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Interplay of dipoles and spins in κ−(BEDT−TTF)2X, where X=Hg(SCN)2Cl, Hg(SCN)2Br, Cu[N(CN)2]Cl, Cu[N(CN)2]Br, and Ag2(CN)3

A. C. Jacko, E. P. Kenny, and B. J. Powell
Phys. Rev. B 101, 125110 – Published 13 March 2020
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  • INTRODUCTION
  • DENSITY-FUNCTIONAL CALCULATIONS
  • COUPLED SPIN AND DIPOLE ORDER
  • SPIN MODEL IN THE DIPOLE SOLID PHASE
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We combine first-principles density functional calculations with empirical relationships for the Coulomb interactions in the monomer model of κ−(BEDT−TTF)2X. This enables us to calculate the parameters for the model of coupled dipolar and spin degrees of freedom proposed by Hotta [Phys. Rev. B 82, 241104 (2010)], and Naka and Ishihara [J. Phys. Soc. Jpn. 79, 063707 (2010)]. In all materials studied, retaining only the largest interactions leads to a transverse-field Ising model of the dipoles. This quantifies, justifies, and confirms recent claims that the dipoles are of crucial importance for understanding these materials. We show that the competition between two effects are responsible for a range of behaviors found in the dipoles in different κ−(BEDT−TTF)2X salts. (i) The intradimer hopping, tb1, which gives rise to the transverse field in the Ising model for the dipoles (HT=2tb1), is between a third and a tenth smaller in the mercuric materials than for the mercury-free salts. (ii) The Ising model of dipoles is in the quasi-one-dimensional limit for the mercuric salts, but quasi-two-dimensional (between the square and isotropic triangular limits) for the mercury-free materials. Thus, the dimensionless critical fields will be quite different in the two sets of materials. Effect (ii) is much larger than effect (i). Simple explanations of both effects based on the band structures of the different salts are given. We show that dipolar order and even short-range dipolar correlations have a profound impact on the nature of the interdimer magnetic (superexchange) interactions. For example, dipole crystallization drives the materials toward quasi-one-dimensional magnetic interactions, which could be important for understanding the spin liquids found in some of these materials.

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    • Received 24 October 2019
    • Revised 10 February 2020
    • Accepted 11 February 2020

    DOI:https://doi.org/10.1103/PhysRevB.101.125110

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Exchange interactionExotic phases of matterFirst-principles calculationsQuantum spin liquid
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    A. C. Jacko, E. P. Kenny, and B. J. Powell

    • School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia

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    Vol. 101, Iss. 12 — 15 March 2020

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    Images

    • Figure 1
      Figure 1

      Structure of models of κ−(BEDT−TTF)2X. (a) A single layer of κ−(BEDT−TTF)2X (hydrogen atoms and counter-ions are not shown). The various intermolecular hopping integrals, i.e., tμνij are labeled according to the standard monomer convention and, for simplicity, only the subscripts μνij∈{b1,b2,p,q} are shown. The two sublattices of ET dimers are highlighted in peach and blue. (b) The dimer model. Here the subscripts 1, 2, or 3 will be used label various interactions, e.g., hopping t, exchange J, dipole-dipole coupling K, or Dzyaloshinskii-Moriya coupling D. (c) This model is topologically equivalent to a square lattice with different couplings across the two diagonals or, if the 3 interactions are negligible, an anisotropic triangular lattice.

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    • Figure 2
      Figure 2

      The calculated band structure of κ−HgCl. The direct density-functional calculations (solid black line) are exactly reproduced by the Wannier model Hamiltonian (dot-dashed red line). The monomer model [Ĥ, blue dashed line, Fig. 1, Eq. (3)], which retains only the four largest hopping integrals, captures the main features of the band structure.

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    • Figure 3
      Figure 3

      Sketches of prototypical second-order processes leading to the Ising coupling between dipoles. Recall that second-order processes always lower the energy of the ground state. Processes like a→b→c are only available if dipoles on the two dimers are antiparallel. Thus, this leads to an antiferrodipolar coupling (XTT<0). Processes like d→e→f are only allowed if dipoles on the two dimers are the same sign and therefore favor ferrodipolar coupling (YTT>0). However, processes like g→h→i are only possible if dipoles on the two dimers are antialigned and therefore favor antiferrodipolar coupling (YTT<0). The competition between the processes d→e→f and g→h→i is vital for understanding the different dimensionalities of the TFIM in the mercuric and mercury-free salts as it means that YTT∝tp2−tq2.

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    • Figure 4
      Figure 4

      Variation of the effective interdimer superexchange interaction with the charge disproportionation, 〈n̂μ2−n̂μ1〉, for (a) antiferrodipolar ordering and (b) ferrodipolar ordering. For ease of comparison, both panels use the same axis scales.

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    • Figure 5
      Figure 5

      Dipole ordering patterns for ferrodipolar interactions. Shaded rectangles indicate the dimers, as in Fig. 1. The head of the arrows indicates the monomer that contains fewer electrons than the monomer at the tail of the arrow. To understand the microscopic dipolar order shown here it is helpful to compare with Fig. 1. Only the supperexchange interactions that are strongest when the dipoles order are marked in this figure. Strong charge disproportionation combined with dipole order leads to a quasi-one-dimensional spin system.

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    • Figure 6
      Figure 6

      Variation of the effective interdimer Dzyaloshinskii-Moriya antisymmetric exchange with the charge disproportionation, n̂μ2−n̂μ1, for an antiferrodipolar configuration of dimers. (a) Magnitude for all materials and Cartesian components for (b) κ−HgCl, (c) κ−HgBr, (d) κ−CuCl, (e) κ−CuBr, and (f) κ−AgCN.

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    • Figure 7
      Figure 7

      Variation of the effective interdimer Dzyaloshinskii-Moriya antisymmetric exchange with the charge disproportionation, n̂μ2−n̂μ1, for a ferrodipolar configuration of dimers. (a) Magnitude for all materials and Cartesian components for (b) κ−HgCl, (c) κ−HgBr, (d) κ−CuCl, (e) κ−CuBr, and (f) κ−AgCN.

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