Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

Enhanced Nonlinear Response by Manipulating the Dirac Point at the (111) LaTiO_{3}/SrTiO_{3} Interface

Tunable spin-orbit interaction (SOI) is an important feature for future spin-based devices. In the presence of a magnetic field, SOI induces an asymmetry in the energy bands, which can produce nonlinear transport effects (V∼I^{2}). Here, we focus on such effects to study the role of SOI in the (111) LaTiO_{3}/SrTiO_{3} interface. This system is a convenient platform for understanding the role of SOI since it exhibits a single-band Hall response through the entire gate-voltage range studied. We report a pronounced rise in the nonlinear longitudinal resistance at a critical in-plane field H_{cr}. This rise disappears when a small out-of-plane field component is present. We explain these results by considering the location of the Dirac point formed at the crossing of the spin-split energy bands. An in-plane magnetic field pushes this point outside of the Fermi contour, and consequently changes the symmetry of the Fermi contours and intensifies the nonlinear transport. An out-of-plane magnetic field opens a gap at the Dirac point, thereby significantly diminishing the nonlinear effects. We propose that magnetoresistance effects previously reported in interfaces with SOI could be comprehended within our suggested scenario.

Review of Systematic Tendencies in (001), (011) and (111) Surfaces Using B3PW as Well as B3LYP Computations of BaTiO3, CaTiO3, PbTiO3, SrTiO3, BaZrO3, CaZrO3, PbZrO3 and SrZrO3 Perovskites

We performed B3PW and B3LYP computations for BaTiO3 (BTO), CaTiO3 (CTO), PbTiO3 (PTO), SrTiO3 (STO), BaZrO3 (BZO), CaZrO3 (CZO), PbZrO3 (PZO) and SrZrO3 (SZO) perovskite neutral (001) along with polar (011) as well as (111) surfaces. For the neutral AO- as well as BO2-terminated (001) surfaces, in most cases, all upper-layer atoms relax inwards, although the second-layer atoms shift outwards. On the (001) BO2-terminated surface, the second-layer metal atoms, as a rule, exhibit larger atomic relaxations than the second-layer O atoms. For most ABO3 perovskites, the (001) surface rumpling s is bigger for the AO- than BO2-terminated surfaces. In contrast, the surface energies, for both (001) terminations, are practically identical. Conversely, different (011) surface terminations exhibit quite different surface energies for the O-terminated, A-terminated and BO-terminated surfaces. Our computed ABO3 perovskite (111) surface energies are always significantly larger than the neutral (001) as well as polar (011) surface energies. Our computed ABO3 perovskite bulk B-O chemical bond covalency increases near their neutral (001) and especially polar (011) surfaces.

Enhancement of the Rashba Effect in a Conducting SrTiO3 Surface by MoO3 Capping

Systems having inherent structural asymmetry retain the Rashba-type spin-orbit interaction, which ties the spin and momentum of electrons in the band structure, leading to coupled spin and charge transport. One of the electrical manifestations of the Rashba spin-orbit interaction is nonreciprocal charge transport, which could be utilized for rectifying devices. Further tuning of the Rashba spin-orbit interaction allows additional functionalities in spin-orbitronic applications. In this work, we present our study of nonreciprocal charge transport in a conducting SrTiO3 (001) surface and its significant enhancement by a capping layer. The conductive strontium titanate SrTiO3 (STO) (001) surface was created through oxygen vacancies by Ar+ irradiation, and the nonreciprocal signal was probed by angle- and magnetic field-dependent second harmonic voltage measurement with an AC current. We observed robust directional transport in the Ar+-irradiated sample at low temperatures. The magnitude of the nonreciprocal signal is highly dependent on the irradiation time as it affects the depth of the conducting layer and the impact of the topmost conducting layer. Moreover, the nonreciprocal resistance was significantly enhanced by simply adding a MoO3 capping layer on the conductive STO surface. These results show a simple methodology for tuning and investigating the Rashba effect in a conductive STO surface, which could be adopted for various two-dimensional (2D) conducting layers for spin-orbitronic applications.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO₃ two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Visualization of the Rashbasplit bands in oxide two-dimensional electron gases is lacking, which hampers understanding of their rich spin-orbit physics. Here, the authors investigate KTaO₃ two dimensional electron gases and their Rashba-split bands.

Rashba splitting in organic-inorganic lead-halide perovskites revealed through two-photon absorption spectroscopy

The Rashba splitting in hybrid organic-inorganic lead-halide perovskites (HOIP) is particularly promising and yet controversial, due to questions surrounding the presence or absence of inversion symmetry. Here we utilize two-photon absorption spectroscopy to study inversion symmetry breaking in different phases of these materials. This is an all-optical technique to observe and quantify the Rashba effect as it probes the bulk of the materials. In particular, we measure two-photon excitation spectra of the photoluminescence in 2D, 3D, and anionic mixed HOIP crystals, and show that an additional band above, but close to the optical gap is the signature of new two-photon transition channels that originate from the Rashba splitting. The inversion symmetry breaking is believed to arise from ionic impurities that induce local electric fields. The observation of the Rashba splitting in the bulk of HOIP has significant implications for the understanding of their spintronic and optoelectronic device properties.

