Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

Abstract

The structural-magnetic models of 25 AFM kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2) - a perspective spin liquid - have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in length J3 magnetic couplings (strong J3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFM J3(Jd) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality of J3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dual J3 couplings with anisotropic DM interactions are capable to suppress frustration of kagome AFM. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighbor J1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in length J3 magnetic couplings.

arXiv comment50 pages, 20 figures, and 5 tables. Published in J.Phys.: Condens.Matter

References in corpus (61)

• Quantum Spin Liquids
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Vesignieite BaCu3V2O8(OH)2 as a Candidate Spin-1/2 Kagome Antiferromagnet
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Orbital physics in transition metal compounds: new trends
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Low temperature magnetization of the S=1/2 kagome antiferromagnet ZnCu_3(OH)_6Cl_2
• Pinwheel VBS state and triplet excitations in the two-dimensional deformed kagome lattice
• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
• Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules
• Phase Diagram and Spin Dynamics in Volborthite with a Distorted Kagome Lattice
• Nature of chiral spin liquids on the kagome lattice
• Emergence of nontrivial magnetic excitations in a spin liquid state of kagome volborthite
• Ground state of the Kagome-like S=1/2 antiferromagnet, Volborthite Cu3V2O7(OH)2.2H2O
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Dualities and non-Abelian mechanics
• Magnetic susceptibility and specific heat of the spin-1/2 Heisenberg model on the kagome lattice and experimental data on ZnCu3(OH)6Cl2
• Quantum Magnetism in Minerals
• Spin Liquid Ground State in the Frustrated Kagome Antiferromagnet MgCu3(OH)6Cl2
• Weak ferromagnetic order breaking the threefold rotational symmetry of the underlying kagomé lattice in CdCu${}_3$(OH)${}_6$(NO${}_3$)${}_2\cdot$H${}_2$O
• Haydeeite: a spin-1/2 kagome ferromagnet
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Singlet Ground State and Spin Gap in S=1/2 Kagome Antiferromagnet Rb${}_2$Cu${}_3$SnF${}_{12}$
• Magnetic susceptibilities in a family of S=1/2 Kagome antiferromagnet
• Coexistence of magnetic order and persistent spin dynamics in a quantum kagome antiferromagnet with no intersite mixing
• Dissipationless Multiferroic Magnonics
• Origin of Magnetic Ordering in a Structurally-Perfect Quantum Kagome Antiferromagnet
• Magnetic Order in the Spin-1/2 Kagome Antiferromagnet Vesignieite
• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Vesignieite: a $S=\frac{1}{2}$ kagome antiferromagnet with dominant third-neighbor exchange
• Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
• Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3)
• Crystal chemistry aspects of the magnetically induced ferroelectricity in TbMn2O5 and BiMn2O5
• Direct Calculation of Spin-Stiffness for Spin-1/2 Heisenberg Models
• Magnetoelectric ordering of BiFeO3 from the perspective of crystal chemistry
• Pair Correlations, Short Range Order and Dispersive Excitations in the Quasi-Kagome Quantum Magnet Volborthite
• Role of structural factors in formation of chiral magnetic soliton lattice in Cr1/3NbS2
• Large Negative Quantum Renormalization of Excitation Energies in the Spin-1/2 Kagome Lattice Antiferromagnet Cs${}_2$Cu${}_3$SnF${}_{12}$
• Magnetic structure and high-field magnetization of the distorted kagome lattice antiferromagnet Cs${}_2$Cu${}_3$SnF${}_{12}$
• A novel crystal polymorph of volborthite, Cu3V2O7(OH)2 2H2O
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Magnetic Properties of the Spin-1/2 Deformed Kagome Antiferromagnet Edwardsite
• Antiferromagnetic spin-frustrated layers of corner-sharing Cu4 tetrahedra on the kagome lattice in volcanic minerals Cu5O2(VO4)2(CuCl), NaCu5O2(SeO3)2Cl3, and K2Cu5Cl8(OH)4 2H2O
• Schwinger Boson mean field theory of kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interaction
• Structural phase transitions in the kagome lattice based materials Cs2-xRbxSnCu3F12 (x = 0, 0.5, 1.0, 1.5)
• Ghost modes and continuum scattering in the dimerized distorted kagome lattice antiferromagnet Rb${}_2$Cu${}_3$SnF${}_{12}$
• Antiferromagnetism in kagome $\alpha$-Cu${}_3$Mg(OH)${}_6$Br${}_2$
• Re-entrant Structural Phase Transition in a Frustrated Kagome Magnet, Rb2SnCu3F12
• Quantum spin liquids: a large-S route
• Imitation of spin density wave order in Cu${}_3$Nb${}_2$O${}_8$
• Gauge Theories as String Theories: the First Results
• Spin-Frustrated Pyrochlore Chains in the Volcanic Mineral Kamchatkite (KCu3OCl(SO4)2)
• Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

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