Unusual ordered phases of highly frustrated magnets: a review

Abstract

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R, and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with $S^z=\pm 1$. We discuss extensively R-h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S=1/2 limit. When possible, we point out connections with experimental findings.

22 pages, 12 figures. This is the originally submitted version of the invited review, to be published in Reports on Progress in Physics in 2015. The link, via DOI, to the accepted and published version of the manuscript, which is updated according to the referees comments, will be provided upon its actual publication

References in corpus (57)

• Half-metallic ferromagnets: From band structure to many-body effects
• Identifying Topological Order by Entanglement Entropy
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• Spontaneous Magnon Decays
• Electronic Orbital Currents and Polarization in Mott Insulators
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Ordering in spatially anisotropic triangular antiferromagnets
• New high magnetic field phase of the frustrated $S=1/2$ chain compound LiCuVO${}_4$
• Quantum stabilization of 1/3-magnetization plateau in Cs_2CuBr_4
• Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Critical magnetization behaviors of the triangular and Kagome lattice quantum antiferromagnets
• Evidence of a bond-nematic phase in LiCuVO4
• Magnon Decay in Noncollinear Quantum Antiferromagnets
• Flat spin wave dispersion in a triangular antiferromagnet
• Slow Magnetic Order-Order Transition in the Spin Chain Antiferromagnet Ca3Co2O6
• Magnetic phase diagram of the S=1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region: cusp and plateau
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• Search for a spin-nematic phase in the quasi-one-dimensional frustrated magnet LiCuVO${}_4$
• Spin Liquid Phase in Anisotropic Triangular Lattice Heisenberg Model: Exact diagonalization and density-matrix renormalization group calculations
• Novel ordering of an S = 1/2 quasi one-dimensional Ising-like anitiferromagnet in magnetic field
• Spin-modulated quasi-1D antiferromagnet LiCuVO_4
• Spin-Nematic and Spin-Density-Wave Orders in Spatially Anisotropic Frustrated Magnets in a Magnetic Field
• Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
• Magnetic phase diagrams of classical triangular and kagome antiferromagnets
• Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
• Magnetic phase diagram, critical behaviour and 2D-3D crossover in a triangular lattice antiferromagnet RbFe(MoO4)2
• Longitudinal SDW order in a quasi-1D Ising-like quantum antiferromagnet
• Ground States of Spin-1/2 Triangular Antiferromagnets in a Magnetic Field
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Vector chiral order in frustrated spin chains
• Low temperature broken symmetry phases of spiral antiferromagnets
• Field-induced incommensurate order for the quasi-one-dimensional XXZ model in a magnetic field
• Ground states of a frustrated spin-1/2 antifferomagnet: Cs_2CuCl_4 in a magnetic field
• Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains
• Quantum vs. Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains
• Phases of triangular lattice antiferromagnet near saturation
• Thermodynamics of the Up-Up-Down Phase of the S = 1/2 Triangular-Lattice Antiferromagnet Cs${}_2$CuBr${}_4$
• Spin dynamics of the quasi two dimensional spin-1/2 quantum magnet Cs_2CuCl_4
• Gapless Spin Liquids: Stability and Possible Experimental Relevance
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry
• Spontaneous quantum Hall effect via thermally induced quadratic Fermi point
• Spin Structure Factor of the Frustrated Quantum Magnet Cs_2CuCl_4
• Geometric phases and the magnetization process in quantum antiferromagnets
• Insulator, conductor and commensurability: a topological approach
• Magnetization Process of the Classical Heisenberg Model on the Shastry-Sutherland Lattice
• Low temperature properties of the triangular-lattice antiferromagnet: a bosonic spinon theory
• Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors
• An Exact Diagonalization Study of the Anisotropic Triangular Lattice Heisenberg Model Using Twisted Boundary Conditions
• Half-metallic magnetization plateaux
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model

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• Six magnetization plateau phases in a spin-1/2 distorted kagome antiferromagnet: application to ${\mathrm{Y}}_3{\mathrm{Cu}}_9(\mathrm{OH}{)}_{19}{\mathrm{Cl}}_8$
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• Low-energy spin dynamics in a Kitaev material Na3Ni2BiO6 investigated by NMR
• Exact staggered dimer ground state and its stability in a two-dimensional magnet
• Magnetic properties of van der Waals layered single crystals DyOBr and SmOCl
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Magnetic phase diagram in three-dimensional triangular-lattice antiferromagnet Sr${}_3$CoTa${}_2$O${}_9$ with small easy-axis anisotropy
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• Raman scattering study of multimagnon (bi- and tri-magnon) excitations and rotonlike points in the distorted triangular lattice antiferromagnet
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