Tunable Rashba spin-orbit interaction at oxide interfaces

Tuning the interface conductivity of LaAlO3/SrTiO3 using ion beams: implications for patterning

Patterning of the two-dimensional electron gas formed at the interface of two band insulators such as LaAlO3/SrTiO3 is one of the key challenges in oxide electronics. The use of energetic ion beam exposure for engineering the interface conductivity has been investigated. We found that this method can be utilized to manipulate the conductivity at the LaAlO3/SrTiO3 interface by carrier localization, arising from the defects created by the ion beam exposure, eventually producing an insulating ground state. This process of ion-beam-induced defect creation results in structural changes in SrTiO3 as revealed by the appearance of first-order polar TO2 and TO4 vibrational modes which are associated with Ti-O bonds in the Raman spectra of the irradiated samples. Furthermore, significant observation drawn from the magnetotransport measurements is that the irradiated (unirradiated) samples showed a negative (positive) magnetoresistance along with simultaneous emergence of first-order (only second order) Raman modes. In spectroscopic ellipsometry measurements, the optical conductivity features of the irradiated interface are broadened because of the localization effects, along with a decrease of spectral weight from 4.2 to 5.4 eV. These experiments allow us to conclude that the interface ground state (metallic/insulating) at the LaAlO3/SrTiO3 can be controlled by tailoring the defect structure of the SrTiO3 with ion beam exposure. A resist-free, single-step direct patterning of a conducting LaAlO3/SrTiO3 interface has been demonstrated. Patterns with a spatial resolution of 5 μm have been fabricated using a stencil mask, while nanometer scale patterns may be possible with direct focused ion beam writing.

Locally enhanced conductivity due to the tetragonal domain structure in LaAlO3/SrTiO3 heterointerfaces

The ability to control materials properties through interface engineering is demonstrated by the appearance of conductivity at the interface of certain insulators, most famously the {001} interface of the band insulators LaAlO3 and TiO2-terminated SrTiO3 (STO; refs 1, 2). Transport and other measurements in this system show a plethora of diverse physical phenomena. To better understand the interface conductivity, we used scanning superconducting quantum interference device microscopy to image the magnetic field locally generated by current in an interface. At low temperature, we found that the current flowed in conductive narrow paths oriented along the crystallographic axes, embedded in a less conductive background. The configuration of these paths changed on thermal cycling above the STO cubic-to-tetragonal structural transition temperature, implying that the local conductivity is strongly modified by the STO tetragonal domain structure. The interplay between substrate domains and the interface provides an additional mechanism for understanding and controlling the behaviour of heterostructures.

Chirality from interfacial spin-orbit coupling effects in magnetic bilayers

As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

Oxide-based platform for reconfigurable superconducting nanoelectronics

We report quasi-1D superconductivity at the interface of LaAlO3 and SrTiO3. The material system and nanostructure fabrication method supply a new platform for superconducting nanoelectronics. Nanostructures having line widths w ~ 10 nm are formed from the parent two-dimensional electron liquid using conductive atomic force microscope lithography. Nanowire cross-sections are small compared to the superconducting coherence length in LaAlO3/SrTiO3, placing them in the quasi-1D regime. Broad superconducting transitions versus temperature and finite resistances in the superconducting state well below Tc ≈ 200 mK are observed, suggesting the presence of fluctuation- and heating-induced resistance. The superconducting resistances and V-I characteristics are tunable through the use of a back gate. Four-terminal resistances in the superconducting state show an unusual dependence on the current path, varying by as much as an order of magnitude. This new technology, i.e., the ability to 'write' gate-tunable superconducting nanostructures on an insulating LaAlO3/SrTiO3 'canvas', opens possibilities for the development of new families of reconfigurable superconducting nanoelectronics.

Superconductivity with Rashba spin-orbit coupling and magnetic field

Two-dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin-orbit coupling, which is tunable by a transverse electric field. Ferromagnetism near the interface can simultaneously induce strong local magnetic fields. This combination of spin-orbit coupling and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both the Bardeen-Cooper-Schrieffer superconductor with inter-band pairing and a mixed parity state with finite-momentum intra-band pairing. We present a phase diagram for the superconducting groundstates and analyze the density of states, the spectra, and the momentum distribution functions of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3-SrTiO3 interfaces and superconductors with broken inversion symmetry.