Universal Structural Influence on the 2D Electron Gas at SrTiO3 Surfaces

The 2-dimensional electron gas (2DEG) found at the surface of SrTiO3 and related interfaces has attracted significant attention as a promising basis for oxide electronics. In order to utilize its full potential, the response of this 2DEG to structural changes and surface modification must be understood in detail. Here, a study of the detailed electronic structure evolution of the 2DEG as a function of sample temperature and surface step density is presented. By comparing the experimental results with ab initio calculations, it is shown that local structure relaxations cause a metal-insulator transition of the system around 135 K. This study presents a new and simple way of tuning the 2DEG via surface vicinality and identifies how the operation of prospective devices will respond to changes in temperature.

Emerging perovskite monolayers

The library of two-dimensional (2D) materials has been enriched over recent years with novel crystal architectures endowed with diverse exciting functionalities. Bulk perovskites, including metal-halide and oxide systems, provide access to a myriad of properties through molecular engineering. Their tunable electronic structure offers remarkable features from long carrier-diffusion lengths and high absorption coefficients in metal-halide perovskites to high-temperature superconductivity, magnetoresistance and ferroelectricity in oxide perovskites. Emboldened by the 2D materials research, perovskites down to the monolayer limit have recently emerged. Like other 2D species, perovskites with reduced dimensionality are expected to exhibit new physics and to herald next-generation multifunctional devices. In this Review, we critically assess the preliminary studies on the synthetic routes and inherent properties of monolayer perovskite materials. We also discuss how to exploit them for widespread applications and provide an outlook on the challenges and opportunities that lie ahead for this enticing class of 2D materials.

Pure Spin Currents Driven by Colossal Spin-Orbit Coupling on Two-Dimensional Surface Conducting SrTiO3

Spin accumulation is generated by passing a charge current through a ferromagnetic layer and sensed by other ferromagnetic layers downstream. Pure spin currents can also be generated in which spin currents flow and are detected as a nonlocal resistance in which the charge current is diverted away from the voltage measurement point. Here, we report nonlocal spin-transport on two-dimensional surface-conducting SrTiO₃ (STO) without a ferromagnetic spin-injector via the spin Hall effect (and inverse spin Hall effect). By applying magnetic fields to the Hall bars at different angles to the nonlocal spin-diffusion, we demonstrate an anisotropic spin-signal that is consistent with a Hanle precession of a pure spin current. We extract key transport parameters for surface-conducting STO, including: a spin Hall angle of γ ≈ (0.25 ± 0.05), a spin lifetime of τ ∼ 49 ps, and a spin diffusion length of λ_s ≈ (1.23 ± 0.7) μm at 2 K.

Soft x-ray irradiation induced metallization of layered TiNCl

We have performed soft x-ray spectroscopy in order to study the photoirradiation time dependence of the valence band structure and chemical states of layered transition metal nitride chloride TiNCl. Under the soft x-ray irradiation, the intensities of the states near the Fermi level (E_F) and the Ti³⁺component increased, while the Cl 2pintensity decreased. Ti 2p-3dresonance photoemission spectroscopy confirmed a distinctive Fermi edge with Ti 3dcharacter. These results indicate the photo-induced metallization originates from deintercalation due to Cl desorption, and thus provide a new carrier doping method that controls the conducting properties of TiNCl.

Giant Zeeman-type spin splitting of free electron/hole states on quasi-2D perovskite niobates: a theoretical prediction

We study the spin-orbit interaction of two-dimensional electron/hole gas (2DEGs/2DHGs) on quasi-2D potassium niobates (KNs) via first-principles calculations. The strong surface polarity changes the free surface states from 2DEGs to 2DHGs. The in-plane dipole maintained on 2D models leads to giant Zeeman-type spin splitting, as high as 566 meV for the (001)_c facet KN and 1.21 eV for the (111)_c facet KN. The thickness-dependent Zeeman-type spin splitting shows a linear relation with respect to 1/r, while the corresponding in-plane polarization quantum has a linear relation of 1/(2^0.5)with respect to a decrease in thickness. Interestingly, the 2DHGs with molecular-like orbital character is solely constituted by O 2p states, showing logic switchable behavior at extremely thin samples with enormous Zeeman-type splitting that can switch between insulator and conductor by opposite spin polarization.

