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Possible stripe phases in the multiple magnetization plateaus in TbB4 from single-crystal neutron diffraction under pulsed high magnetic fields

N. Qureshi, F. Bourdarot, E. Ressouche, W. Knafo, F. Iga, S. Michimura, L.-P. Regnault, and F. Duc
Phys. Rev. B 106, 094427 – Published 22 September 2022
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  • INTRODUCTION
  • EXPERIMENT
  • RESULTS
  • DISCUSSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We present a single-crystal neutron diffraction study on the Shastry-Sutherland lattice system TbB4 at zero magnetic field and under pulsed high magnetic fields up to 35 T applied along the crystallographic c axis. While our results confirm the magnetic structures at zero field as well as those at the half- and full-magnetization plateaus, they offer insight into the 2/9- and 1/3-magnetization plateaus observed in this system. A stripe model of polarized 4-spin plaquettes whose stripe density proportionally increases with the macroscopic magnetization is in full agreement with the neutron diffraction data. Equally well-suited alternative models exist which explain the observed Bragg peaks being inherently limited in a pulsed high magnetic field experiment. We discuss the different intensity distributions in Q space which can be used to distinguish these models in future experiments.

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    • Received 8 July 2022
    • Revised 26 August 2022
    • Accepted 13 September 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.094427

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    High magnetic fieldsMagnetic orderMagnetic phase transitions
    1. Techniques
    Neutron diffraction
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    N. Qureshi1,*, F. Bourdarot2, E. Ressouche2, W. Knafo3, F. Iga4, S. Michimura5,6, L.-P. Regnault1, and F. Duc3,†

    • 1Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, 38042 Grenoble Cedex 9, France
    • 2Service de Modélisation et d'Exploration des Matériaux, Université Grenoble Alpes et Commissariat à l'Energie Atomique, INAC, 38054 Grenoble, France
    • 3CNRS, Laboratoire National des Champs Magnétiques Intenses, Université Grenoble Alpes, Université Toulouse 3, INSA Toulouse, EMFL, 31400 Toulouse, France
    • 4Institute of Quantum Beam Science, Ibaraki University, Mito 310-8512, Japan
    • 5Research and Development Bureau, Saitama University, Saitama 338-8570, Japan
    • 6Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan

    • *Corresponding author: qureshi@ill.fr
    • †Corresponding author: fabienne.duc@lncmi.cnrs.fr

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    Issue

    Vol. 106, Iss. 9 — 1 September 2022

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    Images

    • Figure 1
      Figure 1

      View along the c axis of the crystal structure of TbB4 which maps onto the Shastry-Sutherland lattice consisting of connected triangles and squares (emphasized by blue bonds between the Tb ions). The cell edges are shown as black lines (a range from −0.2 to 2.2 expressed in multiples of lattice parameters is depicted along the a and b directions).

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    • Figure 2
      Figure 2

      (a) Magnetization vs magnetic field at T=4.2 K for an applied magnetic field along the c axis. The arrows and fractions corresponding to the magnetization ratio M/MS indicate the transitions into the corresponding fractionalized magnetization plateaus. (b) Temperature vs magnetic field phase diagram deduced from these magnetization measurements [(a) and (b) are both adapted from Ref. 15].

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    • Figure 3
      Figure 3

      Magnetic structures of TbB4. (a) At 35 K the magnetic moments are aligned along the diagonal of the a−b plane, while (b) at 11 K they tilt towards the a axis by about 27∘.

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    • Figure 4
      Figure 4

      Peak intensities of the (a) (100), (b) (200), and (c) (110) reflections as a function of increasing (open symbols) and decreasing (solid symbols) magnetic field applied along the c axis. The number of accumulated pulses are mentioned in each graph. The orange circles denote the calculated peak intensities within the distinct phases which were investigated in detail (see main text) and the broad orange line is a guide to the eye joining the calculated points.

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    • Figure 5
      Figure 5

      Magnetic field dependence of neutron diffracted intensities at: (a) Q=(100) and (b) Q=(200) in fields up to 35 T for different temperatures between 2 and 50 K. The magnetic field was applied along the c axis. Open and solid symbols correspond to rising and falling fields, respectively. Data below 30 K are shifted on the vertical axis for clarity.

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    • Figure 6
      Figure 6

      Magnetic structure models for the different phases in TbB4, where a blue (orange) square represents a 4-spin plaquette with magnetic moments within (perpendicular to) the a−b plane. Black lines denote the magnetic unit cells. (a) Zero-field magnetic structure with all magnetic moments lying within the a−b plane. (b) 2/9-magnetization plateau phase with a 9×9 supercell, in which polarized spin-plaquette stripes are alternately separated by three or four nonpolarized stripes (note that this separation cannot be deduced from the data at hand and that this illustration would correspond to repelling polarized stripes). (c) 1/3-magnetization phase with a 3×3 supercell featuring polarized plaquettes along the diagonal of each magnetic unit cell. (d) 1/2-magnetization phase with a 2×2 supercell. (e) Fully polarized state with magnetic moments along the c axis. Note that in (b)–(d) the magnetic moments represented by blue (orange) squares do not lie fully within (perpendicular to) the a−b plane and that they produce superstructure reflections at Q=(1/91/90), Q=(1/31/30), and Q=(1/21/20), respectively, expressed with the conventional 1×1 unit cell. (f) Detailed view on two 4-spin plaquettes used as building blocks in the models (a)–(e). The upper (blue) one consists of magnetic moments predominantly aligned in the a−b plane with a nonzero ferromagnetic c component for the intermediate structures, while the lower (orange) one is almost fully polarized in (b)–(d) and fully polarized in (e).

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    • Figure 7
      Figure 7

      Alternative models which explain the observed peak intensities of the plateau phases equally well as the models shown in Figs. 6–6. (a) and (b) are 9×1×1 and 1×1×9 supercells, respectively, and yield exactly the same structure factors for the three reflections which were followed as a function of magnetic field (Fig. 4). (c) and (d) are 3×1×1 and 1×1×3 supercells, respectively, and constitute alternative models for the 1/3-magnetization plateau phase. (e) and (f) are possible models for the 1/2-magnetization plateau and consist of 1×2×1 and 1×1×2 supercells, respectively. Note that the in-plane modulation can exist along the b axis as well due to the presence of 90∘ twins.

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