Spin-1 antiferromagnets are abundant in nature, but few theories exist to understand their properties and behavior when geometric frustration is present. Here we study the S=1 kagome compound Na2Ti3Cl8 using a combination of density functional theory, exact diagonalization, and density matrix renormalization group approaches to achieve a first principles supported explanation of its exotic magnetic phases. 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 Na2Ti3Cl8 is a compound that cannot be understood from only electronic or only lattice Hamiltonians, very much like VO2.
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We thank Z. Kelly, T. McQueen, W. Ku, V. Dobrosavljevic, K. Yang, E. Manousakis, K. Plumb, C. Broholm, C. Hickey, and Y. Kim for discussions. We also thank T. McQueen for introducing us to this material. H. J. C. thanks A. Lauchli and (late) C. L. Henley for an earlier collaboration on the kagome system. H. J. C. was supported by start up funds from Florida State University and the National High Magnetic Field Laboratory. We also thank the Research Computing Cluster (RCC) at Florida State University and XSEDE allocation (DMR190020) for computing resources. The National High Magnetic Field Laboratory is supported by the National Science Foundation through NSF/DMR-1644779 and the state of Florida. The DMRG calculations were performed using the ITensor c ++ library (version 2.1.1) . The work at the University of Minnesota was supported by NSF DMREF Grant No. DMR-1629260. We acknowledge the Minnesota Supercomputing Institute for providing resources for the first principles calculations reported within this Letter.
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