Rashba effect at magnetic metal surfaces

Abstract

We give experimental and theoretical evidence of the Rashba effect at the magnetic rare-earth metal surface Gd(0001). The Rashba effect is substantially enhanced and the Rashba parameter changes its sign when a metal-oxide surface layer is formed. The experimental observations are quantitatively described by ab initio calculations that give a detailed account of the near-surface charge density gradients causing the Rashba effect. Since the sign of the Rashba splitting depends on the magnetization direction, the findings open up new opportunities for the study of surface and interface magnetism.PACS numbers: 71.70. Ej, A key issue in condensed-matter research aiming at future spintronic devices [1] is to control and manipulate the electron spin in a two-dimensional electron gas (2DEG) of semiconductor systems without the need of applying an external magnetic field. Rashba had realized early on [2] that this can be achieved by an electric field which acts as a magnetic field in the rest frame of a moving electron. The interaction between the spin s of a moving electron of momentumhk with an electric field oriented along the z-axis e z is described by the Rashba HamiltonianThe Rashba parameter α R is proportional to the electric field and depends on the effective, material-dependent spin-orbit coupling (SOC) strength. In nonmagnetic systems the Rashba effect lifts the spin-degeneracy of the energy dispersion ǫ(k) of an electronic state, and the energy difference between ǫ ↑ (k) and ǫ ↓ (k) is called Rashba splitting ∆ǫ(k) = α R |k|. Even though spintronic research currently focuses on spin-polarized electrons in semiconductors [3,4], it is important to explore the Rashba effect in other material classes as well. A necessary condition for the Rashba effect to occur is the absence of inversion symmetry and, while in the proposed FET-type spin transistor [5] a gate voltage must be applied to break inversion symmetry of the 2DEG, this condition is naturally fulfilled by the structural inversion asymmetry (SIA) existing at any crystal surface or interface. Owing to SIA, electrons in a two-dimensional surface or interface state experience an effective crystal potential gradient perpendicular to their plane of propagation, hereby optimizing (e z × k) in Eq. (1). One should expect that the Rashba effect is a general surface and interface phenomenon, but up to now Rashba splittings have only been observed for surface states at Au(111) [6,7] and W(110) [8,9]. Recently relativistic density functional theory (DFT) calculations were able to reproduce the observed splitting of the Au sp-like surface state [10] and the analogy to a 2DEG has been pointed out [11]. Yet, it is still a challenging task to give a physical picture of the Rashba effect from the electronic structure point of view.This Letter presents the first experimental and theoretical evidence of a Rashba splitting of exchange-split two-dimensional electron states. Using the surface state of ferromagnetic Gd metal as example we report on the novel finding of a k-depe...

Current-induced spin–orbit torques

“…This was first recognized in angle-resolved photoemission measurements of the surface states of non-magnetic 5d elements, in particular Au [32,80,81], W [82] and Bi [83]. Investigations of rare-earth surface states, notably of Gd [34] and Tb [42], later revealed clear signatures of coexisting Rashba and exchange coupling in the case of FM metal films in the form of magnetization-dependent asymmetry of the electron band dispersion, similar to that sketched in figure 2c. These studies coincide in showing that a heavy metal interface induces large Rashba splittings of the order of 100 meV and that increasing the asymmetry of the charge distribution at a metal surface leads to an increase of such an effect [34,84,85], in agreement with equation (2.6).…”

“…Equations (2.1)-(2.3) are relevant not only for quantum well structures in zinc blende semiconductors [21,29,30], but also for (Ga,Mn)As films [18] and metal/semiconductor layers such as Fe/GaAs [31]. In the case of metal surfaces [32,33] and metal layers deposited between asymmetric cubic and amorphous interfaces [19,34], g = b = l = 0, i.e. only the Rashba interaction survives.…”

“…The orientation of B SO (k) in four particular cases is shown in figure 1. Note that, in the presence of an external magnetic field [41] or exchange splitting [34,42,43], both time-reversal and inversion symmetry may be broken, leading to a more complex relationship between k and spin depending on the relative strength of the SO relative to exchange splitting ( §4a). In real two-dimensional systems, the point-group symmetry of the surface lattice and the presence of in-plane electric field gradients between dissimilar atomic species may further lead to out-of-plane components of the k-dependent spin polarization [39,44].…”

Spin relaxation and spin Hall transport in5dtransition-metal ultrathin films

“…Owing to the breaking of translational symmetry in thin films, many parameters have to be taken into account, such as the thickness and the crystalline orientation of the films. Importantly, Rashba surface states 26,27 can be formed around the Fermi level and they were shown to enhance the spin-flip relaxation rate. 23,28,29 Thin film is a keyword for reducing the size of spintronics devices.…”

Theoretical Investigation of the Interfaces and Mechanisms of Induced Spin Polarization of 1D Narrow Zigzag Graphene- and h-BN Nanoribbons on a SrO-Terminated LSMO(001) Surface

“…19 For nonmagnetic surfaces, the Rashba field lifts the spin degeneracy of the surface states, 19 whereas for magnetic ones, it leads to an asymmetric shift of the spin nondegenerate bands. 20 Using both experimental and theoretical approaches it was found that indirect exchange interactions between transitional metal ions mediated by oxygen ions of the crystalline lattices play a critical role in formation of the main features in the electronic structure of complex manganites 21,22 in accordance with RKKY mechanism. [23][24][25] The photoemission and X-ray spectroscopy 26,27 revealed antiferromagnetic bonding of the oxygen holes with spin configurations of Mn +3 ions in La 1-x Sr x MnO 3 .…”