We show that the Rashba spin-orbit interaction in d electron solids, which originates from the broken inversion symmetry at surfaces or interfaces, is strongly dependent on the orbital characters of the bands involved. This is studied by developing a tight-binding model in the presence of a uniform perpendicular electric field and spin-orbit coupling. We argue that for valence electrons, the spin-orbit coupling strength scales only as the square of the atomic number. The electric field distorts the d orbitals through admixture of p and f states and also introduces new inter-site overlap parameters. Expressions for Rashba coefficients for the bands are obtained in both weak and strong spin-orbit interaction limits and are shown to be orbital dependent. The results are compared with first-principles calculations for model systems, showing good agreement. Our study demonstrates the orbital dependent gate control of the Rashba effect for the purposes of oxide electronics.

We show that the Rashba effect at the polar perovskite surfaces and interfaces can be tuned by manipulating the two-dimensional electron gas (2DEG) by an applied electric field, using it to draw the 2DEG out to the surface or push it deeper into the bulk, thereby controlling the surfacesensitive phenomenon. These ideas are illustrated by a comprehensive density-functional study of the recently-discovered polar KTaO3 surface. Analytical results obtained with a tight-binding model unravel the interplay between the various factors affecting the Rashba effect such as the strength of the spin-orbit interaction and the surface-induced asymmetry. Our work helps interpret the recent experiments on the KTaO3 surface as well as the SrTiO3/LaAlO3 interface.PACS numbers: 71.70. Ej,The Rashba effect describes the momentum-dependent spin splitting of the electron states at a surface or interface and is the combined result of the spin-orbit interaction (SOI) and the inversion-symmetry breaking[1]. It is commonly described by the Hamiltonianwhere k and σ are the electron momentum and spin,ẑ is along the surface normal, and α R is the Rashba coefficient, which leads to the linear spin splitting in the band structure ε k =hThe control of the Rashba effect by an applied electric field is at the heart of a class of proposed spintronics devices for manipulating the electron spin [2]. The perovskite interfaces [3, 4] are expected to have a much larger Rashba effect than their semiconductor counterparts [5], owing to the presence of high Z elements and a strongly localized 2DEG formed by the polar catastrophe. In fact, a strong Rashba effect was recently observed in the LaAlO 3 /SrTiO 3 interface [6, 7], which also showed an ill-understood asymmetric dependence on the direction of the applied electric field.In this Letter, we show that the polar perovskite structures constitute an excellent system for the field control of the Rashba effect, aided by the relative ease with which the 2DEG can be manipulated in these polar structures. Detail density-functional results are presented for the KTaO 3 (KTO) surface to illustrate the ideas.2DEG at the KTO surface -The KTaO 3 (KTO) surface is an ideal system for the study of the Rashba effect because Ta is a high Z element with strong SOI, a polar-catastrophe induced 2DEG has been observed there recently [8, 9] similar to the LAO/STO interface, and finally a surface rather than an interface is more easily amenable to external electric fields. Fig. 1 shows the basic features of the 2DEG formed at the KTO surface obtained from our calculations using density-functional theory (DFT), performed with the GGA functional and the projector augmented wave pseudopotential method as implemented in the Vienna ab initio simulation package [10,11]. To simulate the TaO 2 -terminated surface, we used a slab geometry consisting of 17 TaO 2 and 16 KO alternating layers corresponding to the formula unit (KTO) 16.5 and 24Å of vacuum. We studied the Rashba effect by applying a series of electric fields and by full...

The metallic helimagnet MnSi has been found to exhibit skyrmionic spin textures when subjected to magnetic fields at low temperatures. The Dzyaloshinskii-Moriya (DM) interaction plays a key role in stabilizing the skyrmion state. With the help of first-principles calculations, crystal field theory and a tight-binding model we study the electronic structure and the origin of the DM interaction in the B20 phase of MnSi. The strength of D parameter is determined by the magnitude of the spin-orbit interaction and the degree of orbital mixing, induced by the symmetry-breaking distortions in the B20 phase. Our calculations suggest strong coupling between Mn-d and Si-p states, which is consistent with a mixed valence ground state |d 7−x p 2+x configuration. Consistent with previous calculations, we find that DFT+U leads to the experimental magnetic moment of 0.4 µB, which redistributes electrons between the majority and minority spin channels. We derive the magnetic interaction parameters J and D for Mn-Si-Mn superexchange paths using Moriya's theory assuming the interaction to be mediated by eg electrons near the Fermi level. Using parameters from our calculations, we get reasonable agreement with the observations.

We present a systematic method for developing a five band Hamiltonian for the metal d orbitals that can be used to study the effect of electric and magnetic fields on multilayer MX 2 (M=Mo,W and X=S,Se) systems. On a hexagonal lattice of d orbitals, the broken inversion symmetry of the monolayers is incorporated via fictitious s orbitals at the chalcogenide sites. A tight-binding Hamiltonian is constructed and then downfolded to get effective d orbital overlap parameters using quasidegenerate perturbation theory. The steps to incorporate the effects of multiple layers, external electric and magnetic fields are also detailed. We find that an electric field produces a linear-k Rashba splitting around the Γ point, while a magnetic field removes the valley pseudospin degeneracy at the ±K points. Our model provides a simple tool to understand the recent experiments on electric and magnetic control of valley pseudospin in monolayer dichalcogendies.