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Upper limit on spontaneous supercurrents in Sr2RuO4

J. R. Kirtley, C. Kallin, C. W. Hicks, E.-A. Kim, Y. Liu, K. A. Moler, Y. Maeno, and K. D. Nelson
Phys. Rev. B 76, 014526 – Published 26 July 2007
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  • INTRODUCTION
  • MAGNETIC IMAGING
  • MODELING
  • SURFACE SCREENING EFFECTS
  • DISCUSSION
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    It is widely believed that the perovskite Sr2RuO4 is an unconventional superconductor with broken time-reversal symmetry. It has been predicted that superconductors with broken time-reversal symmetry should have spontaneously generated supercurrents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr2RuO4 single crystals using scanning Hall bar and superconducting quantum interference device microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents at edges and domain walls as a function of domain size. For a single domain, this upper limit is below the predicted signal by 2 orders of magnitude. We speculate on the causes and implications of the lack of large spontaneous supercurrents in this very interesting superconducting system.

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    • Received 25 April 2007

    DOI:https://doi.org/10.1103/PhysRevB.76.014526

    ©2007 American Physical Society

    Authors & Affiliations

    J. R. Kirtley1,2,3, C. Kallin4, C. W. Hicks1, E.-A. Kim5,6, Y. Liu7, K. A. Moler1,5, Y. Maeno8, and K. D. Nelson7

    • 1Department of Applied Physics, Stanford University, Palo Alto, California 94305, USA
    • 2IBM Watson Research Center, Yorktown Heights, New York 10598, USA
    • 3Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
    • 4Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
    • 5Department of Physics, Stanford University, Palo Alto, California 94305, USA
    • 6Stanford Institute of Theoretical Physics, Stanford University, Palo Alto, California 94305, USA
    • 7Department of Physics, Pennsylvania State University, University Park, Pennsylvania, 16802, USA
    • 8Department of Physics, Kyoto University, Kyoto 606-8502, Japan

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    Vol. 76, Iss. 1 — 1 July 2007

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    Images

    • Figure 1
      Figure 1
      SQUID microscope image of the ab face of a Sr2RuO4 single crystal, cooled in a field Bz<10nT and imaged at T=0.27K with an 8μm square pickup loop. (a) Pseudocolor image with full-scale variation of 0.2 Φ0 (Φ0=h∕2e) in magnetic flux through the SQUID pickup loop. The dashed line in (a) shows the outlines of the crystal. (b) Same image as (a) but with the pseudocolor scale expanded to 0.02 Φ0. The dashed line in (b) shows the line traced by the cross section in (c). The dashed rectangle in (b) shows the area of the image expanded in (d). (e) is a histogram of pixel values for the data displayed in (d).Reuse & Permissions
    • Figure 2
      Figure 2
      Comparison of SQUID microscope images of an ab face of a Sr2RuO4 crystal after three different cooldowns in slightly different magnetic fields.Reuse & Permissions
    • Figure 3
      Figure 3
      SQUID microscope image of the ac face of a Sr2RuO4 single crystal cooled in nominally zero field and imaged at T=0.27K with an 8μm square pickup loop. (a) Pseudocolor image ΔΦs=0.8Φ0. The dashed line in (a) shows the positions of the outer edges of the crystal. (b) Same image as (a) but with ΔΦs=0.08Φ0. A few interlayer vortices with both positive and negative signs are visible near the lower-left edge of the crystal. The dashed line in (b) is along the a axis and shows the data traced by the cross section in (c). The arrows in (c) indicate the edges of the crystal. The dashed square in (b) shows the area of the image expanded in (d). The diagonal stripes visible in (d) are due to 60Hz noise. (e) is a histogram of pixel values for the data displayed in (d).Reuse & Permissions
    • Figure 4
      Figure 4
      (a) Scanning Hall bar image of the ab face of Sr2RuO4 single crystal, cooled in ∼2.5μT and imaged at a temperature below 100mK using a Hall bar with a sensor area 0.5μm on a side. In this image, the mean of each scan line was subtracted from the raw data to remove slow drift in the sensor Hall voltage. (b) Same area as (a) but with an expanded pseudocolor scale. The dashed line in (b) shows the line traced by the data cross section in (c). The dashed square in (b) shows the area for which a histogram of pixel inductance values is displayed in (d).Reuse & Permissions
    • Figure 5
      Figure 5
      Cross section through the image of the ab face of Sr2CuO4 displayed in Fig. 1 (solid line). The short-dashed line is the prediction for a superconducting disk in a uniform residual field of 3nT. The long-dashed line (with a peak at Φs∕Φ0=1.1) is the prediction for a single domain px+ipy superconductor of the extended Matsumoto-Sigrist model as described in the text, assuming a square pickup loop 8μm on a side, at a height of 3μm above the sample. Here, the superconductor is positioned to the left of 0μm, with epoxy to the right.Reuse & Permissions
    • Figure 6
      Figure 6
      Predicted magnetic fluxes through an 8μm square pickup loop, 3μm above the sample surface, for a 64μm square px±py superconductor with various domain sizes, using the predictions for the edge and domain wall currents of Matsumoto and Sigrist as described in the text. The dashed lines in the figure show the positions of the cross sections displayed in Fig. 7.Reuse & Permissions
    • Figure 7
      Figure 7
      Cross sections through the modeling images of Fig. 6 for various domain sizes.Reuse & Permissions
    • Figure 8
      Figure 8
      (Color online) (a) Plots of the predicted peak flux signals for an 8μm square SQUID pickup loop, 3μm above the sample surface, for a 64μm square px±ipy superconductor with various domain sizes, using the predictions of Matsumoto and Sigrist (Ref. 26) for the spontaneously generated edge and domain supercurrents. The dashed lines represent the estimated SQUID noise in the measurements within the sample (lower line) and at the sample edges (upper line). (b) Plots of the predicted peak fields for a square Hall bar 0.5μm on a side, 1.2μm above the sample surface, with the corresponding Hall bar noise floor. (c) Upper limits on the size of the scaling fields Bs, normalized by Bc=Φ0∕22πξ0λL, as a function of domain size, given by our failure to observe spontaneously generated supercurrents at edges and domain walls in the SQUID measurements. In this figure, the extended Matsumoto-Sigrist predictions are represented by Bs∕Bc=1. (d) Upper limits on Bs∕Bc as a function of domain size set by the Hall bar measurements.Reuse & Permissions
    • Figure 9
      Figure 9
      Comparison of the predicted magnetic field sensed by a 0.5μm square Hall bar, 1.2μm above a single domain in a px±ipy superconductor, using the spontaneous domain currents predicted by Matsumoto and Sigrist (Ref. 26), with (dashed line) and without (solid line) surface screening effects as described in the text. The solid line corresponds to the extended Matsumoto-Sigrist model.Reuse & Permissions
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