Planar Hall effect and anisotropic magnetoresistance in polar-polar interface of LaVO3-KTaO3 with strong spin-orbit coupling

Among the perovskite oxide family, KTaO₃ (KTO) has recently attracted considerable interest as a possible system for the realization of the Rashba effect. In this work, we report a novel conducting interface by placing KTO with another insulator, LaVO₃ (LVO) and report planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) measurements. This interface exhibits a signature of strong spin-orbit coupling. Our experimental observations of two fold AMR and PHE at low magnetic fields (B) is similar to those obtained for topological systems and can be intuitively understood using a phenomenological theory for a Rashba spin-split system. Our experimental data show a B² dependence of AMR and PHE at low magnetic fields that could also be explained based on our model. At high fields (~8 T), we see a two fold to four fold transition in the AMR that could not be explained using only Rashba spin-split energy spectra.

Two dimensional electron gas (2DEG) at oxide interfaces is promising in modern electronic devices. Here, Wadehra et al. realize 2DEG at a novel interface composed of LaVO₃ and KTaO₃, where strong spin-orbit coupling and relativistic nature of the electrons in the 2DEG, leading to anisotropic magnetoresistance and planar Hall effect.

Controlling a Van Hove singularity and Fermi surface topology at a complex oxide heterostructure interface

The emergence of saddle-point Van Hove singularities (VHSs) in the density of states, accompanied by a change in Fermi surface topology, Lifshitz transition, constitutes an ideal ground for the emergence of different electronic phenomena, such as superconductivity, pseudo-gap, magnetism, and density waves. However, in most materials the Fermi level, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{{\rm{F}}}$$\end{document}EF, is too far from the VHS where the change of electronic topology takes place, making it difficult to reach with standard chemical doping or gating techniques. Here, we demonstrate that this scenario can be realized at the interface between a Mott insulator and a band insulator as a result of quantum confinement and correlation enhancement, and easily tuned by fine control of layer thickness and orbital occupancy. These results provide a tunable pathway for Fermi surface topology and VHS engineering of electronic phases.

A singularity in a material’s density of states at the Fermi energy can drive the formation of unconventional electronic phases. Here the authors show a Van Hove singularity is tunable across the Fermi energy in an oxide heterostructure, leading to enhanced electronic correlations.

In-gap state generated by La-on-Sr substitutional defects within the bulk of SrTiO3

Local distortion in the conduction pathway has a significant influence on the conducting properties of oxides. The electronic states induced in the band gap of SrTiO3 by La doping were investigated using photoemission spectroscopy (PES) and soft X-ray emission spectroscopy (SXES); moreover, the local distortion in the conduction pathway was examined using extended X-ray absorption fine structure (EXAFS). An itinerant state and a localized state were observed as a metallic state and an in-gap state, respectively, in the PES spectra and as inelastic peaks in the SXES spectra. This implied that the itinerant state and the in-gap state coexisted within the bulk. From EXAFS results, it was observed that La doped into SrTiO3 substituted Sr and locally distorted the conduction pathway. The results showed that some electrons doped by La-on-Sr substitution are trapped/localized by the local distortion in the conduction pathway, whereas the remaining doped electrons itinerate in the pristine conduction pathway with no distortion.

Nonlinear Planar Hall Effect

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Diluted Oxide Interfaces with Tunable Ground States

The metallic interface between two oxide insulators, such as LaAlO₃ /SrTiO₃ (LAO/STO), provides new opportunities for electronics and spintronics. However, due to the presence of multiple orbital populations, tailoring the interfacial properties such as the ground state and metal-insulator transitions remains challenging. Here, an unforeseen tunability of the phase diagram of LAO/STO is reported by alloying LAO with a ferromagnetic LaMnO₃ insulator without forming lattice disorder and at the same time without changing the polarity of the system. By increasing the Mn-doping level, x, of LaAl_{1- x} Mn_x O₃ /STO (0 ≤ x ≤ 1), the interface undergoes a Lifshitz transition at x = 0.225 across a critical carrier density of n_c = 2.8 × 10¹³ cm^-2 , where a peak T_SC ≈255 mK of superconducting transition temperature is observed. Moreover, the LaAl_{1- x} Mn_x O₃ turns ferromagnetic at x ≥ 0.25. Remarkably, at x = 0.3, where the metallic interface is populated by only d_xy electrons and just before it becomes insulating, a same device with both signatures of superconductivity and clear anomalous Hall effect (7.6 × 10¹² cm^-2 < n_s ≤ 1.1 × 10¹³ cm^-2 ) is achieved reproducibly. This provides a unique and effective way to tailor oxide interfaces for designing on-demand electronic and spintronic devices.

A spin-orbit playground: surfaces and interfaces of transition metal oxides

Within the last twenty years, the status of the spin-orbit interaction has evolved from that of a simple atomic contribution to a key effect that modifies the electronic band structure of materials. It is regarded as one of the basic ingredients for spintronics, locking together charge and spin degrees of freedom and recently it is instrumental in promoting a new class of compounds, the topological insulators. In this review, we present the current status of the research on the spin-orbit coupling in transition metal oxides, discussing the case of two semiconducting compounds, [Formula: see text] and [Formula: see text], and the properties of surface and interfaces based on these. We conclude with the investigation of topological effects predicted to occur in different complex oxides.

