Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$

Abstract

Spin-1 antiferromagnets are abundant in nature, but few theories or results exist to understand their general properties and behavior, particularly in situations when geometric frustration is present. Here we study the $S=1$ Kagome compound Na${}_2$Ti${}_3$Cl${}_8$ using a combination of Density Functional Theory, Exact Diagonalization, and Density Matrix Renormalization Group methods to achieve a first principles supported explanation of exotic magnetic phases in this compound. We find that the effective magnetic Hamiltonian includes essential non-Heisenberg terms that do not stem from spin-orbit coupling, and both trimerized and spin-nematic magnetic phases are relevant. The experimentally observed structural transition to a breathing Kagome phase is driven by spin--lattice coupling, which favors the trimerized magnetic phase against the quadrupolar one. We thus show that lattice effects can be necessary to understand the magnetism in frustrated magnetic compounds, and surmise that Na${}_2$Ti${}_3$Cl${}_8$ is a compound which cannot be understood from only electronic or only lattice Hamiltonians, very much like VO${}_2$.

arXiv comment6 pages, 4 figures. 9 pages of supplementary material with 10 figures

References in corpus (45)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Dynamical singlets and correlation-assisted Peierls transition in VO2
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Orbital-assisted metal-insulator transition in VO${}_2$
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Order by distortion and string modes in pyrochlore antiferromagnet
• Spin Driven Jahn-Teller Distortion in a Pyrochlore system
• Vanadium dioxide : A Peierls-Mott insulator stable against disorder
• High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S=1$ quantum spin-liquids based on Ni^{2+}
• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Systematic derivation of realistic spin-models for beyond-Heisenberg solids
• Resolving the VO${}_2$ controversy: Mott mechanism dominates the insulator-to-metal transition
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Correlation-driven insulator-metal transition in near-ideal vanadium dioxide films
• Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi${}_2$F${}_7$
• The insulating phases of vanadium dioxide are Mott-Hubbard insulators
• Biquadratic and ring exchange interactions in orthorhombic perovskite manganites
• The Magnetoelectric Effect in Transition Metal Oxides: Insights and the Rational Design of New Materials from First Principles
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• The mother of all states of the kagome quantum antiferromagnet
• Simplex solid states of SU(N) quantum antiferromagnets
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Ground State and Elementary Excitations of the S=1 Kagome Heisenberg Antiferromagnet
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• On the origin of biquadratic exchange in spin 1 chains
• Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice
• Exotic S=1 spin liquid state with fermionic excitations on triangular lattice
• Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet
• From real materials to model Hamiltonians with density matrix downfolding
• Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
• Unconventional magnetism in the 4d${}^4$ based ($S=1$) honeycomb system Ag${}_3$LiRu${}_2$O${}_6$
• Magnetically induced phonon splitting in ACr${}_2$O${}_4$ spinels from first principles
• Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 Kagomé antiferromagnet
• Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m=\frac{2}{3}$ magnetization
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• Nature of the Magnetic Interactions in Sr${}_3$NiIrO${}_6$

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• The Chemistry of Quantum Spin Liquids
• Origin and stability of the charge density wave in ScV${}_6$Sn${}_6$
• Orbital Peierls mechanism of the formation of molecular clusters in Na2Ti3Cl8 and in similar systems
• Investigating the magneto-elastic properties in FeSn and Fe${}_3$Sn${}_2$ flat band metals
• Multimagnon dynamics and thermalization in the $S=1$ easy-axis ferromagnetic chain
• First-principles characterization of the magnetic properties of Cu${}_2$(OH)${}_3$Br
• The Future of the Correlated Electron Problem
• Dynamic Spin-Lattice Coupling and Statistical Interpretation for the Molecular-Like Excitations in Frustrated Pyrochlores
• Survival of magnetic correlations above ordering temperature in a ferromagnetically ordered classical kagomé magnet: Li9Cr3(P2O7)3(PO4)2
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Electronic and structural properties of Rh- and Pd-based kagome layered shandites from first principles
• Response to comment on "Spin-lattice coupling and the emergence of the trimerized phase in the $S=1$ kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$", Phys. Rev. Lett. 124, 167203 (2020)