Spin–orbit coupling can induce spin polarization in nonmagnetic 3D crystals when the inversion symmetry is broken, as manifested by the bulk Rashba and Dresselhaus effects. We establish that these spin-polarization effects originate fundamentally from specific atomic site asymmetries, rather than, as generally accepted, from the asymmetry of the crystal space group. This understanding leads to the recognition that a previously overlooked hidden form of spin polarization should exist in centrosymmetric crystals. Although all energy bands must be doubly degenerate in centrosymmetric materials, we find that the two components of such doubly degenerate bands could have opposite polarizations, each spatially localized on one of the two separate sectors forming the inversion partners. We demonstrate such hidden spin polarizations in particular centrosymmetric crystals by first-principles calculations. This new understanding could considerably broaden the range of currently useful spintronic materials and enable the control of spin polarization by means of operations on the atomic scale.
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A.Z. is grateful to E. Rashba for important discussions on the manuscript and to M. Lahav for discussing the analogy to anti-pyroelectricity (ref. 19). This work was supported by NSF Grant No. DMREF-13-34170. X.Z. also acknowledges the administrative support of REMRSEC at the Colorado School of Mines. J.-W.L. was supported by the Center for Inverse Design, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number DEAC 36-08GO28308.
The authors declare no competing financial interests.
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Zhang, X., Liu, Q., Luo, J. et al. Hidden spin polarization in inversion-symmetric bulk crystals. Nature Phys 10, 387–393 (2014) doi:10.1038/nphys2933
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