Mechanical dissipation from charge and spin transitions in oxygen-deficient SrTiO3 surfaces

Bodies in relative motion separated by a gap of a few nanometers can experience a tiny friction force. This non-contact dissipation can have various origins and can be successfully measured by a sensitive pendulum atomic force microscope tip oscillating laterally above the surface. Here, we report on the observation of dissipation peaks at selected voltage-dependent tip-surface distances for oxygen-deficient strontium titanate (SrTiO₃) surface at low temperatures (T = 5 K). The observed dissipation peaks are attributed to tip-induced charge and spin state transitions in quantum-dot-like entities formed by single oxygen vacancies (and clusters thereof, possibly through a collective mechanism) at the SrTiO₃ surface, which in view of technological and fundamental research relevance of the material opens important avenues for further studies and applications.

Non-contact atomic force microscope (AFM) dissipation contains rich information on the electron, phonon and spin states, but has been poorly understood. Here the authors demonstrated that tip-induced charge and spin state transitions in oxygen vacancies at SrTiO₃ surface are revealed by AFM dissipation measurements.

n-type Rashba spin splitting in a bilayer inorganic halide perovskite with external electric field

Here, we investigated the Rashba effect of the CsPbBr₃ bilayers under the external electric field (EEF) with first-principles calculations. For the PbBr₂ terminated bilayer, we found that only electrons experience the Rashba splitting under EEF, while holes do not. Such an n-type Rashba effect can be ascribed to the surface relaxation effect that reverses the positions of the top valence bands. The n-type Rashba parameter can be tuned monotonically to the maximum of 0.88 eV Å at EEF of 1.35 V nm^-1 at which the sequence of top valence bands recover to the bulk style. During this process the p-type spins will not survive in this 2D CsPbBr₃, that indeed reveals a new way for making advanced functional spintronic devices.

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

The manipulation of the spin degrees of freedom in a solid has been of fundamental and technological interest recently for developing high-speed, low-power computational devices. There has been much work focused on developing highly spin-polarized materials and understanding their behavior when incorporated into so-called spintronic devices. These devices usually require spin splitting with magnetic fields. However, there is another promising strategy to achieve spin splitting using spatial symmetry breaking without the use of a magnetic field, known as Rashba-type splitting. Here we report evidence for a giant Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃. Analysis of the magnetotransport reveals anisotropic magnetoresistance, weak anti-localization and quantum oscillation behavior consistent with a large Rashba-type splitting. It is surprising to find a large Rashba-type splitting in 3d transition metal oxide-based systems such as the LaTiO₃/SrTiO₃ interface, but it is promising for the development of a new kind of oxide-based spintronics.

Rashba-type splitting is an effective way to manipulate the spin degrees of freedom in a solid without external magnetic field. Here, the authors demonstrate a strong Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃ which is promising for the development of oxide-based spintronics.

Characterization and Manipulation of Spin Orbit Torque in Magnetic Heterostructures

Electrical-current-induced magnetization switching is a keystone concept in the development of spintronics devices. In the last few years, this field has experienced a significant boost with the discovery of spin orbit torque (SOT) in magnetic heterostructures. Here, the recent results as to the characterization and manipulation of SOT in various heavy-metal/ferromagnet heterostructures are summarized. First, different electrical measurement methods that allow the physical features of SOT to be revealed are introduced. Second, it is shown that SOT in magnetic heterostructures can be manipulated via various material engineering approaches. The interfacial and bulk contributions of SOT are also discussed. These results advance the understanding of SOT and provide novel approaches toward energy-efficient spintronic devices.

Discovery of a magnetic conductive interface in PbZr0.2Ti0.8O3 /SrTiO3 heterostructures

Emergent physical properties often arise at interfaces of complex oxide heterostructures due to the interplay between various degrees of freedom, especially those with polar discontinuities. It is desirable to explore if these structures may generate pure and controllable spin currents, which are needed to attain unmatched performance and energy efficiency in the next-generation spintronic devices. Here we report the emergence of a spin-polarized two-dimensional electron gas (SP-2DEG) at the interface of two insulators, SrTiO₃ and PbZr_0.2Ti_0.8O₃. This SP-2DEG is strongly localized at the interfacial Ti atoms, due to the interplay between Coulomb interaction and band bending, and can be tuned by the ferroelectric polarization. Our findings open a door for engineering ferroelectric/insulator interfaces to create tunable ferroic orders for magnetoelectric device applications and provide opportunities for designing multiferroic materials in heterostructures.

Two-dimensional electron gases that form in some complex oxide heterostructures may have useful functional behavior due to the interaction of the parent materials. Here the authors show that PZT/STO interfaces can host a spin-polarized electron gas, even though the bulk materials are nonmagnetic.

