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Hastatic order in the heavy-fermion compound URu2Si2

Abstract

The development of collective long-range order by means of phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry, whereas superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5 kelvin in the heavy-fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such ‘hastatic’ order hybridizes uranium-atom conduction electrons with Ising 5f2 states to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction-electron ‘sea’, a colossal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant, energy-dependent nematicity in the tunnelling density of states.

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Figure 1: Phenomenological interpretation of the anomalous spin susceptibility in URu2Si2.
Figure 2: Spinor hybridization and signatures of hastatic order.
Figure 3: Magnetic response of hastatic order.
Figure 4: Density of states and resonant nematicity predicted by theory.

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Acknowledgements

An early version of this work was begun in collaboration with P. Fazekas, since deceased. We thank N. Andrei, S. Burdin, B. Coleman, L. Greene, N. Harrison, K. Haule, G. Kotliar, P. Lee, G. Luke, Y. Matsuda, J. Mydosh, P. Niklowitz, C. Pépin, T. Senthil, A. Toth and T. Timusk for discussions. We acknowledge funding from the Simons Foundation (R.F.), the US National Science Foundation grant DMR 0907179 (R.F., P. Coleman), the US National Science Foundation I2CAM International Materials Institute Award Grant DMR-0844115 (R.F., P. Coleman) and the US National Science Foundation grant 1066293 (all authors) while at the Aspen Center for Physics. We are grateful for the hospitality of the Aspen Center for Physics.

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All authors contributed equally in the discussions and development of the hastatic-order concept, the experimental consequences and its mean-field description pertinent to URu2Si2. R.F. and P. Coleman carried out the detailed numerical calculations of the microscopic model. All authors contributed towards the writing of the paper and Supplementary Information.

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Correspondence to Piers Coleman.

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Chandra, P., Coleman, P. & Flint, R. Hastatic order in the heavy-fermion compound URu2Si2. Nature 493, 621–626 (2013). https://doi.org/10.1038/nature11820

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