Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces

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Spin–orbit coupling (SOC) describes the relativistic interaction between the spin and momentum degrees of freedom of electrons, and is central to the rich phenomena observed in condensed matter systems. In recent years, new phases of matter have emerged from the interplay between SOC and low dimensionality, such as chiral spin textures and spin-polarized surface and interface states. These low-dimensional SOC-based realizations are typically robust and can be exploited at room temperature. Here we discuss SOC as a means of producing such fundamentally new physical phenomena in thin films and heterostructures. We put into context the technological promise of these material classes for developing spin-based device applications at room temperature.

At a glance


  1. Emergent phenomena from spin–orbit coupling (SOC) at surfaces and interfaces.
    Figure 1: Emergent phenomena from spin–orbit coupling (SOC) at surfaces and interfaces.

    A schematic illustration of the connection between the presence of strong SOC at material surfaces and interfaces (inner ellipse) and the resulting emergence of new interactions and electronic states (middle ellipse), such as Dzyaloshinskii–Moriya interaction (DMI; see Fig. 4a, e for details), Rashba interfaces (Fig. 2b, d) and topological surface states (TSS; Fig. 2a, c). These emergent phenomona can in turn be used to generate new 2D spintronics effects (outer ellipse), such as spin–charge conversion (Fig. 2e, f and 3), the photogalvanic effect, enhanced SOC in 2D materials, such as graphene (Fig. 3d, e), magnetic skyrmions (Fig. 4b) and chiral domain walls (Fig. 4c), which have direct device applications (periphery). FM, ferromagnet; NM, non-magnetic material.

  2. Band structure and spin–charge conversion in spin-polarized 2D states.
    Figure 2: Band structure and spin–charge conversion in spin-polarized 2D states.

    a, b, Schematic of the spin-polarized band structure (electron energy E as a function of in-plane momentum k) of 2D electron states at the surfaces and interfaces of topological insulators (a) and at Rashba systems (b). The arrows indicate electron spin, with blue and red dispersion surfaces corresponding to opposite spin helicities. c, d, ARPES measurements of the 2D band structure, with respect to the Fermi level (E = 0), at the surface of the topological insulator Bi2−xCaxSe3 (c) and at the Rashba surface of Au(111) (d). The red arrows in c indicate the spin orientation, and the bulk bands are schematized in brown. e, k-space schematic of charge-to-spin conversion in topological insulators via the Edelstein effect. A charge current Jc at the surface causes a shift Δk of the Fermi contour, resulting in a non-zero spin density as a result of the helical spin orientation. This spin density can diffuse as a spin current in the adjacent material. f, Spin-to-charge conversion by the inverse Edelstein effect in topological insulators. Injecting a spin current (Js; spin-polarized wiggles) into the surface states of the topological insulator overpopulates states on one side of the Fermi contour and depopulates states on the other, generating a charge current. Panels a and b were adapted from figures 11.3(a) and 11.5(a), pages 181 and 183, of ref. 5, by permission of Oxford University Press. Panel c adapted from ref. 20, Nature Publishing Group. Panel d adapted from ref. 13, American Physical Society.

  3. Spin–charge conversion experiments.
    Figure 3: Spin–charge conversion experiments.

    a, Charge-to-spin conversion by the Edelstein effect in spin torque ferromagnetic resonance (ST-FMR) experiments on the topological insulator (Bi1−xSbx)2Te3 at T = 10 K. The graph shows the spin–charge conversion coefficient qICS for several Sb concentrations x, and the corresponding Fermi levels in the Dirac cone. (Error bars represent the standard deviation over five samples with different dimensions.) Inset, schematic of the device, in which an applied longitudinal a.c. charge current Jc (associated with an a.c. magnetic field Hrf) is converted by the Edelstein effect into a vertical spin current Js. This spin current is injected through a Cu layer into the top NiFe layer and detected by a ST-FMR-induced d.c. voltage, in an external d.c. field Hdc applied at an angle θ. b, c, Spin-to-charge conversion by the inverse Edelstein effect in spin-pumping experiments on the topological insulator α-Sn. b, ARPES intensity maps (for varying electron energy E with respect to the Fermi level and in-plane momentum k) show that the surface-state Dirac cone on α-Sn is preserved (symbols on the red lines represent maxima in ARPES intensity scans) even after Ag deposition (to a thickness of 2.3 nm). c, A d.c. voltage generated by the inverse Edelstein effect is observed when α-Sn is covered by Ag (blue), but not when it is directly covered by Fe, which destroys the Dirac cone (green). Inset, a FMR spin-pumping device (the magnetization M of the ferromagnetic layer in an external field B = μ0Hdc, where μ0 is the permeability of free space, excited by an a.c. field) injects a vertical spin current Js through an Ag layer into the surface states of the topological insulator, which generates a charge current Ic. d, Calculated band structure of graphene after Au intercalation between graphene and substrate, matched to ARPES measurements near the point. Blue and red symbols indicate opposite spin orientations derived from fits to spin-resolved ARPES measurements. e, Spin-to-charge conversion by spin pumping from yttrium iron garnet (YIG) into graphene: experimental set-up (inset) and lateral voltage V induced by the inverse Edelstein effect for opposite applied fields. Panel a adapted from ref. 28, Nature Publishing Group. Panels b and c adapted from ref. 31, American Physical Society. Panel d adapted from ref. 47, Nature Publishing Group. Panel e adapted from ref. 50, American Physical Society.