Physics of SrTiO3-based heterostructures and nanostructures: a review

This review provides a summary of the rich physics expressed within SrTiO3-based heterostructures and nanostructures. The intended audience is researchers who are working in the field of oxides, but also those with different backgrounds (e.g., semiconductor nanostructures). After reviewing the relevant properties of SrTiO3 itself, we will then discuss the basics of SrTiO3-based heterostructures, how they can be grown, and how devices are typically fabricated. Next, we will cover the physics of these heterostructures, including their phase diagram and coupling between the various degrees of freedom. Finally, we will review the rich landscape of quantum transport phenomena, as well as the devices that elicit them.

Quantum confined two-dimensional electron/hole gas switching by facet orientation of perovskite oxides

The Polar discontinuity at heterointerface and the bare surface reconstructs the electronic phase of perovskite oxides.

Angle-resolved photoemission spectroscopy studies of metallic surface and interface states of oxide insulators

Over the last decade, conducting states embedded in insulating transition metal oxides (TMOs) have served as gateways to discovering and probing surprising phenomena that can emerge in complex oxides, while also opening opportunities for engineering advanced devices. These states are commonly realized at thin film interfaces, such as the well-known case of LaAlO3 (LAO) grown on SrTiO3 (STO). In recent years, the use of angle-resolved photoemission spectroscopy (ARPES) to investigate the k-space electronic structure of such materials led to the discovery that metallic states can also be formed on the bare surfaces of certain TMOs. In this topical review, we report on recent studies of low-dimensional metallic states confined at insulating oxide surfaces and interfaces as seen from the perspective of ARPES, which provides a direct view of the occupied band structure. While offering a fairly broad survey of progress in the field, we draw particular attention to STO, whose surface is so far the best-studied, and whose electronic structure is probably of the most immediate interest, given the ubiquitous use of STO substrates as the basis for conducting oxide interfaces. The ARPES studies provide crucial insights into the electronic band structure, orbital character, dimensionality/confinement, spin structure, and collective excitations in STO surfaces and related oxide surface/interface systems. The obtained knowledge increases our understanding of these complex materials and gives new perspectives on how to manipulate their properties.

Controlled manipulation of oxygen vacancies using nanoscale flexoelectricity

Oxygen vacancies, especially their distribution, are directly coupled to the electromagnetic properties of oxides and related emergent functionalities that have implications for device applications. Here using a homoepitaxial strontium titanate thin film, we demonstrate a controlled manipulation of the oxygen vacancy distribution using the mechanical force from a scanning probe microscope tip. By combining Kelvin probe force microscopy imaging and phase-field simulations, we show that oxygen vacancies can move under a stress-gradient-induced depolarisation field. When tailored, this nanoscale flexoelectric effect enables a controlled spatial modulation. In motion, the scanning probe tip thereby deterministically reconfigures the spatial distribution of vacancies. The ability to locally manipulate oxygen vacancies on-demand provides a tool for the exploration of mesoscale quantum phenomena and engineering multifunctional oxide devices.The properties of complex oxides such as strontium titanate are strongly affected by the presence and distribution of oxygen vacancies. Here, the authors demonstrate that a scanning probe microscope tip can be used to manipulate vacancies by the flexoelectric effect.

Rashba and Dresselhaus Couplings in Halide Perovskites: Accomplishments and Opportunities for Spintronics and Spin-Orbitronics

In halide hybrid organic-inorganic perovskites (HOPs), spin-orbit coupling (SOC) presents a well-documented large influence on band structure. However, SOC may also present more exotic effects, such as Rashba and Dresselhaus couplings. In this Perspective, we start by recalling the main features of this effect and what makes HOP materials ideal candidates for the generation and tuning of spin-states. Then, we detail the main spectroscopy techniques able to characterize these effects and their application to HOPs. Finally, we discuss potential applications in spintronics and in spin-orbitronics in those nonmagnetic systems, which would complete the skill set of HOPs and perpetuate their ride on the crest of the wave of popularity started with optoelectronics and photovoltaics.

Giant Magnetic Band Gap in the Rashba-Split Surface State of Vanadium-Doped BiTeI: A Combined Photoemission and Ab Initio Study

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s-wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI. We show that the vanadium-induced magnetization in the 2DEG breaks time-reversal symmetry, lifting Kramers degeneracy of the Rashba-split surface state at the Brillouin zone center via formation of a huge gap of about 90 meV. As a result, the constant energy contour inside the gap consists of only one circle with spin-momentum locking. These findings reveal a great potential of the magnetically-doped semiconductors with a giant Rashba-type splitting for realization of novel states of matter.

Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin-Orbit and Exchange-Magnetic Interactions

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRh₂Si₂ appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

Interfacial memristors in Al–LaNiO3heterostructures

Self-assembled interfacial memristive systems in Al–LaNiO₃heterostructures.

