Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate

Journal name:
Nature Physics
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A rare combination of strong spin–orbit coupling and electron–electron correlations makes the iridate Mott insulator Sr2IrO4 a promising host for novel electronic phases of matter1, 2. The resemblance of its crystallographic, magnetic and electronic structures1, 2, 3, 4, 5, 6 to La2CuO4, as well as the emergence on doping of a pseudogap region7, 8, 9 and a low-temperature d-wave gap10, 11, has particularly strengthened analogies to cuprate high-Tc superconductors12. However, unlike the cuprate phase diagram, which features a plethora of broken symmetry phases13 in a pseudogap region that includes charge density wave, stripe, nematic and possibly intra-unit-cell loop-current orders, no broken symmetry phases proximate to the parent antiferromagnetic Mott insulating phase in Sr2IrO4 have been observed so far, making the comparison of iridate to cuprate phenomenology incomplete. Using optical second-harmonic generation, we report evidence of a hidden non-dipolar magnetic order in Sr2IrO4 that breaks both the spatial inversion and rotational symmetries of the underlying tetragonal lattice. Four distinct domain types corresponding to discrete 90°-rotated orientations of a pseudovector order parameter are identified using nonlinear optical microscopy, which is expected from an electronic phase that possesses the symmetries of a magneto-electric loop-current order14, 15, 16, 17, 18. The onset temperature of this phase is monotonically suppressed with bulk hole doping, albeit much more weakly than the Néel temperature, revealing an extended region of the phase diagram with purely hidden order. Driving this hidden phase to its quantum critical point may be a path to realizing superconductivity in Sr2IrO4.

At a glance


  1. Symmetry of the hidden order in Sr2IrO4.
    Figure 1: Symmetry of the hidden order in Sr2IrO4.

    a, Crystal structure of a single perovskite layer in Sr2IrO4 (tetragonal point group 4/m). Inset shows the basic IrO6 unit of the magneto-electric loop-current order, with the arrows pointing in the direction of current flow. b, Schematic of the RA-SHG experiment. The electric field polarizations of the obliquely incident fundamental beam (in) and outgoing SHG beam (out) can be independently selected to lie either parallel (P) or perpendicular (S) to the light scattering plane (shaded). RA-SHG data are acquired by measuring the SHG intensity I(2ω) reflected from the (001) surface of Sr2IrO4 as a function of the angle ϕ between the scattering plane and crystal a–c-plane. c, RA-SHG data collected under Pin–Pout and Pin–Sout polarization geometries using λ = 800nm incident light at T = 295K. d, Analogous data to c collected at T = 170K. All data sets are plotted on the same intensity scale, normalized to a value of 1, which corresponds to ~20fW. The high-temperature data are fitted to time-reversal invariant bulk electric-quadrupole-induced SHG (orange lines). The low-temperature data can only be fitted to the coherent sum of time-reversal invariant bulk electric-quadrupole-induced and time-reversal broken bulk electric-dipole-induced SHG (purple lines), as described in the text.

  2. Spatial mapping of hidden order domains.
    Figure 2: Spatial mapping of hidden order domains.

    a,b, Wide-field reflection SHG microscopy images of the cleaved (001) plane of Sr2IrO4 measured under Pin–Sout polarization geometry at ϕ = 78° at T = 295K (a) and at T = 175K (b). A patchwork of light and dark regions present in the low-temperature image arises from domains of the hidden order. The dark curves at the sample edge and dark micrometre-sized spots near the sample centre that are visible in both the high- and low-temperature images are structural defects.

  3. Degenerate ground-state configurations of the hidden order.
    Figure 3: Degenerate ground-state configurations of the hidden order.

    Four different types of RA-SHG patterns found by performing local measurements within all of the domains mapped in Fig. 2b. Red lines are fits to the expressions described in the text. The large lobes are shaded pink to emphasize the orientation of each pattern. Schematics of the four degenerate magneto-electric loop-current order configurations are shown below each pattern to illustrate the possible correspondence. The red arrows denote the direction of the toroidal moment Ω in each plaquette.

  4. Temperature and hole-doping dependence of the hidden order.
    Figure 4: Temperature and hole-doping dependence of the hidden order.

    a-c, Change in SHG intensity from Sr2Ir1−xRhxO4 at x = 0 (a),x = 0.04 (b) and x = 0.11 (c) measured relative to their room-temperature values as a function of temperature. Data were taken under Pin–Sout polarization geometry at ϕ = 78°. The error bars represent the standard deviation over 60 independent measurements. No difference was observed between curves measured on cooling and heating. Lines are guides to the eye. The dashed red lines mark the transition temperature T of the hidden order phase deduced from our SHG data and the dashed black lines mark the Néel temperature TN determined from d.c. magnetic susceptibility measurements. d, Temperature versus doping phase diagram of Sr2Ir1−xRhxO4 showing the boundaries of the hidden order and the long-range (LRO) and short-range (SRO) Néel ordered regions. Points where a pseudogap is present are also marked, although a pseudogap phase boundary is not yet experimentally known.


