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 $J_2,J_3$, that is particularly rich because frustration effects allow the single-magnon energy dispersion to have six-fold 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 $J_0\to 0$, 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.

12 pages, 11 figures; v2 48-spin exact diagonalization added, matches published version

References in corpus (2)

• Spin current and magneto-electric effect in non-collinear magnets
• Octupolar order in the multiple spin exchange model on a triangular lattice

Cited by in corpus (21)

• Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
• Topological spin crystals by itinerant frustration
• Néel- and Bloch-Type Magnetic Vortices in Rashba Metals
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions
• Locking of skyrmion cores on a centrosymmetric discrete lattice: onsite versus offsite
• Multiple-$q$ states of the $J_1$-$J_2$ classical honeycomb-lattice Heisenberg antiferromagnet under magnetic fields
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Three-Dimensional Crystallization of Vortex Strings in Frustrated Quantum Magnets
• Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerant magnets
• Magnetic phase diagram slightly below the saturation field in the stacked $J_1$-$J_2$ model in the square lattice with the $J_{\text{C}}$ interlayer coupling
• Umbrella-coplanar transition in the triangular XXZ model with arbitrary spin
• Anyonic Liquids in Nearly Saturated Spin Chains
• Skyrmion crystal with integer and fractional skyrmion numbers in a nonsymmorphic lattice structure with the screw axis
• Spin-orbit interaction driven dimerization in one dimensional frustrated magnets
• Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice
• Double-$Q$ chiral stripe order in the anomalous Hall antiferromagnet CoNb${}_3$S${}_6$