Abstract
Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3,4,5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin–orbit coupling limit6,7,8,9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.
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Acknowledgements
We thank N. Shannon, G. Khaliullin and Y. B. Kim for helpful discussions. This project is supported by the Institute for Basic Science (Project IBS-R014-A2) and the Samsung Science and Technology Foundation (Project SSTF-BA2201-04). Experiments at the PLS-II 1C beamline were supported in part by the Ministry of Science and ICT of Korea. The use of the Advanced Photon Source at the Argonne National Laboratory was supported by the US Department of Energy (Contract DE-AC02-06CH11357). We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities (Proposal HC-5311), and we also thank F. Gerbon for assistance and support in using beamline ID20. J.-K.K. was supported by the Global PhD Fellowship Program by the National Research Foundation of Korea (Grant 2018H1A2A1059958). G.Y.C. is supported by the National Research Foundation of Korea (Grants 2020R1C1C1006048, RS-2023-00208291, 2023M3K5A1094810 and 2023M3K5A1094813) funded by the Korean Government (Ministry of Science and ICT), the Institute of Basic Science (Project IBS-R014-D1), the Air Force Office of Scientific Research (Award FA2386-22-1-4061) and the Samsung Science and Technology Foundation (Project SSTF-BA2002-05). H.H. and J.J. are supported by the National Research Foundation of Korea (Grant 2020R1A5A1016518) and the Creative-Pioneering Researchers Program through Seoul National University.
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B.J.K. conceived and managed the project. H.K., K.K. and Jonghwan Kim performed Raman experiments. H.K., J. Kwon and S.H. performed resonant X-ray diffraction experiments with help from J.S., G.F., Y.C., D.H. and J.W.K.; H.K., J.-K.K., J. Kwon and H.-W.J.K. performed resonant inelastic X-ray scattering experiments and analysed the data with help from C.J.S., A.L. and Jungho Kim. Jimin Kim grew single crystals. H.H. and J.J. performed Kerr measurements. H.K. and B.J.K. performed representation analysis. W.L. and G.Y.C. assisted in the interpretation of the data. H.K., J.-K.K. and B.J.K. wrote the manuscript with inputs from all authors.
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Extended data figures and tables
Extended Data Fig. 1 Temperature evolution of the low-energy Raman modes.
The Raman spectra of the A1g and B2g modes shown in Fig. 2c,e are displayed with vertical offset for clarity. The A1g (red) and B2g (black) spectra were measured on the same crystal under the same experimental conditions including laser power and acquisition time, and the spectra are plotted in the same arbitrary unit.
Extended Data Fig. 2 Magneto-optical Kerr measurement.
a, Relative Kerr angle in the 0.35 T in-plane magnetic field (red line) and ambient magnetic field near 0 T (black line). The relative Kerr angle (left axis) is converted to magnetization (right axis) using a conversion factor of 7.7 × 10−4 (μB/Ir ion)/(μ rad). b, Magnified plot of the 0 T data in a. Dashed line indicates the standard deviation for the T = 230 ~ 300 K range. The Kerr signal at B = 0 T in the range of 230 K < T < 300 K shows that no net magnetization is present within our experimental resolution, 3.4 × 10−5 μB/ion (dashed line), thus confirming the preservation of time-reversal symmetry above TN ~ 230 K.
Extended Data Fig. 3 Polarziation-resolved RIXS spectra.
a–f, RIXS spectra along the zone boundary from (π/2, π/2) to (π, 0) with the spin components transverse (T) and longitudinal (L) to the ordered AF moments resolved. The spectra were acquired with the same experimental setup in Fig. 4. The error bars are derived using error propagation based on the standard deviations of the raw spectra.
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Supplementary Notes 1–6.
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Kim, H., Kim, JK., Kwon, J. et al. Quantum spin nematic phase in a square-lattice iridate. Nature 625, 264–269 (2024). https://doi.org/10.1038/s41586-023-06829-4
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DOI: https://doi.org/10.1038/s41586-023-06829-4
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