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Hidden spin polarization in inversion-symmetric bulk crystals


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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Figure 1: The three classes of spin polarization in nonmagnetic bulk crystals.
Figure 2: Rhombohedral α-SnTe (R3m) with R-1 (dominant over D-1) spin textures.
Figure 3: NaCaBi (P63/mmc) with D-2 effect.
Figure 4: LaOBiS2 (P4/nmm) with R-2 and D-2 effects.

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  1. Wolf, S. A. et al. Spintronics: A spin-based electronics vision for the future. Science 294, 1488–1495 (2001).

    Article  ADS  Google Scholar 

  2. Žutić, I., Fabian, J. & Das Sarma, S. Spintronics: Fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    Article  ADS  Google Scholar 

  3. Luo, J.-W., Bester, G. & Zunger, A. Full-zone spin splitting for electrons and holes in bulk GaAs and GaSb. Phys. Rev. Lett. 102, 056405 (2009).

    Article  ADS  Google Scholar 

  4. Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).

    Article  ADS  Google Scholar 

  5. Rashba, E. I. Properties of semiconductors with an extremum loop 1 cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys.-Solid State 2, 1109–1122 (1960).

    Google Scholar 

  6. Ishizaka, K. et al. Giant Rashba-type spin splitting in bulk BiTeI. Nature Mater. 10, 521–526 (2011).

    Article  ADS  Google Scholar 

  7. Di Sante, D., Barone, P., Bertacco, R. & Picozzi, S. Electric control of the Giant Rashba Effect in bulk GeTe. Adv. Mater. 25, 509–513 (2013).

    Article  Google Scholar 

  8. Herman, F., Kuglin, C. D., Cuff, K. F. & Kortum, R. L. Relativistic corrections to the band structure of tetrahedrally bonded semiconductors. Phys. Rev. Lett. 11, 541–545 (1963).

    Article  ADS  Google Scholar 

  9. Tilley, R. Crystals and Crystal Structures 67–79 (Wiley, 2006).

    Google Scholar 

  10. Winkler, R. Spin orientation and spin precession in inversion-asymmetric quasi-two-dimensional electron systems. Phys. Rev. B 69, 045317 (2004).

    Article  ADS  Google Scholar 

  11. Winkler, R. Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003).

    Book  Google Scholar 

  12. Flurry, R. L. Site symmetry in molecular point groups. Int. J Quant. Chem. 6, 455–458 (1972).

    Article  Google Scholar 

  13. Hsieh, T. H. et al. Topological crystalline insulators in the SnTe material class. Nature Commun. 3, 982 (2012).

    Article  ADS  Google Scholar 

  14. Chadov, S. et al. Tunable multifunctional topological insulators in ternary Heusler compounds. Nature Mater. 9, 541–545 (2010).

    Article  ADS  Google Scholar 

  15. Littlewood, P. B. Phase transitions and optical properties of IV-VI compounds. Lect. Notes Phys. 152, 238–246 (1982).

    Article  ADS  Google Scholar 

  16. Dash, S. P., Sharma, S., Patel, R. S., de Jong, M. P. & Jansen, R. Electrical creation of spin polarization in silicon at room temperature. Nature 462, 491–494 (2009).

    Article  ADS  Google Scholar 

  17. Zhang, L., Luo, J-W., Saraiva, A., Koiller, B. & Zunger, A. Genetic design of enhanced valley splitting towards a spin qubit in silicon. Nature Commun. 4, 2396 (2013).

    Article  ADS  Google Scholar 

  18. Mizuguchi, Y. et al. Superconductivity in novel BiS2-based layered superconductor LaO1-xFxBiS2. J. Phys. Soc. Jpn. 81, 114725 (2012).

    Article  ADS  Google Scholar 

  19. Vaida, M. et al. The structure and symmetry of crystalline solid solutions: a general revision. Science 241, 1475–1479 (1988).

    Article  ADS  Google Scholar 

  20. ICSD, Inorganic Crystal Structure Database (Fachinformationszentrum Karlsruhe, Germany, 2006).

    Google Scholar 

  21. Cao, Y. et al. Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators. Nature Phys. 9, 499–504 (2013).

    Article  ADS  Google Scholar 

  22. Liu, Q., Guo, Y. & Freeman, A. J. Tunable Rashba effect in two-dimensional LaOBiS2 films: Ultrathin candidates for spin field effect transistors. Nano Lett. 13, 5264–5270 (2013).

    Article  ADS  Google Scholar 

  23. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  24. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  Google Scholar 

  25. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  26. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).

    Article  Google Scholar 

  27. Zhang, X., Yu, L., Zakutayev, A. & Zunger, A. Sorting stable versus unstable hypothetical compounds: the case of multi-functional abx half-Heusler filled tetrahedral structures. Adv. Func. Mater. 22, 1425–1435 (2012).

    Article  Google Scholar 

  28. Tanryverdiev, V. S., Aliev, O. M. & Aliev, I. I. Synthesis and physicochemical properties of LnBiOS2 . Inorg. Mater. 31, 1361–1363 (1995).

    Google Scholar 

  29. Bloński, P. & Hafner, J. Magnetic anisotropy of transition-metal dimers: Density functional calculations. Phys. Rev. B 79, 224418 (2009).

    Article  ADS  Google Scholar 

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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.

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X.Z. and Q.L. carried out the electronic structure calculations. A.Z. led the analysis and writing of the paper. J.-W.L. contributed equally with Q.L. and X.Z. to the preparation of the figures and writing of the paper. A.J.F. and A.Z. supervised the study.

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Correspondence to Jun-Wei Luo or Alex Zunger.

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The authors declare no competing financial interests.

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Zhang, X., Liu, Q., Luo, JW. et al. Hidden spin polarization in inversion-symmetric bulk crystals. Nature Phys 10, 387–393 (2014).

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