  4. Interfacial DMI and chiral spin textures.
    Figure 4: Interfacial DMI and chiral spin textures.

    a, Anatomy of interfacial DMI from ab initio calculations. Bottom, Layer-resolved DMI in a Pt/Co bilayer. Top, distribution of SOC energies associated with the DMI in the interfacial Co layer. Inset, a schematic of DMI at the interface between a ferromagnetic metal with out-of-plane magnetization (Co, grey) and a strong SOC metal (Pt, blue). The DMI vector D12, associated with the triangle composed of two Co atoms and a Pt atom, is perpendicular to the plane of the triangle. S1,2, neighbouring spins. b, c, Schematics of the spin configuration in interfacial-DMI-induced chiral spin textures such as magnetic skyrmions (b) and chiral Néel domain walls (c), with the colour scale corresponding to the out-of-plane magnetization component. d, SP-STM imaging of an individual skyrmion (with a diameter of 8 nm at a field of 3.25 T) in a Fe/Pd bilayer on Ir(111), acquired in constant-current topographic mode, with an in-plane magnetized tip, with the modelled magnetization overlaid (arrows). e, Skyrmion stabilization in multilayers, illustrated using a multilayer stack of Ir/Co/Pt. The close-up of the trilayer shows DMI vectors (D12 and D34) at the top (Co/Ir) and bottom (Pt/Co) interfaces of Co. The effective DMI magnitude is enhanced by the same direction of D12 and D34 at the different interfaces. f, Room-temperature skyrmions in a Pt/Co/MgO multilayer in a lithographed 400 nm × 400 nm square, seen by XMCD-PEEM, with the magnetization profile along the red line shown below. g, Room-temperature skyrmions in (Ir/Co/Pt) × 10 multilayers patterned into 300-nm-diameter disks (left) or 200-nm-wide tracks (right), seen by STXM. Panel a (main panel) adapted from ref. 72, American Physical Society. Panel a (inset) adapted from ref. 70, Nature Publishing Group. Panel d reproduced from ref. 62, American Association for the Advancement of Science. Panels e and g adapted from ref. 67, Nature Publishing Group. Panel f adapted from ref. 78, Nature Publishing Group.

  5. Manipulation of magnetic skyrmions.
    Figure 5: Manipulation of magnetic skyrmions.

    a, Individual skyrmions (with diameters of 8 nm at a field of 3.25 T) in Fe/Pd/Ir(111) before and after SP-STM manipulation, demonstrating the creation and annihilation of individual skyrmions at specific locations. b, Skyrmions in a Ta/CoFeB/TaOx structure, before (top) and after (bottom) applying a current pulse through a constriction, with current-induced nucleation and subsequent motion of several skyrmions, as seen by magneto-optical Kerr effect (MOKE) microscopy. c, Experimental measurement of the current-induced skyrmion velocity in tracks of Pt/Co/Ta and Pt/CoFeB/MgO (different symbols represent results from different devices) multilayers using STXM. (Error bars denote the standard deviation of multiple measurements.) d, Schematic of a skyrmion-based memory device in which skyrmions could be deleted, moved and written by the corresponding current j. Panel a adapted from ref. 62, American Association for the Advancement of Science. Panel b adapted from ref. 69, American Association for the Advancement of Science. Panel c reproduced from ref. 68, Nature Publishing Group. Panel d adapted from ref. 100, American Association for the Advancement of Science.


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  1. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore

    • Anjan Soumyanarayanan &
    • Christos Panagopoulos
  2. Data Storage Institute, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way #08-01, 138634 Singapore

    • Anjan Soumyanarayanan
  3. Unité Mixte de Physique, CNRS, Thales, Université Paris-Sud, Université Paris-Saclay, Palaiseau 91767, France

    • Nicolas Reyren &
    • Albert Fert


All authors contributed equally to this work.

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