Letter | Published:

Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking

Nature volume 549, pages 492496 (28 September 2017) | Download Citation


Engineering and enhancing the breaking of inversion symmetry in solids—that is, allowing electrons to differentiate between ‘up’ and ‘down’—is a key goal in condensed-matter physics and materials science because it can be used to stabilize states that are of fundamental interest and also have potential practical applications. Examples include improved ferroelectrics for memory devices and materials that host Majorana zero modes for quantum computing1,2. Although inversion symmetry is naturally broken in several crystalline environments, such as at surfaces and interfaces, maximizing the influence of this effect on the electronic states of interest remains a challenge. Here we present a mechanism for realizing a much larger coupling of inversion-symmetry breaking to itinerant surface electrons than is typically achieved. The key element is a pronounced asymmetry of surface hopping energies—that is, a kinetic-energy-coupled inversion-symmetry breaking, the energy scale of which is a substantial fraction of the bandwidth. Using spin- and angle-resolved photoemission spectroscopy, we demonstrate that such a strong inversion-symmetry breaking, when combined with spin–orbit interactions, can mediate Rashba-like3,4 spin splittings that are much larger than would typically be expected. The energy scale of the inversion-symmetry breaking that we achieve is so large that the spin splitting in the CoO2- and RhO2-derived surface states of delafossite oxides becomes controlled by the full atomic spin–orbit coupling of the 3d and 4d transition metals, resulting in some of the largest known Rashba-like3,4 spin splittings. The core structural building blocks that facilitate the bandwidth-scaled inversion-symmetry breaking are common to numerous materials. Our findings therefore provide opportunities for creating spin-textured states and suggest routes to interfacial control of inversion-symmetry breaking in designer heterostructures of oxides and other material classes.

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  1. 1.

    , , , & Strong polarization enhancement in asymmetric three-component ferroelectric superlattices. Nature 433, 395–399 (2005)

  2. 2.

    et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012)

  3. 3.

    & Properties of a 2d electron gas with lifted spectral degeneracy. JETP Lett. 39, 78–81 (1984)

  4. 4.

    , , , & New perspectives for Rashba spin–orbit coupling. Nat. Mater. 14, 871–882 (2015)

  5. 5.

    et al. Emergent phenomena at oxide interfaces. Nat. Mater. 11, 103–113 (2012)

  6. 6.

    , & Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy. Phys. Rev. Lett. 77, 3419–3422 (1996)

  7. 7.

    , , & Gate control of spin–orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure. Phys. Rev. Lett. 78, 1335–1338 (1997)

  8. 8.

    et al. Spin structure of the Shockley surface state on Au(111). Phys. Rev. B 69, 241401 (2004)

  9. 9.

    et al. Giant spin splitting through surface alloying. Phys. Rev. Lett. 98, 186807 (2007)

  10. 10.

    et al. Tunable Rashba spin–orbit interaction at oxide interfaces. Phys. Rev. Lett. 104, 126803 (2010)

  11. 11.

    et al. Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3. Phys. Rev. Lett. 107, 096802 (2011)

  12. 12.

    et al. Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces. Nat. Mater. 15, 1261–1266 (2016)

  13. 13.

    & RKKY interaction in a disordered two-dimensional electron gas with Rashba and Dresselhaus spin–orbit couplings. Phys. Rev. B 82, 165303 (2010)

  14. 14.

    Weak-and strong-coupling limits of the two-dimensional Frohlich polaron with spin–orbit Rashba interaction. Phys. Rev. B 77, 024306 (2008)

  15. 15.

    & Superconducting 2D system with lifted spin degeneracy: mixed singlet-triplet state. Phys. Rev. Lett. 87, 037004 (2001)

  16. 16.

    , , , & Quantitative analysis on electric dipole energy in Rashba band splitting. Sci. Rep. 5, 13488 (2015)

  17. 17.

    & Microscopic mechanism for the Rashba spin-band splitting: perspective from formation of local orbital angular momentum. J. Electron Spectrosc. Relat. Phenom. 201, 6–17 (2015)

  18. 18.

    , , , & Orbital-angular-momentum based origin of Rashba-type surface band splitting. Phys. Rev. Lett. 107, 156803 (2011)

  19. 19.

    , & Chemistry of noble metal oxides. I. Syntheses and properties of ABO2 delafossite compounds. Inorg. Chem. 10, 713–718 (1971)

  20. 20.

    et al. Roles of high-frequency optical phonons in the physical properties of the conductive delafossite PdCoO2. J. Phys. Soc. Jpn. 76, 104701 (2007)

  21. 21.

    The properties of ultrapure delafossite metals. Rep. Prog. Phys. 80, 032501 (2017)

  22. 22.

    et al. Nearly free electrons in a 5d delafossite oxide metal. Sci. Adv. 1, e1500692 (2015)

  23. 23.

    , & Fermi surface and surface electronic structure of delafossite PdCoO2. Phys. Rev. B 80, 035116 (2009)

  24. 24.

    et al. Anisotropic electric conductivity of delafossite PdCoO2 studied by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 102, 256404 (2009)

  25. 25.

    et al. Chiral orbital-angular momentum in the surface states of Bi2Se3. Phys. Rev. Lett. 108, 046805 (2012)

  26. 26.

    Spin and Orbital Degrees of Freedom in Transition Metal Oxides and Oxide Thin Films Studied by Soft X-Ray Absorption Spectroscopy. PhD thesis, Univ. Cologne, (2005)

  27. 27.

