Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions

Abstract

Spin liquid crystals are magnetic analogs of liquid crystals, possessing properties of both liquids and solids, a typical example of which are spin nematics. Spin nematics share many features with spin liquids, and the interplay between them is a promising, but little explored, route to uncovering new phases of matter. Here, we address this question in the context of a spin-$1$ magnet on the honeycomb lattice, by considering a model with both biquadratic interactions, favouring spin-nematic states, and Kitaev-like interactions, supporting spin liquids. Accompanying these, where dipole and quadrupole moments compete, we find a plethora of exotic phases, including multiple-$q$ states with nonzero scalar spin chirality; a quasi-one-dimensional coplanar phase; a twisted conical phase; and a noncoplanar order state which gives way to a chiral spin liquid at finite temperature. The implication of these results for experiment is discussed.

11 pages, 9 figures

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• Spin-orbit phase behaviors of Na2Co2TeO6 at low temperatures
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• Ghost in the machine: Theory of inelastic neutron scattering in a field-induced spin-nematic state
• Classical spin dynamics based on SU($N$) coherent states
• Geometric integration of classical spin dynamics via a mean-field Schrödinger equation
• Langevin dynamics of generalized spins as SU($N$) coherent states
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Semi-classical simulation of spin-1 magnets
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Range of biquadratic and triquadratic Heisenberg effective couplings deduced from multiorbital Hubbard models
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Cited by in corpus (22)

• Easy-plane multi-$\mathbf{q}$ magnetic ground state of Na${}_3$Co${}_2$SbO${}_6$
• Effect of ring-exchange interactions in the extended Kitaev honeycomb model
• Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na${}_2$Co${}_2$TeO${}_6$
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• Material-based analysis of spin-orbital Mott insulators
• Robust triple-q magnetic order with trainable spin vorticity in Na${}_2$Co${}_2$TeO${}_6$
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Spin waves in Na${}_2$Co${}_2$TeO${}_6$ studied by high-frequency/high-field ESR: Successes and failures of the triple-$\mathbf{q}$ model
• Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
• Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States
• Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain