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Normal State O17 NMR Studies of Sr2RuO4 under Uniaxial Stress

Yongkang Luo, A. Pustogow, P. Guzman, A. P. Dioguardi, S. M. Thomas, F. Ronning, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, A. P. Mackenzie, C. W. Hicks, E. D. Bauer, I. I. Mazin, and S. E. Brown
Phys. Rev. X 9, 021044 – Published 31 May 2019
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • Supplemental Material
    References

    Abstract

    The effects of uniaxial compressive stress on the normal state O17 nuclear-magnetic-resonance properties of the unconventional superconductor Sr2RuO4 are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal a-axis strain ϵaa≡ϵv that maximizes the superconducting transition temperature Tc. The spin susceptibility weakly increases on lowering the temperature below T≃10  K, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the γ band formed by the Ru dxy states hybridized with in-plane O pπ orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalization S by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.

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    • Received 23 September 2018
    • Revised 1 February 2019

    DOI:https://doi.org/10.1103/PhysRevX.9.021044

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Spin-triplet pairingvan Hove singularity
    1. Techniques
    Nuclear magnetic resonance
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Yongkang Luo1,2,*, A. Pustogow1,‡, P. Guzman1, A. P. Dioguardi3, S. M. Thomas3, F. Ronning3, N. Kikugawa4, D. A. Sokolov5, F. Jerzembeck5, A. P. Mackenzie5,6, C. W. Hicks5, E. D. Bauer3, I. I. Mazin7, and S. E. Brown1,†

    • 1Department of Physics & Astronomy, University of California, Los Angeles, Los Angeles, California 90095, USA
    • 2Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
    • 3Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
    • 4National Institute for Materials Science, Tsukuba 305-0003, Japan
    • 5Max Planck Institute for Chemical Physics of Solids, Dresden 01187, Germany
    • 6Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, United Kingdom
    • 7Code 6393, Naval Research Laboratory, Washington, D.C. 20375, USA

    • *mpzslyk@gmail.com
    • †brown@physics.ucla.edu
    • ‡Present address: IFW Dresden, Institute for Solid State Research, P.O. Box 270116, D-01171 Dresden, Germany.

    Popular Summary

    After 25 years of study, the unconventional superconductor Sr2RuO4 continues to challenge researchers. While evidence for “in-triplet” pairing—where electrons pair up with their spins pointing in the same direction—emerges in several key measurements, other experimental outcomes are not easily understood in that framework. Resolving this issue is important to condensed-matter physicists because Sr2RuO4 is a notable example of a strongly correlated, quasi-2D system that has few defects or impurities and because the underlying experimental techniques are used throughout the field of superconductivity.

    A consequence of the proposed spin-triplet pairing is the expectation that when the material is strained, two different superconducting transition temperatures appear. Here, we use nuclear magnetic resonance to infer the strain-dependent spin susceptibility (a measure of the number of possible states at each energy level, known as the “density of states”), and we identify two physical consequences: an increase in the density of states at the Fermi energy and an associated enhancement in the Stoner factor, which is a signature of intensified ferromagnetic fluctuations that couple paired electrons.

    Our study provides two possible explanations for the increase in the superconducting temperature in stressed Sr2RuO4: While the density-of-states effect is directly more beneficial in the case of spin-singlet pairing, the coincident enhanced Stoner factor could play a role in stabilizing a triplet state. Extending these investigations to the superconducting state will provide a more conclusive answer.

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    Vol. 9, Iss. 2 — April - June 2019

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    • Figure 1
      Figure 1

      (a) Configurations of planar O(1) and O(1′) in the RuO2 plane and apical O(2) in the SrO layer around Ru ion in a unit cell of Sr2RuO4. Compressive strain is applied along the a axis (ϵaa); magnetic fields are applied orthogonal, ∥b,∥c. Arrows signify the principal axes of Knight-shift tensors. (b) Orbitals forming the γ band at the X (left) and Y (right) points in the Brillouin zone. The blue (red) double arrows show positive (negative) signs of orbital overlaps. Note that at the Y point, only O(1)px orbitals participate in the band formation, while O(1′)py suffers from cancellation of the left and right overlaps. The weak O(1)−O(1′) overlaps also cancel out, as shown in the figure.

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    • Figure 2
      Figure 2

      (a) Bands along the Γ−X and Γ−Y directions. The partial weights of the O(1)px, O(1′)py, O(1)pz, and O(1′)pz orbitals are shown in green, blue, red, and purple, respectively. Other oxygen orbitals have far lesser weight near the Fermi energy. (b) Depictions of the 2D Fermi surfaces, with quasi-2D γ (dxy) and quasi-1D α, β (dzx,yz) bands.

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    • Figure 3
      Figure 3

      NMR spectra of the central transitions (12↔−12) of O(1), O(1′), and O(2) at various strains for magnetic field along the b (left) and c axes (right). The measurements are carried out at fixed temperature (T=4.3  K) and field (B=8.0970  T) and radio frequency f0=46.80  MHz. The curves are vertically offset for clarity. The dash vertical line corresponds to γ17=−5.7719  MHz/T (D217O) [30] with zero shift.

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    • Figure 4
      Figure 4

      Measured NMR shifts for B∥b (a) and for B∥c (b) at T=4.3  K. The solid (open) symbols represent increasing (decreasing) |ϵaa|. The error bars are determined by the half-width of the peaks. Similar results are reproduced from several samples; see Fig. S5(a) in the Supplemental Material [32].

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    • Figure 5
      Figure 5

      (a) Calculated DOS at the critical strain, at which the calculated van Hove singularity is located exactly at the Fermi level. Note the very small width (3 meV) and weight (0.0015 e− per spin channel) of the peak in the DOS. (b) Partial DOS projected onto different O orbitals. The orbitals that are not shown have negligible weight.

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    • Figure 6
      Figure 6

      Main panel: Temperature dependence of K1∥ and K1′⊥ evaluated at the critical strain ϵv, B=8.0970  T, and B∥b. Inset: Field dependence of K1∥ and K1′⊥ measured at ϵv and 4.3 K.

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    • Figure 7
      Figure 7

      (a) Calculated magnetic susceptibility in DFT. χs0DFT≡μB2N(EF) is the noninteracting susceptibility, χsDFT is obtained by dividing the calculated magnetization by the applied field, Ms/μBH. The average DFT Stoner factor S=χsDFT/χs0DFT and SRPA=1/[1−IN(EF)]. Here, SRPA is normalized to S obtained from the calculated DFT result at zero strain. Its variation with strain is calculated from Eq. (4) and the strain-dependent DFT density of states. (b) Calculated total Knight shifts for H∥b for the three sites, O(1), O(1′), and O(2), as a function of normalized strain. See the text for details.

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    • Figure 8
      Figure 8

      Calculated Fermi surfaces (nonrelativistic) with no orthorhombic strain (left) and the strain corresponding to the VHS (right). No additional scaling of the Stoner interaction is applied, as opposed to the Knight-shift calculation (Fig. 7 and main text). The surfaces are colored with the calculated exchange splitting in a small uniform external field H normalized to μBH=1.6  meV. Note the different color scales for the two panels.

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