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Pseudospin-lattice coupling in the spin-orbit Mott insulator Sr2IrO4

J. Porras, J. Bertinshaw, H. Liu, G. Khaliullin, N. H. Sung, J.-W. Kim, S. Francoual, P. Steffens, G. Deng, M. Moretti Sala, A. Efimenko, A. Said, D. Casa, X. Huang, T. Gog, J. Kim, B. Keimer, and B. J. Kim
Phys. Rev. B 99, 085125 – Published 15 February 2019
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  • INTRODUCTION
  • GROUND STATE AND LOW-FIELD MAGNETISM
  • MAGNETIC EXCITATIONS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    Spin-orbit entangled magnetic dipoles, often referred to as pseudospins, provide a new avenue to explore novel magnetism inconceivable in the weak spin-orbit coupling limit, but the nature of their low-energy interactions remains to be understood. We present a comprehensive study of the static magnetism and low-energy pseudospin dynamics in the archetypal spin-orbit Mott insulator Sr2IrO4. We find that in order to understand even basic magnetization measurements, a formerly overlooked in-plane anisotropy is fundamental. In addition to magnetometry, we use neutron diffraction, inelastic neutron scattering, and resonant elastic and inelastic x-ray scattering to identify and quantify the interactions that determine the global symmetry of the system and govern the linear responses of pseudospins to external magnetic fields and their low-energy dynamics. We find that a pseudospin-only Hamiltonian is insufficient for an accurate description of the magnetism in Sr2IrO4 and that pseudospin-lattice coupling is essential. This finding should be generally applicable to other pseudospin systems with sizable orbital moments sensitive to anisotropic crystalline environments.

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    • Received 4 September 2018
    • Revised 10 November 2018

    DOI:https://doi.org/10.1103/PhysRevB.99.085125

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Magnetic anisotropyMagnetismMagnetostrictionSpin dynamics
    1. Physical Systems
    2-dimensional systemsAntiferromagnetsMott insulatorsStrongly correlated systems
    1. Techniques
    DC susceptibility measurementsInelastic neutron scatteringNeutron diffractionResonant elastic x-ray scattering
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    J. Porras1, J. Bertinshaw1, H. Liu1, G. Khaliullin1, N. H. Sung1, J.-W. Kim2, S. Francoual3, P. Steffens4, G. Deng5, M. Moretti Sala6,7, A. Efimenko6, A. Said2, D. Casa2, X. Huang2, T. Gog2, J. Kim2, B. Keimer1, and B. J. Kim1,8,9,*

    • 1Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
    • 2Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
    • 3Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany
    • 4Institut Laue-Langevin 6, rue Jules Horowitz, Boîte Postale 156, 38042 Grenoble Cedex 9, France
    • 5Australian Nuclear Science and Technology Organization, Lucas Height, New South Wales 2233, Australia
    • 6European Synchrotron Radiation Facility, Boîte Postale 220, 38043 Grenoble Cedex, France
    • 7Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
    • 8Department of Physics, Pohang University of Science and Technology, Pohang 790-784, South Korea
    • 9Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, 77 Cheongam-Ro, Pohang 790-784, South Korea

    • *bjkim6@postech.ac.kr

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    Issue

    Vol. 99, Iss. 8 — 15 February 2019

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    Images

    • Figure 1
      Figure 1

      (a) The crystal structure of Sr2IrO4 is tetragonal (space group I41/a), with a=b=5.49Å and c=25.80Å at room temperature. The tetragonal a and b axes are rotated by 45∘ from the Ir-O-Ir bond directions. Ir atoms lie in the center of oxygen octahedra. IrO2 layers are separated by SrO layers. (b) Interlayer pseudospin couplings between the nearest layers and the next-nearest layers via J1c and J2c, respectively. (c) Top view on the IrO2 planes, with arrows indicating canted pseudospins (black) and net ferromagnetic moments (blue), following the possible magnetic domain configurations in the 41 crystal symmetry.

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    • Figure 2
      Figure 2

      Top view of possible stacking of pseudospins (black arrows) and the corresponding net ferromagnetic moment (blue arrows) in each layer, where the labeling up (u), down (d), left (l), and right (r) refers to their orientation in the ab plane. The energy difference between each of these configurations and the ground state of Eq. (1) and its allowed reflections are indicated at the bottom. The energy is written in terms of the effective couplings between the net moments j1c=4S2J1csin2ϕ, j2c=−S2J2c(cos2ϕ−sin2ϕ), and δc=4S2Δccos2ϕ, where ϕ is the canting angle. Here uddu or uudd is stabilized when j2c>0 and j1c<2j2c. With δc>0 uudd or lrrl becomes more favorable than uddu (or llrr, not shown).

