Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin S

Patrick Müller, Andre Lohmann, Johannes Richter, Oleg Menchyshyn, and Oleg Derzhko
Phys. Rev. B 96, 174419 – Published 15 November 2017
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • MODEL
  • METHODS
  • FINITE-TEMPERATURE PROPERTIES
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-S Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number S on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number z=6. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    5 More
    • Received 5 July 2017
    • Revised 22 October 2017

    DOI:https://doi.org/10.1103/PhysRevB.96.174419

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    FerromagnetismSpin waves
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Patrick Müller1, Andre Lohmann1, Johannes Richter1, Oleg Menchyshyn2, and Oleg Derzhko2,1,3,4

    • 1Institut für theoretische Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany
    • 2Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 L'viv, Ukraine
    • 3Department for Theoretical Physics, Ivan Franko National University of L'viv, Drahomanov Street 12, 79005 L'viv, Ukraine
    • 4Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 96, Iss. 17 — 1 November 2017

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      The pyrochlore lattice can be visualized as a structure which consists of alternating kagome and triangular planar layers. The kagome (triangular) planes are colored in green (blue). The four-site unit cell is marked with the red bonds.

      Reuse & Permissions
    • Figure 2
      Figure 2

      Dispersion of the excitation energies ωqγ [Eq. (9), J=−1] at zero temperature T=0 (upper panel) and in the infinite-temperature limit T→∞ (lower panel). Note that ωqγ/S is independent of S at T=0, whereas ωqγ/S(S+1) is independent of S at T→∞. The points Γ, X, W, and K in the first Brillouin zone of a face-centered-cubic Bravais lattice are given by Γ=(0,0,0),X=(0,2π,0),W=(π,2π,0),K=(3π/2,3π/2,0), see, e.g., Ref. [50].

      Reuse & Permissions
    • Figure 3
      Figure 3

      Main panel: normalized spin stiffness ρ/(S|J|) (dashed) and normalized excitation velocity v/(S|J|) (solid) as a function of the normalized temperature T/Tc. We report results for different spin values S=1/2,1,3/2,3 for the pyrochlore-lattice case (thin lines) and for S=1/2 for the simple-cubic case (thick lines). Inset: spin stiffness ρ/ρ(0) versus T/|J| for the S=1/2 pyrochlore (dashed thin red line) and simple-cubic (dashed thick black line) lattices.

      Reuse & Permissions
    • Figure 4
      Figure 4

      RGM data for the normalized magnetization M/S of the ferromagnet on the simple-cubic lattice (S=1/2) (thick solid black line) and the pyrochlore lattice (S=1/2,1,3/2,3) (thin solid lines) as a function of the normalized temperature T/Tc. Dashed curves correspond to the inverse uniform susceptibility 1/χ0 above Tc. Note that the thin dashed curves for S>1/2 almost coincide.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Inverse uniform susceptibility 1/χ0 of the ferromagnet on the pyrochlore lattice obtained by the RGM (thin solid lines) and by the HTE approach (Padé [5,6]—thin dashed lines) as a function of the normalized temperature T/(S(S+1)) for several spin quantum numbers S. We also show the RGM results for the simple-cubic-lattice case with S=1/2 (thick black line). Note that the energy scale is set by J=−1.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Normalized Curie temperatures Tc/(S(S+1)) of the ferromagnet on the simple-cubic lattice and the pyrochlore lattice within the RGM approach and the HTE approach (up to the eleventh order) as a function of the inverse spin quantum number 1/S. The HTE data labeled by “pyro,HTE,[5,5]” are taken from Ref. [14].

      Reuse & Permissions
    • Figure 7
      Figure 7

      Main panel: normalized correlation functions 〈Ŝ0·ŜR〉/S2 (nearest neighbors—solid; next-nearest neighbors—dashed) as a function of the normalized temperature T/Tc for the spin-S pyrochlore ferromagnet for several spin quantum numbers S (thin lines). We also show the results for the S=1/2 simple-cubic ferromagnet (thick lines). Inset: 〈Ŝ0·ŜR〉/S2 versus T/|J| for the S=1/2 case.

      Reuse & Permissions
    • Figure 8
      Figure 8

      Specific heat of the ferromagnet on the pyrochlore lattice within the RGM (thin solid lines) and the HTE approach (Padé [5,6]—thin dashed lines) as a function of the normalized temperature T/(S(S+1)) for several values of the spin quantum numbers S. We also show the RGM results for the S=1/2 simple-cubic ferromagnet (thick solid line).

      Reuse & Permissions
    • Figure 9
      Figure 9

      Two top rows: magnetic structure factor Sq/(S(S+1)) of the S=1/2 ferromagnet on the pyrochlore lattice within the RGM approach at T=1.3Tc (upper row) and T=2Tc (middle row) in the Bragg plane qz=0 (left panels) and in the Bragg plane qx=qy (right panels). Bottom row: magnetic structure factor Sq/(S(S+1)) of the S=1/2 ferromagnet on the pyrochlore lattice within the HTE approach (ninth order) at T=2Tc in the Bragg plane qz=0 (left panel) and in the Bragg plane qx=qy (right panel).

      Reuse & Permissions
    • Figure 10
      Figure 10

      Magnetic structure factor Sq/(S(S+1)) of the pyrochlore ferromagnet along the line qx=qy=qz for two temperatures: 1.3Tc (red) and 2Tc (blue). RGM results are shown by solid lines, whereas HTE results are shown by dashed lines. Thin lines correspond to the S=1/2 case, thick lines correspond to the S=3 case.

      Reuse & Permissions
    • Figure 11
      Figure 11

      Dynamic structure factor Sqzz(ω) of the S=1/2 pyrochlore ferromagnet along the line qx=qy=qz for T=0.0425 (top) and T=0.425 (bottom). We set ε=0.1. The white lines correspond to the excitation energies ωγq (9).

      Reuse & Permissions
    • Figure 12
      Figure 12

      Dynamic structure factor Sqzz(ω) of the S=1/2 pyrochlore ferromagnet as a function of the reduced momentum t=2−Dq with q=(q,q,q) for T=0.0425. We set ε=0.1. The white lines correspond to the excitation energies ωγq (9).

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×