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Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order

Nature volume 463, pages 210–213 (2010)Cite this article

Abstract

Spin liquids are magnetically frustrated systems, in which spins are prevented from ordering or freezing, owing to quantum or thermal fluctuations among degenerate states induced by the frustration. Chiral spin liquids are a hypothetical class of spin liquids in which the time-reversal symmetry is macroscopically broken in the absence of an applied magnetic field or any magnetic dipole long-range order. Even though such chiral spin-liquid states were proposed more than two decades ago1,2,3, an experimental realization and observation of such states has remained a challenge. One of the characteristic order parameters in such systems is a macroscopic average of the scalar spin chirality, a solid angle subtended by three nearby spins. In previous experimental reports, however, the spin chirality was only parasitic to the non-coplanar spin structure associated with a magnetic dipole long-range order or induced by the applied magnetic field4,5,6,7,8,9,10, and thus the chiral spin-liquid state has never been found. Here, we report empirical evidence that the time-reversal symmetry can be broken spontaneously on a macroscopic scale in the absence of magnetic dipole long-range order. In particular, we employ the anomalous Hall effect4,11 to directly probe the broken time-reversal symmetry for the metallic frustrated magnet Pr2Ir2O7. An onset of the Hall effect is observed at zero field in the absence of uniform magnetization, within the experimental accuracy, suggesting an emergence of a chiral spin liquid. The origin of this spontaneous Hall effect is ascribed to chiral spin textures4,5,12,13, which are inferred from the magnetic measurements indicating the spin ice-rule formation14,15.

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Figure 1: Chiral spin state and pyrochlore lattice.
Figure 2: Temperature dependence of the magnetic and transport properties of Pr2Ir2O2.
Figure 3: Field dependence of the Hall conductivity and magnetization of Pr 2 Ir 2 O 2 along the [111] field direction.

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Acknowledgements

We thank L. Balicas, H. Kawamura, Y. Maeno, Y. Matsumoto, N. Nagaosa, Y. Ohta and T. Taniguchi for their support and discussions. This work is partially supported by Grants-in-Aid from the Japanese Society for the Promotion of Science, by Grants-in-Aid for Scientific Research on Priority Areas and Scientific Research on Innovative Areas from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and by the Kurata Grant. Y.M. is supported by JSPS research fellowships. The calculations were performed in part by using the RIKEN Super Combined Cluster (RSCC).

Author Contributions S.N. planned the experimental project, and Y.M. and S.N. collected data and wrote the paper; S.O. gave the theoretical interpretation, performed the calculations, and wrote the paper; T.T. and T.S. collected data. All authors discussed the results and commented on the manuscript.

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  1. Yo Machida & Takashi Tayama

    Present address: Present addresses: Department of Physics, Tokyo Institute of Technology, Meguro 152-8551, Japan (Y.M.); Department of Physics, University of Toyama, Toyama 930-8555, Japan (T.T.).,

Authors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan

    Yo Machida, Satoru Nakatsuji, Takashi Tayama & Toshiro Sakakibara

  2. Condensed Matter Theory Laboratory, RIKEN, Wako 351-0198, Japan ,

    Shigeki Onoda

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Correspondence to Satoru Nakatsuji.

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Machida, Y., Nakatsuji, S., Onoda, S. et al. Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order. Nature 463, 210–213 (2010). https://doi.org/10.1038/nature08680

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