  1. Kim, B. J. et al. Novel Jeff = 1/2 Mott state induced by relativistic spin–orbit coupling in Sr2IrO4. Phys. Rev. Lett. 101, 076402 (2008).
  2. Kim, B. J. et al. Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4. Science 323, 13291332 (2009).
  3. Dhital, C. et al. Neutron scattering study of correlated phase behavior in Sr2IrO4. Phys. Rev. B 87, 144405 (2013).
  4. Ye, F. et al. Magnetic and crystal structures of Sr2IrO4: A neutron diffraction study. Phys. Rev. B 87, 140406 (2013).
  5. Boseggia, S. et al. Locking of iridium magnetic moments to the correlated rotation of oxygen octahedra in Sr2IrO4 revealed by X-ray resonant scattering. J. Phys. Condens. Matter 25, 422202 (2013).
  6. Torchinsky, D. H. et al. Structural distortion induced magneto-elastic locking in Sr2IrO4 revealed through nonlinear optical harmonic generation. Phys. Rev. Lett. 114, 096404 (2015).
  7. Kim, Y. K. et al. Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet. Science 345, 187190 (2014).
  8. Cao, Y. et al. Hallmarks of the Mott-Metal Crossover in the Hole Doped J = 1/2 Mott insulator Sr2IrO4. Preprint at http://arXiv.org/abs/1406.4978 (2014).
  9. De la Torre, A. et al. Collapse of the Mott gap and emergence of a nodal liquid in lightly doped Sr2IrO4. Preprint at http://arXiv.org/abs/1506.00616 (2015).
  10. Kim, Y. K., Sung, N. H., Denlinger, J. D. & Kim, B. J. Observation of a d-wave gap in electron-doped Sr2IrO4. Preprint at http://arXiv.org/abs/1506.06639 (2015).
  11. Yan, Y. J. et al. Signature of high temperature superconductivity in electron doped Sr2IrO4. Preprint at http://arXiv.org/abs/1506.06557 (2015).
  12. Wang, F. & Senthil, T. Twisted Hubbard model for Sr2IrO4: Magnetism and possible high temperature superconductivity. Phys. Rev. Lett. 106, 136402 (2011).
  13. Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179186 (2015).
  14. Varma, C. M. Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 1455414580 (1997).
  15. Weber, C., Läuchli, A., Mila, F. & Giamarchi, T. Orbital currents in extended Hubbard models of high-Tc cuprate superconductors. Phys. Rev. Lett. 102, 017005 (2009).
  16. Kung, Y. F. et al. Numerical exploration of spontaneous broken symmetries in multiorbital Hubbard models. Phys. Rev. B 90, 224507 (2014).
  17. Orenstein, J. Optical nonreciprocity in magnetic structures related to high-Tc superconductors. Phys. Rev. Lett. 107, 067002 (2011).
  18. Yakovenko, V. M. Tilted loop currents in cuprate superconductors. Physica B 460, 159164 (2015).
  19. Fiebig, M., Pavlov, V. V. & Pisarev, R. V. Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: Review. J. Opt. Soc. Am. B 22, 96118 (2005).
  20. Simon, M. E. & Varma, C. M. Symmetry considerations for the detection of second-harmonic generation in cuprates in the pseudogap phase. Phys. Rev. B 67, 054511 (2003).
  21. Chikara, S. et al. Giant magnetoelectric effect in the Jeff = 1/2 Mott insulator Sr2IrO4. Phys. Rev. B 80, 140407 (2009).
  22. Ganguly, S., Granas, O. & Nordstrom, L. Non-trivial order parameter in Sr2IrO4. Phys. Rev. B 91, 020404(R) (2015).
  23. Lovesey, S. W. & Khalyavin, D. D. Strange magnetic multipoles and neutron diffraction by an iridate perovskite (Sr2IrO4). J. Phys. Condens. Matter 26, 322201 (2014).
  24. Fischer, M. H. & Kim, E.-A. Mean-field analysis of intra-unit-cell order in the Emery model of the CuO2 plane. Phys. Rev. B 84, 144502 (2011).
  25. Scagnoli, V. et al. Observation of orbital currents in CuO. Science 332, 696698 (2011).
  26. Di Matteo, S. & Norman, M. R. Orbital currents, anapoles, and magnetic quadrupoles in CuO. Phys. Rev. B 85, 235143 (2012).
  27. Qi, T. F. et al. Spin–orbit tuned metal-insulator transitions in single-crystal Sr2Ir1−xRhxO4 (0 ≤ x ≤ 1). Phys. Rev. B 86, 125105 (2012).
  28. Clancy, J. P. et al. Dilute magnetism and spin-orbital percolation effects in Sr2Ir1−xRhxO4. Phys. Rev. B 89, 054409 (2014).
  29. Watanabe, H., Shirakawa, T. & Yunoki, S. Monte Carlo study of an unconventional superconducting phase in iridium oxide Jeff = 1/2 Mott insulators induced by carrier doping. Phys. Rev. Lett. 110, 027002 (2013).
  30. Meng, Z. Y., Kim, Y. B. & Kee, H.-Y. Odd-parity triplet superconducting phase in multiorbital materials with a strong spin–orbit coupling: Application to doped Sr2IrO4. Phys. Rev. Lett. 113, 177003 (2014).
  31. Torchinsky, D. H., Chu, H., Qi, T., Cao, G. & Hsieh, D. A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries. Rev. Sci. Instrum. 85, 083102 (2014).
  32. Moon, S. J. et al. Electronic structures of layered perovskite Sr2MO4 (M=Ru, Rh, and Ir). Phys. Rev. B 74, 113104 (2006).

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Author information


  1. Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

    • L. Zhao,
    • D. H. Torchinsky,
    • V. Ivanov,
    • R. Lifshitz &
    • D. Hsieh
  2. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

    • L. Zhao,
    • D. H. Torchinsky,
    • H. Chu &
    • D. Hsieh
  3. Department of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA

    • H. Chu
  4. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

    • R. Lifshitz
  5. Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

    • R. Flint
  6. Center for Advanced Materials, Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA

    • T. Qi &
    • G. Cao


L.Z. and D.H. planned the experiment. L.Z., D.H.T., H.C. and V.I. performed the measurements. L.Z. and R.L. performed the magnetic point group symmetry analysis. R.F. performed the Landau free energy calculation. T.Q. and G.C. prepared and characterized the samples. L.Z., R.F. and D.H. analysed the data and wrote the manuscript.

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