Gate-tunable polarized phase of two-dimensional electrons at the LaAlO3/SrTiO3 interface

Controlling the coupling between localized spins and itinerant electrons can lead to exotic magnetic states. A novel system featuring local magnetic moments and extended 2D electrons is the interface between LaAlO3 and SrTiO3. The magnetism of the interface, however, was observed to be insensitive to the presence of these electrons and is believed to arise solely from extrinsic sources like oxygen vacancies and strain. Here we show the existence of unconventional electronic phases in the LaAlO3/SrTiO3 system pointing to an underlying tunable coupling between itinerant electrons and localized moments. Using anisotropic magnetoresistance and anomalous Hall effect measurements in a unique in-plane configuration, we identify two distinct phases in the space of carrier density and magnetic field. At high densities and fields, the electronic system is strongly polarized and shows a response, which is highly anisotropic along the crystalline directions. Surprisingly, below a density-dependent critical field, the polarization and anisotropy vanish whereas the resistivity sharply rises. The unprecedented vanishing of the easy axes below a critical field is in sharp contrast with other coupled magnetic systems and indicates strong coupling with the moments that depends on the symmetry of the itinerant electrons. The observed interplay between the two phases indicates the nature of magnetism at the LaAlO3/SrTiO3 interface as both having an intrinsic origin and being tunable.

Electric-field-induced polar order and localization of the confined electrons in LaAlO3/SrTiO3 heterostructures

With ellipsometry, x-ray diffraction, and resistance measurements we investigated the electric-field effect on the confined electrons at the LaAlO3/SrTiO3 interface. We obtained evidence that the localization of the electrons at negative gate voltage is induced, or at least enhanced, by a polar phase transition in SrTiO3 which strongly reduces the lattice polarizability and the subsequent screening. In particular, we show that the charge localization and the polar order of SrTiO3 both develop below ∼50  K and exhibit similar, unipolar hysteresis loops as a function of the gate voltage.

Metal-insulator transition in SrIrO3 with strong spin-orbit interaction

The thickness-dependent metal-insulator transition is observed in meta-stable orthorhombic SrIrO3 thin films synthesized by pulsed laser deposition. SrIrO3 films with thicknesses less than 3 nm demonstrate insulating behaviour, whereas those thicker than 4 nm exhibit metallic conductivity at high temperature, and insulating-like behaviour at low temperature. Weak/Anderson localization is mainly responsible for the observed thickness-dependent metal-insulator transition in SrIrO3 films. Temperature-dependent resistance fitting shows that electrical-conductivity carriers are mainly scattered by the electron-boson interaction rather than the electron-electron interaction. Analysis of the magneto-conductance proves that the spin-orbit interaction plays a crucial role in the magneto-conductance property of SrIrO3.

Anomalous high mobility in LaAlO3/SrTiO3 nanowires

Nanoscale control of the metal-insulator transition at the interface between LaAlO(3) and SrTiO(3) provides a pathway for reconfigurable, oxide-based nanoelectronics. Four-terminal transport measurements of LaAlO(3)/SrTiO(3) nanowires at room temperature (T = 300 K) reveal an equivalent 2D Hall mobility greatly surpassing that of bulk SrTiO(3) and approaching that of n-type Si nanowires of comparable dimensions. This large enhancement of mobility is relevant for room-temperature device applications.

Model for magnetic flux patterns induced by the influence of in-plane magnetic fields on spatially inhomogeneous superconducting interfaces of LaAlO3-SrTiO3 bilayers

The effect of spatial inhomogeneity on the properties of a two-dimensional noncentrosymmetric superconductor in an in-plane magnetic field is investigated, as it can be realized in LaAlO(3)-SrTiO(3) interfaces. We demonstrate that the spatial variation of Rashba spin-orbit coupling yields a local magnetic flux pattern due to the field-induced inhomogeneous helical phase. For sufficiently strong fields, vortices can nucleate at inhomogeneities of the Rashba spin-orbit coupling.

