Electric Field Tuning of the Rashba Effect in the Polar Perovskite Structures

Abstract

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...

Nonzero Berry phase in quantum oscillations from giant Rashba-type spin splitting in LaTiO3/SrTiO3 heterostructures

“…Tight-binding calculations have shown that the d xy , d xz , and d yz orbitals all give rise to a linear Rashba-type splitting 29,32,33 , so the above frequencies and effective masses can be used to estimate the Rashba-type coupling constant responsible for the splitting of the hybridized d xz+yz band. In order to properly model the properties of the hybridized d xz+yz band, we extended the tight-binding model described by Rödel et al 34 to include a linear Rashba-type splitting (see Supplementary Note 5).…”

Anisotropic electronic transport of the two-dimensional electron system in Al2O3/SrTiO3 heterostructures

“…The polar discontinuity at the LAO/STO interface leads to a rather strong Rashba-type SOC [7] and is considered to play an important role with respect to interfacial conductivity [8].…”

Electronic structure and anisotropic Rashba spin-orbit coupling in monolayer black phosphorus

“…41 In the present case of BP, however, since the SOC is small and the energies of the p x and p y states that would spinorbit couple to the p z orbitals making up the valence and conduction band extrema are far away in energy, the pseudospins are nearly spin pure states |p z ↑ and |p z ↓ .…”

“…These ideas are well known in the literature and developed further in our recent work on Rashba effect in the d electron solids. 36,41 Rashba Hamiltonian (Anisotropic case) -Now, consider the case with an anisotropic mass, with the effective mass tensor [m * −1 ( k)] ij =h −2 ∂ 2 ε( k)/∂k i ∂k j and the velocity v i =h −1 ∂ε( k)/∂k i =h j [m * −1 ] ij k j . A straightforward generalization of the isotropic case yields the desired anisotropic Rashba Hamiltonian…”