Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces
Résumé
T he electric field experienced by a travelling electron translates, in its rest frame, to a magnetic field proportional to its velocity-a relativistic effect which is notable in crystalline lattices with heavy atoms. The Zeeman interaction between the electron spin and this effective magnetic field is equivalent to the coupling of the electronic spin and momentum degrees of freedom, known as SOC. SOC can split degenerate bands with finite angular momentum (p, d and f), modifying the electronic band structure. Importantly, SOC effects are greatly enhanced in reduced dimensions (Fig. 1, left and right). First, inversion symmetry is broken at the surface or interface, and the resultant electric field couples to the spin of itinerant electrons. This phenomenon, known as Rashba SOC 1 , produces spin-split dispersion even at the surfaces of conventional metals (such as Au and Bi) 2. Recently discovered topological insulators, have spin-polarized surface states with additional topological properties. In both these cases, strong two-dimensional (2D) SOC locks the electron spin and momentum. Spin-momentum locking in 2D geometries has direct consequences for the interplay between the charge and spin transport (Fig. 1, top left). An in-plane charge current induces a transverse spin accumulation (uniform non-zero spin density). This spin accumulation can be used to eject a spin current into an adjacent layer (Edelstein effect 3). Conversely, the injection of a spin current induces the associated spin polarization and charge current in the 2D states. Other types of conversion between charge and spin currents can also be obtained by SOC effects in three-dimensional (3D) conductors, namely the spin Hall effect of heavy metals 4 ; however, the observed effects in two dimensions are considerably enhanced. Such spin-charge conversion phenomena have direct applications for spintronics technologies, which are based on the creation and detection of spin currents 5. Given that the 3D spin Hall effect is already used in spintronics devices 6 , the observed effects in two dimensions offer much promise for device applications (Fig. 1, top). The interplay between SOC and magnetism is of increasing importance. In conventional magnetic materials, ferromagnetic order, which results from exchange interaction, aligns neighbouring spins. A well-known consequence of SOC is magneto-crystalline anisotropy-the preferential alignment of electron moments along certain crystallographic directions ('easy axes'), via the coupling of electron motion to the crystalline lattice field. In systems that lack inversion symmetry, SOC induces a chiral Dzyaloshinskii-Moriya interaction (DMI) 7,8 , which takes the form: = − × ⋅ S S D H () (1) DM 1 2 12 Here S 1 and S 2 are neighbouring spins and D 12 is the Dzyaloshinskii-Moriya vector. The DMI is a chiral interaction that decreases or increases the energy of the spins depending on whether the rotation from S 1 to S 2 around D 12 is clockwise or anticlockwise. If S 1 and S 2 are initially parallel, then the effect of a sufficiently strong DMI (with respect to exchange and anisotropy) is to introduce a tilt around D 12. DMI was initially understood as a super-exchange interaction in magnetic insu-lators 7,8 , and later extended to non-centrosymmetric magnetic metals 9. In a disordered magnetic alloy, a large SOC element could mediate such an interaction between two nearby magnetic atoms, with the resulting Dzyaloshinskii-Moriya vector being perpendicular to the plane formed by the three atoms. Crucially, this model was extended to magnetic mul-tilayers, wherein inversion symmetry is broken by the presence of an interface 10 (Fig. 1, bottom right). The existence of interfacial DMI was first demonstrated by the observation of spiral-like spatial modulations of the spin orientation with a winding periodicity related to the magnitude of the DMI (ref. 11). DMI also enables the formation of other chiral spin structures-in particular, chiral domain walls and skyrmions-that are possibly relevant to next-generation information storage devices (Fig. 1, bottom). Recent developments in the techniques for thin-film growth and in the capabilities of ab initio calculations have enabled the synthesis of atomically flat surfaces and heterostructures, and the prediction of their electronic properties. A common thread across several such thin-film materials and heterostructures-heavy metal compounds and multilayers-is that the SOC strength at surfaces and interfaces is comparable to the other relevant energy scales, and so plays a pivotal part. In combination with surface and interface effects, this engenders fundamentally new spin-based phenomena that are robust to disorder and thermal fluctuations, with much promise for room-temperature spin-based applications. Here we describe these diverse low-dimensional spin-based phenomena in the context of their SOC origin. We begin by detailing the progress on spin-polarized states at the surfaces of topological insulators, Rashba 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.