Magnon condensation with finite degeneracy on the triangular lattice

Abstract

We study the spin 1/2 triangular-lattice ${J}_{1}$-${J}_{2}$-${J}_{3}$ antiferromagnet close to the saturation field using the dilute Bose gas theory, where the magnetic structure is determined by the condensation of magnons. We focus on the case of ferromagnetic ${J}_{1}$ and antiferromagnetic ${J}_{2},{J}_{3}$, which is particularly rich because frustration effects allow the single-magnon energy dispersion to have sixfold degenerate minima at incommensurate momenta. Our calculation also includes an interlayer coupling ${J}_{0}$, which covers both antiferromagnetic and ferromagnetic cases including negligibly small regime (two-dimensional case). Besides the spiral and fan phases, we find a new double-$q$ phase (superposition of two modes), dubbed ``${\mathbf{Q}}_{0}$-${\mathbf{Q}}_{1}$'' (or simply ``01'') phase, that enjoys a new type of multiferroic character. Certain phase boundaries have a singular ${J}_{0}$ dependence for ${J}_{0}\ensuremath{\rightarrow}0$, implying that even a very small interlayer coupling drastically changes the ground state. A mechanism for this singularity is presented. Moreover, in some regions of the parameter space, we show that a dilute gas of magnons can not be stable, and phase separation (corresponding to a magnetization jump) is expected. In the ${J}_{1}$-${J}_{2}$ model (${J}_{3}=0$), formation of two-magnon bound states is observed, which can lead to a quadrupolar (spin-nematic) ordered phase. Exact diagonalization analysis is also applied to the search of bound states.