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Order in a spatially anisotropic triangular antiferromagnet

Sedigh Ghamari, Catherine Kallin, Sung-Sik Lee, and Erik S. Sørensen
Phys. Rev. B 84, 174415 – Published 14 November 2011
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  • INTRODUCTION
  • MODEL AND RG EQUATIONS
  • GENERAL RG FLOWS
  • INITIAL CONDITIONS AND RG RESULTS
  • NUMERICAL RESULTS
  • DZYALOSHINSKII-MORIYA INTERACTION
  • CONCLUSIONS AND DISCUSSION
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    The phase diagram of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice of weakly coupled chains, a model relevant to Cs2CuCl4, is investigated using a renormalization group analysis, which includes marginal couplings important for connecting to numerical studies of this model. In particular, the relative stability of incommensurate spiral spin-density order and collinear antiferromagnetic order is studied. While incommensurate spiral order is found to exist over most of the phase diagram in the presence of a Dzyaloshinskii-Moriya (DM) interaction, at small interchain and extremely weak DM couplings, collinear antiferromagnetic order can survive. Our results imply that Cs2CuCl4 is well within the part of the phase diagram where spiral order is stable. The implications of the renormalization group analysis for numerical studies, many of which have found spin-liquidlike behavior, are discussed.

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    • Received 18 August 2011

    DOI:https://doi.org/10.1103/PhysRevB.84.174415

    ©2011 American Physical Society

    Authors & Affiliations

    Sedigh Ghamari1, Catherine Kallin1, Sung-Sik Lee1,2, and Erik S. Sørensen1

    • 1Department of Physics and Astronomy, McMaster University, 1280 Main St. W., Hamilton, Canada, ON L8S 4M1
    • 2Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Canada, ON N2L 2Y5

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    Issue

    Vol. 84, Iss. 17 — 1 November 2011

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    • Figure 1
      Figure 1
      (a) Triangular lattice with anisotropic exchanges J and J′. Staggered magnetization operators, N, at sites with the same color are accompanied with the same sign consistent with the depicted choice of y axis. (b) Phase diagram projected onto the plane of initial values of the relevant couplings, gN−γtw. Dimer or other ordered states may be stable in the shaded region.Reuse & Permissions
    • Figure 2
      Figure 2
      The response to a small staggered magnetic field, h, applied to one chain is studied using exact diagonalization for three chains of lengths from L=6 to L=12. The response of a central spin on the second-neighbor chain, 〈Siz〉/hL, is shown along with polynomial fits to the data. The sign of the response is found to be such that 〈Siz〉 always aligns ferromagnetically with the other chain.Reuse & Permissions
    • Figure 3
      Figure 3
      Flows of gN(l) and γtw(l) for several initial values with ferromagnetic gN(0)=αγtw2(0), gɛ=γɛ=0, and J′=0.05. gN and γtw are in scaled units (divided by π2J), and α is varied from −0.26 (CAF flow closest to vertical axis) to −0.30 (spiral flow closest to vertical axis). The inset zooms in on the shaded rectangle. Flows emanating from initial values very close to gNcrit have flow lines substantially away from the γtw=0 axes and grow considerably slower than those close to the vertical axes. Note the extreme sensitivity to initial values close to the critical value gNcrit as shown in the inset.Reuse & Permissions
    • Figure 4
      Figure 4
      The staggered Neel susceptibility, χs, for three chains as a function of chain length, L, at different J′ values, calculated by ED and DMRG. The sign of χs is such that second nn chains are ferromagnetically coupled for all L and J′ studied.Reuse & Permissions
    • Figure 5
      Figure 5
      The scaled susceptibility, χ̃s=χs/[L(1−γbs(0)l)1/2], which is proportional to the relevant coupling, gN, for small J′, is shown for different values of J′/J. Points represent data from ED (for L≤12) and DMRG (L>12) and lines are fits to the RG equations where the initial conditions are used as fitting parameters.Reuse & Permissions
    • Figure 6
      Figure 6
      Suggested phase diagram where the critical interchain Dzyaloshinskii-Moriya coupling, D, vanishes as J′4/J3 at small interchain coupling J′. The ordering wave vector of the spiral state varies continuously and is q=(π,0) for J′=0 and nonzero D. The region of stability of the CAF state is very small since DMax is estimated to be less than 10−4J.Reuse & Permissions
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