Surface magnetism of strontium titanate

SrTiO₃ plays a central role in oxide electronics. It is the substrate of choice for functional oxide heterostructures based on perovskite-structure thin-film stacks, and its surface or interface with a polar oxide such as LaAlO₃ can become a 2D conductor because of electronic reconstruction or the presence of oxygen defects. Inconsistent reports of magnetic order in SrTiO₃ abound in the literature. Here, we report a systematic experimental study aimed at establishing how and when SrTiO₃ can develop a magnetic moment at room temperature. Polished (1 0 0), (1 1 0) or (1 1 1) crystal slices from four different suppliers are characterized before and after vacuum annealing at 750 °C, both in single-crystal and powdered form. Impurity content is analysed at the surface and in the bulk. Besides the underlying intrinsic diamagnetism of SrTiO₃, magnetic signals are of three types-a Curie law susceptibility due to dilute magnetic impurities at the ppm level, a hysteretic temperature-dependent ferromagnetic impurity contribution, and a practically anhysteretic defect-related temperature-independent component that saturates in about 200 mT. The latter component is intrinsic. It is often the largest, reaching 10 μ _B nm^-2 of the surface area or more and dominating the magnetic response in low fields at room temperature. It is associated with defects near the surface, and can be destroyed by treatment with Tiron (C₆H₄Na₂O₈S₂), an electron donor molecule that forms a strong complex with titanium at the surface. The origin of this unusual high-temperature ferromagnetic-like response is discussed.

Entanglement and manipulation of the magnetic and spin-orbit order in multiferroic Rashba semiconductors

Entanglement of the spin–orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelectric α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concentration, indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin–orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelectric and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our experimental results are supported by first-principles calculations of the electron and spin structure.

In α-GeTe, ferroelectric polarization acts to break inversion symmetry of the lattice and induce a strong Rashba-type spin splitting of the electronic band structure. Here, the authors study how this effect competes with Zeeman splitting due to ferromagnetic exchange coupling in Mn-doped GeTe.

In Situ Control of Separate Electronic Phases on SrTiO3 Surfaces by Oxygen Dosing

Insulating SrTiO3 (STO) can host 2D electron systems (2DESs) on its surfaces, caused by oxygen defects. This study shows that the STO surface exhibits phase separation once the 2DES is formed and relates this inhomogeneity to recently reported magnetic order at STO surfaces and interfaces. The results open pathways to exploit oxygen defects for engineering the electronic and magnetic properties of oxides.

Nonvortical Rashba Spin Structure on a Surface with C_{1h} Symmetry

A totally anisotropic peculiar Rashba-Bychkov (RB) splitting of electronic bands was found on the Tl/Si(110)-(1×1) surface with C_{1h} symmetry by angle- and spin-resolved photoelectron spectroscopy and first-principles theoretical calculation. The constant energy contour of the upper branch of the RB split band has a warped elliptical shape centered at a k point located between Γ[over ¯] and the edge of the surface Brillouin zone, i.e., at a point without time-reversal symmetry. The spin-polarization vector of this state is in-plane and points almost the same direction along the whole elliptic contour. This novel nonvortical RB spin structure is confirmed as a general phenomenon originating from the C_{1h} symmetry of the surface.

Imaging of room-temperature ferromagnetic nano-domains at the surface of a non-magnetic oxide

Two-dimensional electron gases at oxide surfaces or interfaces show exotic ordered states of matter, like superconductivity, magnetism or spin-polarized states, and are a promising platform for alternative oxide-based electronics. Here we directly image a dense population of randomly distributed ferromagnetic domains of ∼40 nm typical sizes at room temperature at the oxygen-deficient surface of SrTiO₃, a non-magnetic transparent insulator in the bulk. We use laser-based photoemission electron microscopy, an experimental technique that gives selective spin detection of the surface carriers, even in bulk insulators, with a high spatial resolution of 2.6 nm. We furthermore find that the Curie temperature in this system is as high as 900 K. These findings open perspectives for applications in nano-domain magnetism and spintronics using oxide-based devices, for instance through the nano-engineering of oxygen vacancies at surfaces or interfaces of transition-metal oxides.

The surfaces of transition metal oxides exhibit a wide range of functional behaviours, from magnetism to superconductivity. Here, the authors use high-resolution microscopy to image the temperature dependent development of nanoscale ferromagnetic domains on an oxygen-deficient SrTiO₃ surface.

Anomalous enhancement of the sheet carrier density beyond the classic limit on a SrTiO3 surface

Electrostatic carrier accumulation on an insulating (100) surface of SrTiO₃ by fabricating a field effect transistor with Parylene-C (6 nm)/HfO₂ (20 nm) bilayer gate insulator has revealed a mystifying phenomenon: sheet carrier density is about 10 times as large as ( is the sheet capacitance of the gate insulator, V_G is the gate voltage, and e is the elementary charge). The channel is so clean to exhibit small subthreshod swing of 170 mV/decade and large mobility of 11 cm²/Vs for of 1 × 10¹⁴ cm⁻² at room temperature. Since does not depend on either V_G nor time duration, beyond is solely ascribed to negative charge compressibility of the carriers, which was in general considered as due to exchange interactions among electrons in the small limit. However, the observed is too large to be naively understood by the framework. Alternative ideas are proposed in this work.

