being that our expression allows for a renormalization of the bilinear coupling due to quantum fluctuations. Such renormalization is important to reproduce the exact value of the saturation field for B ĉ.…”

“…This treatment is inspired by the work of Griset et al 21 and it incorporates the effect of quantum fluctuations via the generation of effective coupling constants for the classical spins. These constants are computed by expanding the energy of different spin configurations, which are degenerate solutions in the classical limit in d = 2, to leading order in 1/S.…”

Half-metallic magnetization plateaux

“…(cos(Q · r) takes values 1, −1/2, −1/2 on the triangular lattice.) Parameters η σ are determined self-consistently by the equations similar to (9). Solving them numerically we find discontinuous jump of η σ from zero to finite values when U ≥ 4.30t for a range of h. η ↑ and η ↓ are in general different so that the system displays a co-existence of the spin-density and charge-density wave orders [24].…”

“…It is a remarkably stable state known to survive significant spatial deformation of exchange integrals in both quantum (spin 1/2) and classical versions of the model [8][9][10]. The basic reason for the stability lies in the collinear structure of the UUD configuration.…”