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

  28. 28.

    et al. Quasiparticle dynamics and spin–orbital texture of the SrTiO3 two-dimensional electron gas. Nat. Commun. 5, 3414 (2014)

  29. 29.

    , & Theory of spin–orbit coupling at LaAlO3/SrTiO3 interfaces and SrTiO3 surfaces. Phys. Rev. B 87, 161102 (2013)

  30. 30.

    , & Theory of t2g electron-gas Rashba interactions. Phys. Rev. B 88, 041302 (2013)

  31. 31.

    et al. Hierarchical spin–orbital polarization of a giant Rashba system. Sci. Adv. 1, e1500495 (2015)

  32. 32.

    , & Enhanced Rashba spin–orbit splitting in Bi/Ag(111) and Pb/Ag(111) surface alloys from first principles. Phys. Rev. B 75, 195414 (2007)

  33. 33.

    , & Chemistry of noble metal oxides. II. Crystal structures of platinum cobalt dioxide, palladium cobalt dioxide, coppper iron dioxide, and silver iron dioxide. Inorg. Chem. 10, 719–723 (1971)

  34. 34.

    , , & Chemistry of noble metal oxides. III. Electrical transport properties and crystal chemistry of ABO2 compounds with the delafossite structure. Inorg. Chem. 10, 723–727 (1971)

  35. 35.

    , & Growth and anisotropic physical properties of PdCoO2 single crystals. J. Phys. Soc. Jpn 65, 3973–3977 (1996)

  36. 36.

    et al. Electronic structure of the metallic antiferromagnet PdCrO2 measured by angle-resolved photoemission spectroscopy. Phys. Rev. B 88, 125109 (2013)

  37. 37.

    et al. Very Efficient Spin Polarization Analysis (VESPA): new exchange scattering-based setup for spin-resolved ARPES at APE-NFFA beamline at Elettra. J. Synchrotron Radiat. 24, 750–756 (2017)

  38. 38.

    & Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 59, 1743–1757 (1999)

  39. 39.

    , & Full-potential band-structure calculation of iron pyrite. Phys. Rev. B 60, 14035–14041 (1999)

  40. 40.

    , & Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

  41. 41.

    , & in Theoretical and Computational Chemistry (ed. ) Ch. 12, 723–776 (Elsevier, 2004)

  42. 42.

    & Simplified LCAO method for the periodic potential problem. Phys. Rev. 94, 1498–1524 (1954)

  43. 43.

    , & Multiplets of Transition-Metal Ions in Crystals (Academic Press, 1970)

  44. 44.

    et al. Orbital Symmetry and Electron Correlation in NaxCoO2. Phys. Rev. Lett. 94, 146402 (2005)

  45. 45.

    , , & A tight-binding investigation of the NaxCoO2 Fermi surface. Europhys. Lett. 68, 433–439 (2004)

  46. 46.

    , , & Orbital Rashba effect and its detection by circular dichroism angle-resolved photoemission spectroscopy. Phys. Rev. B 85, 195401 (2012)

  47. 47.

    & Electronic state of a CoO2 layer with hexagonal structure: a Kagomé lattice structure in a triangular lattice. Phys. Rev. Lett. 91, 257003 (2003)

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We thank N. Nandi and B. Schmidt for discussions. We acknowledge support from the European Research Council (through the QUESTDO project), the Engineering and Physical Sciences Research Council, UK (grant no. EP/I031014/1), the Royal Society, the Max-Planck Society and the International Max-Planck Partnership for Measurement and Observation at the Quantum Limit. V.S., L.B., O.J.C. and J.M.R. acknowledge EPSRC for PhD studentship support through grant numbers EP/L015110/1, EP/G03673X/1, EP/K503162/1 and EP/L505079/1. D.K. acknowledges funding by the DFG within FOR 1346. We thank Diamond Light Source and Elettra synchrotrons for access to Beamlines I05 (proposal numbers SI12469, SI14927 and SI18267) and APE (proposal no. 20150019), respectively, that contributed to the results presented here. Additional supporting measurements were performed at the CASIOPEE beamline of SOLEIL, and we are grateful to I. Marković and P. Le Fèvre for their assistance.

Author information


  1. SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK

    • Veronika Sunko
    • , F. Mazzola
    • , L. Bawden
    • , O. J. Clark
    • , J. M. Riley
    • , A. P. Mackenzie
    •  & P. D. C. King
  2. Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany

    • Veronika Sunko
    • , H. Rosner
    • , P. Kushwaha
    • , S. Khim
    • , D. Kasinathan
    • , M. W. Haverkort
    •  & A. P. Mackenzie
  3. Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK

    • J. M. Riley
    • , T. K. Kim
    •  & M. Hoesch
  4. Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany

    • M. W. Haverkort
  5. Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, Area Science Park, S.S.14, Km 163.5, 34149 Trieste, Italy

    • J. Fujii
    •  & I. Vobornik


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V.S., F.M., L.B., O.J.C., J.M.R. and P.D.C.K. measured the experimental data, and V.S. performed the data analysis. P.K and S.K. grew and characterized the samples. V.S. developed the tight-binding models, and H.R., D.K. and M.W.H. performed the first-principles calculations. M.H. and T.K.K. maintained the ARPES end station and J.F. and I.V. the spin-ARPES end station, and all provided experimental support. V.S., P.D.C.K. and A.P.M. wrote the manuscript with input and discussion from co-authors, and were responsible for overall project planning and direction.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to A. P. Mackenzie or P. D. C. King.

Reviewer Information Nature thanks A. MacDonald and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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