Rashba coupling amplification by a staggered crystal field

There has been increasing interest in materials where relativistic effects induce non-trivial electronic states with promise for spintronics applications. One example is the splitting of bands with opposite spin chirality produced by the Rashba spin-orbit coupling in asymmetric potentials. Sizable splittings have been hitherto obtained using either heavy elements, where this coupling is intrinsically strong, or large surface electric fields. Here by means of angular resolved photoemission spectroscopy and first-principles calculations, we give evidence of a large Rashba coupling of 0.25 eV Å, leading to a remarkable band splitting up to 0.15 eV with hidden spin-chiral polarization in centrosymmetric BaNiS₂. This is explained by a huge staggered crystal field of 1.4 V Å⁻¹, produced by a gliding plane symmetry, that breaks inversion symmetry at the Ni site. This unexpected result in the absence of heavy elements demonstrates an effective mechanism of Rashba coupling amplification that may foster spin-orbit band engineering.

Future spintronic devices may exploit spin-orbit interactions, which often emerge from broken symmetries and strongly influence electronic behaviour. Here, the authors evidence the amplification of Rashba coupling by a crystal field that breaks the local inversion symmetry at the Ni site in BaNiS₂.

Magnetism, Spin Texture, and In-Gap States: Atomic Specialization at the Surface of Oxygen-Deficient SrTiO_{3}

Motivated by recent spin- and angular-resolved photoemission (SARPES) measurements of the two-dimensional electronic states confined near the (001) surface of oxygen-deficient SrTiO_{3}, we explore their spin structure by means of ab initio density functional theory (DFT) calculations of slabs. Relativistic nonmagnetic DFT calculations display Rashba-like spin winding with a splitting of a few meV and when surface magnetism on the Ti ions is included, bands become spin-split with an energy difference ∼100  meV at the Γ point, consistent with SARPES findings. While magnetism tends to suppress the effects of the relativistic Rashba interaction, signatures of it are still clearly visible in terms of complex spin textures. Furthermore, we observe an atomic specialization phenomenon, namely, two types of electronic contributions: one is from Ti atoms neighboring the oxygen vacancies that acquire rather large magnetic moments and mostly create in-gap states; another comes from the partly polarized t_{2g} itinerant electrons of Ti atoms lying further away from the oxygen vacancy, which form the two-dimensional electron system and are responsible for the Rashba spin winding and the spin splitting at the Fermi surface.

Multiple Coexisting Dirac Surface States in Three-Dimensional Topological Insulator PbBi₆Te₁₀

By means of angle-resolved photoemission spectroscopy (ARPES) measurements, we unveil the electronic band structure of three-dimensional PbBi6Te10 topological insulator. ARPES investigations evidence multiple coexisting Dirac surface states at the zone-center of the reciprocal space, displaying distinct electronic band dispersion, different constant energy contours, and Dirac point energies. We also provide evidence of Rashba-like split states close to the Fermi level, and deeper M- and V-shaped bands coexisting with the topological surface states. The experimental findings are in agreement with scanning tunneling microscopy measurements revealing different surface terminations according to the crystal structure of PbBi6Te10. Our experimental results are supported by density functional theory calculations predicting multiple topological surface states according to different surface cleavage planes.

Direct-Write X-ray Nanopatterning: A Proof of Concept Josephson Device on Bi2Sr2CaCu2O8+δ Superconducting Oxide

We describe the first use of a novel photoresist-free X-ray nanopatterning technique to fabricate an electronic device. We have produced a proof-of-concept device consisting of a few Josephson junctions by irradiating microcrystals of the Bi2Sr2CaCu2O8+δ (Bi-2212) superconducting oxide with a 17.6 keV synchrotron nanobeam. Fully functional devices have been obtained by locally turning the material into a nonsuperconducting state by means of hard X-ray exposure. Nano-XRD patterns reveal that the crystallinity is substantially preserved in the irradiated areas that there is no evidence of macroscopic crystal disruption. Indications are that O ions have been removed from the crystals, which could make this technique interesting also for other oxide materials. Direct-write X-ray nanopatterning represents a promising fabrication method exploiting material/material rather than vacuum/material interfaces, with the potential for nanometric resolution, improved mechanical stability, enhanced depth of patterning, and absence of chemical contamination with respect to traditional lithographic techniques.