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    • Figure 3
      Figure 3

      Normalized RMXS intensity of magnetic reflections (0 1 24), (0 1 25), and (0 1 26) as a function of magnetic field applied along (a) [010] and (c) [110], compared to simulated domain populations shown in (b) and (d), respectively. In (d), the applied field was slightly tilted away from [110] to mimic the misalignment of the field in experimental conditions. The data were taken at T=60 K, and the intensity was corrected for structure and polarization factors. At around 0.2 T the stacking pattern changes to uuuu (see Fig. 2).

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    • Figure 4
      Figure 4

      (a) Magnetization as a function of temperature along [100] (black) and [110] (red), taken at H=0.3 T. (b) Magnetization as a function of magnetic field for [100] (black) and [110] (red), taken at T=5 K. Inset: detailed measurements for different field angles from [100] to [110] every 11.25∘, focusing on the region where the biggest effect due to anisotropy is seen.

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    • Figure 5
      Figure 5

      An illustration of possible mechanisms for anisotropy. (a) Biaxial in-plane anisotropy K4, shown as purple ellipses, (b) anisotropy in the out-of-plane nearest-neighbor coupling (gray ellipses) connecting pseudospins in two neighboring layers (red and black), and (c) anisotropy Γ1 (blue ellipses) due to coupling of the pseudospins to the orthorhombically deformed lattice.

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    • Figure 6
      Figure 6

      Model calculation of the magnetization as a function of magnetic field applied along [100] (black) and [110] (red) for (a) biaxial anisotropy K4, (b) anisotropy in the interlayer coupling Δc, (d) anisotropy due to spin-lattice coupling Γ1, and (c) uniaxial anisotropy along the hard [100] (black) and easy [010] (blue) axes. The parameters used are (a–d) J1c=16.4μeV and J2c=−6.2μeV, (a), (b), and (d) Δc=0.02J1c, (a) K4=2.7μeV, (c) K2=2.7μeV, and (d) Γ1=2.7μeV and Γ2=0. The moment orientations for different field configurations are shown as colored arrows. The insets in (a), (c), and (d) show schematically the in-plane anisotropy energy. Note that in (d) the anisotropy rotates as the moment does.

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    • Figure 7
      Figure 7

      (a) Schematic of the scattering geometry of the RMXS experiment: (π−σ′)[(π−π′)] is sensitive to domains with net moment along [110] ([11¯0]). Calculated intensity of (4 5¯ 26) and (4 5¯ 27) magnetic reflections for the two polarizations as a function of field for the moment configuration attained with (b) biaxial anisotropy and (c) anisotropy due to spin-lattice coupling compared to the (d) measured integrated intensity taken at T=5 K. The insets in (b) and (c) show the characteristic moment configuration in the intermediate-field region, which can be separated into two components.

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    • Figure 8
      Figure 8

      Temperature evolution of the anisotropy in the magnetization as a function of magnetic field applied along [100] (black) and [110] (red), taken at T=5, 50, 100, 150, 220, and 230 K.

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    • Figure 9
      Figure 9

      Calculated dynamical spin structure factor as a function of momentum Q and energy ω for spin components along the crystallographic directions a (top), b (middle), and c (bottom). A Gaussian broadening δE=10 meV is used for clarity. The magnetic structure is chosen with the main component of the moments aligned along [100]. The in-plane momenta indicated on the top axis refer to the undistorted square-lattice unit cell, which is doubled for the magnetic unit cell indicated in the bottom axis in reciprocal-lattice units. The parameters used for the calculation are J=57 meV, J2=−16.5 meV, J3=12.4 meV, determined from RIXS measurements [15, 16], and ϕ=13∘, determined from neutron diffraction [26], which gives D=28 meV. Taking Jz=2.9 meV results in an out-of-plane gap Δout=40 meV consistent with our measurements shown in [36] (but larger than previously reported [16]).

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    • Figure 10
      Figure 10

      (a) Calculated dynamical spin structure factor Sperp perpendicular to Q⃗ close to the magnetic zone center as a function of L in reciprocal-lattice units (r.l.u.) and energy, taking into account both magnetic twin domains present in the sample. A δE=0.05 meV Gaussian broadening is used for clarity. (b) Real-space representation for Q=(100) of the four different magnon modes (A–D), where blue arrows represent the rotated net moments for each layer. The same parameters as in Fig. 9 were used.

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    • Figure 11
      Figure 11

      Inelastic neutron scattering intensity as a function of H in r.l.u. close to the magnetic zone center (a) (100) and (b) (1 0 2), measured for energy transfer E from 2 to 6 meV. The intensity scale is approximately counts per 10 min. Lines are results of constrained Gaussian fits with amplitudes and a common width as fitting parameters. A common background has been subtracted from the data, and a vertical offset is used for clarity.

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    • Figure 12
      Figure 12

      High-resolution RIXS intensity as a function of energy for incoherent scattering of Scotch tape used as a reference (black) and the in-plane magnon mode in Sr2IrO4 (red) measured at Q=(3228.2) close to the magnetic zone center.

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