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Spin-1/2 XY chain magnetoelectric: Effect of zigzag geometry

Ostap Baran, Vadim Ohanyan, and Taras Verkholyak
Phys. Rev. B 98, 064415 – Published 20 August 2018
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  • INTRODUCTION
  • KNB MECHANISM FOR SPIN CHAINS: THE…
  • MODEL AND EXACT SOLUTION
  • GROUND-STATE PROPERTIES
  • THERMODYNAMICS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    A spin-1/2 XY chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized XY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.

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    • Received 23 May 2018
    • Revised 19 June 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.064415

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Dielectric propertiesElectric polarizationExchange interactionFermionsMagnetic orderMagnetic phase transitionsMagnetismMagnetoelectric effectPhase diagramsQuantum phase transitionsQuantum statistical mechanics
    Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Ostap Baran1, Vadim Ohanyan2,3, and Taras Verkholyak1

    • 1Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 L'viv, Ukraine
    • 2Department of Theoretical Physics, Yerevan State University, Alex Manoogian 1, 0025 Yerevan, Armenia
    • 3Joint Laboratory of Theoretical Physics ICTP Affiliated Centre in Armenia, 2 A. Alikhanian Brothers Street, 0036 Yerevan, Armenia

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    Vol. 98, Iss. 6 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      The zigzag chain with indicated system axes, electric field vector E, polarization P, bond polarization Pj,j+1, and unit vector ej,j+1 pointing from the jth site to the (j+1)th site. Here the z component of the bond polarization is equal zero because E=(Ex,Ey,0).

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    • Figure 2
      Figure 2

      Density plots for the magnetization (top panel) and polarizations px and py (middle and bottom panels) at T=0 for θ=π/8, h=1.25. Dashed lines indicate the boundaries between different ground-state phases.

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    • Figure 3
      Figure 3

      The ground-state phase diagram for θ=π/8 in different directions of the electric field φE=0,π/16,π/8,π/4,3π/8,π/2.

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    • Figure 4
      Figure 4

      The magnetization (top panel), the absolute value (middle panel), and the angle (bottom panel) of the electric polarization vs electric field for θ=π/8, φE=π/16, and different magnetic fields h=0,0.25,0.75,1,1.5,2.5.

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    • Figure 5
      Figure 5

      The magnetization (top panel), the absolute value (middle panel), and the angle (bottom panel) of the electric polarization vs electric field for θ=π/8, φE=3π/8, and different magnetic fields h=0,0.25,0.75,1,1.5,2.5.

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    • Figure 6
      Figure 6

      The magnetization (top panel) the absolute value (middle panel), and the angle (bottom panel) of the electric polarization vs magnetic field for θ=π/8, φE=π/16, and different electric fields E=0,1,2,3.

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    • Figure 7
      Figure 7

      The polarization angle φP as a function of the electric field angle φE for infinitesimally small (solid line) and infinite (dashed line) electric fields at θ=π/8,π/4.

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    • Figure 8
      Figure 8

      The electric susceptibilities χxx, χyy, and χxy at T=0 as a function of the electric field for θ=π/8, φE=π/4, and different values of h.

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    • Figure 9
      Figure 9

      The electric susceptibilities χxx, χyy, and χxy at T=0 as a function of the magnetic field for θ=π/8, φE=π/4, and different values of E.

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    • Figure 10
      Figure 10

      The magnetic susceptibility χzz at T=0 as a function of the electric field (top panel) and the magnetic field (bottom panel) for θ=π/8, φE=π/4.

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    • Figure 11
      Figure 11

      The magnetoelectric tensor at T=0 as a function of the electric field (top panel) and the magnetic field (bottom panel) for θ=π/8, φE=π/4.

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    • Figure 12
      Figure 12

      Specific heat as a function of temperature for θ=π/8, φE=π/16, E=2, h=0,J−,1,J+,1.5.

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    • Figure 13
      Figure 13

      Specific heat as a function of the magnetic field (top panel) for E=2 and of the electric field (bottom panel) for h=1.5 and θ=π/8, φE=π/16, T=0.01,0.05,0.1.

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    • Figure 14
      Figure 14

      Density plot of the entropy as a function of the magnetic field and temperature for the zigzag chain with θ=π/8, φE=π/16, and E=0 (top panel) and E=2 (bottom panel). The curves with constant entropy correspond to S/kB=0.01,0.02,0.03,0.04,0.05,0.1,0.15,0.2,0.25.

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    • Figure 15
      Figure 15

      Density plot of the entropy as a function of the electric field E and temperature for the zigzag chain with θ=π/8, φE=π/16, and h=0 (top panel) and h=1.5 (bottom panel). The curves with constant entropy correspond to S/kB=0.01,0.02,0.03,0.04,0.05,0.1,0.15,0.2,0.25.

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