Universal Fabrication of 2D Electron Systems in Functional Oxides

2D electron systems (2DESs) in functional oxides are promising for applications, but their fabrication and use, essentially limited to SrTiO3 -based heterostructures, are hampered by the need for growing complex oxide overlayers thicker than 2 nm using evolved techniques. It is demonstrated that thermal deposition of a monolayer of an elementary reducing agent suffices to create 2DESs in numerous oxides.

Rashba and Dresselhaus Effects in Hybrid Organic-Inorganic Perovskites: From Basics to Devices

We use symmetry analysis, density functional theory calculations, and k·p modeling to scrutinize Rashba and Dresselhaus effects in hybrid organic-inorganic halide perovskites. These perovskites are at the center of a recent revolution in the field of photovoltaics but have also demonstrated potential for optoelectronic applications such as transistors and light emitters. Due to a large spin-orbit coupling of the most frequently used metals, they are also predicted to offer a promising avenue for spin-based applications. With an in-depth inspection of the electronic structures and bulk lattice symmetries of a variety of systems, we analyze the origin of the spin splitting in two- and three-dimensional hybrid perovskites. It is shown that low-dimensional nanostructures made of CH3NH3PbX3 (X = I, Br) lead to spin splittings that can be controlled by an applied electric field. These findings further open the door for a perovskite-based spintronics.

Spin-orbit coupling at surfaces and 2D materials

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Electronic Degeneracy and Intrinsic Magnetic Properties of EpitaxialNb: SrTiO3 Thin Films Controlled by Defects

We report thermoelectric power experiments in e-doped thin films of SrTiO3 (STO) which demonstrate that the electronic band degeneracy can be lifted through defect management during growth. We show that even small amounts of cationic vacancies, combined with epitaxial stress, produce a homogeneous tetragonal distortion of the films, resulting in a Kondo-like resistance upturn at low temperature, large anisotropic magnetoresistance, and nonlinear Hall effect. Ab initio calculations confirm a different occupation of each band depending on the degree of tetragonal distortion. The phenomenology reported in this Letter for tetragonally distorted e-doped STO thin films, is similar to that observed in LaAlO3/STO interfaces and magnetic STO quantum wells.

Observation of correlated spin-orbit order in a strongly anisotropic quantum wire system

Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate and the associated quasiparticle gap decrease simultaneously as the screened Coulomb interaction decreases with increasing excess coverage, providing a new mechanism for generating and manipulating a spin-orbit entanglement effect via electronic interaction. Despite clear evidence of spontaneous spin-rotation symmetry breaking and modulation of spin-momentum structure as a function of excess coverage, the average spin polarization over the Brillouin zone vanishes, indicating that time-reversal symmetry is intact as theoretically predicted.

Antiferromagnetism of two-dimensional electronic gas on light-irradiated SrTiO3 and at LaAlO3/SrTiO3 interfaces

To gain an insight into the origin of tunable two-dimensional (2D) electronic liquid at the interfaces of transition-metal oxides, we address properties of a conducting layer on the light-irradiated surfaces of SrTiO3; the energy spectrum of the latter is known and consists of the titanium dxz/dyz and dxy bands. Recently, Santander-Syro et al (2014 Nature Mater. 13 1085) revealed that the dxy bands actually comprise two chiral branches with the Kramers degeneracy at the zone center lifted in the absence of a magnetic moment. We suggest that interacting electrons on the irradiated SrTiO3 go over into a magnetic phase as the result of one of the instabilities of the 2D Fermi liquid with exchange interactions, and point out the concrete antiferromagnetic order parameter. Large energy scales of the order of Fermi energy ∼0.1 eV inherent in this mechanism warrant stability of the magnetic ground state against ever-present effects of disorder. Arguments are given that electrons at the irradiated SrTiO3 surface and at the LaAlO3/SrTiO3 interfaces undergo a kind of first-order transformation into one and the same phase of the 2D electronic Fermi liquid with reduced magnetic symmetry.

Engineering two-dimensional superconductivity and Rashba spin-orbit coupling in LaAlO₃/SrTiO₃ quantum wells by selective orbital occupancy

The discovery of two-dimensional electron gases (2DEGs) at oxide interfaces-involving electrons in narrow d-bands-has broken new ground, enabling the access to correlated states that are unreachable in conventional semiconductors based on s- and p- electrons. There is a growing consensus that emerging properties at these novel quantum wells-such as 2D superconductivity and magnetism-are intimately connected to specific orbital symmetries in the 2DEG sub-band structure. Here we show that crystal orientation allows selective orbital occupancy, disclosing unprecedented ways to tailor the 2DEG properties. By carrying out electrostatic gating experiments in LaAlO3/SrTiO3 wells of different crystal orientations, we show that the spatial extension and anisotropy of the 2D superconductivity and the Rashba spin-orbit field can be largely modulated by controlling the 2DEG sub-band filling. Such an orientational tuning expands the possibilities for electronic engineering of 2DEGs at LaAlO3/SrTiO3 interfaces.