Intrinsic instability of electronic interfaces with strong Rashba coupling

We consider a model for the two-dimensional electron gas formed at the interface of oxide heterostructures, which includes a Rashba spin-orbit coupling proportional to the electric field perpendicular to the interface. Based on the standard mechanism of polarity catastrophe, we assume that the electric field has a contribution proportional to the electron density. Under these simple and general assumptions, we show that a phase separation instability (signaled by a negative compressibility) occurs for realistic values of the spin-orbit coupling and of the electronic band-structure parameters. This provides an intrinsic mechanism for the inhomogeneous phases observed at the LaAlO(3)/SrTiO(3) or LaTiO(3)/SrTiO(3) interfaces.

Towards electrical spin injection into LaAlO3-SrTiO3

Future spintronics devices will be built from elemental blocks allowing the electrical injection, propagation, manipulation and detection of spin-based information. Owing to their remarkable multi-functional and strongly correlated character, oxide materials already provide such building blocks for charge-based devices such as ferroelectric field-effect transistors (FETs), as well as for spin-based two-terminal devices such as magnetic tunnel junctions, with giant responses in both cases. Until now, the lack of suitable channel materials and the uncertainty of spin-injection conditions in these compounds had however prevented the exploration of similar giant responses in oxide-based lateral spin transport structures. In this paper, we discuss the potential of oxide-based spin FETs and report magnetotransport data that suggest electrical spin injection into the LaAlO(3)-SrTiO(3) interface system. In a local, three-terminal measurement scheme, we analyse the voltage variation associated with the precession of the injected spin accumulation driven by perpendicular or longitudinal magnetic fields (Hanle and 'inverted' Hanle effects). The spin accumulation signal appears to be much larger than expected, probably owing to amplification effects by resonant tunnelling through localized states in the LaAlO(3). We give perspectives on how to achieve direct spin injection with increased detection efficiency, as well on the implementation of efficient top gating schemes for spin manipulation.

Spin-orbit density wave induced hidden topological order in URu2Si2

The conventional order parameters in quantum matters are often characterized by 'spontaneous' broken symmetries. However, sometimes the broken symmetries may blend with the invariant symmetries to lead to mysterious emergent phases. The heavy fermion metal URu2Si2 is one such example, where the order parameter responsible for a second-order phase transition at Th=17.5 K has remained a long-standing mystery. Here we propose via ab-initio calculation and effective model that a novel spin-orbit density wave in the f-states is responsible for the hidden-order phase in URu2Si2. The staggered spin-orbit order spontaneously breaks rotational, and translational symmetries while time-reversal symmetry remains intact. Thus it is immune to pressure, but can be destroyed by magnetic field even at T=0 K, that means at a quantum critical point. We compute topological index of the order parameter to show that the hidden order is topologically invariant. Finally, some verifiable predictions are presented.

Scanning probe manipulation of magnetism at the LaAlO3/SrTiO3 heterointerface

Manipulation of magnetism is a longstanding goal of research in exotic materials. In this work, we demonstrate that the small ferromagnetic patches in LaAlO(3)/SrTiO(3) heterostructures can be dramatically changed by in situ contact of a scanning probe. Our results provide a platform for manipulation of small magnets through either a strong magneto-elastic coupling or sensitivity to surface modification. The ability to locally control magnetism is particularly interesting due to the presence of superconductivity with strong spin-orbit coupling in LaAlO(3)/SrTiO(3).

Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide

We present evidence of cubic Rashba spin splitting in a quasi-two-dimensional electron gas formed at a surface of (001) SrTiO3 single crystal from the weak localization or antilocalization (WAL) analysis of the low-temperature magnetoresistance. Our WAL data were well fitted by the model assuming mj=±3/2 for the spin-split pair, in which 2π rotation of the electron wave vector k∥ in the kx-ky plane accompanies 6π rotation of the spin quantization axis. This finding pertains to the p symmetry of the t2g electronic band derived from d electrons in SrTiO3, which provides insights into the surface electronic state of (001) SrTiO3.

Tunable spin-orbit interaction in trilayer graphene exemplified in electric-double-layer transistors

Taking advantage of ultrahigh electric field generated in electric-double-layer transistors (EDLTs), we investigated spin-orbit interaction (SOI) and its modulation in epitaxial trilayer graphene. It was found in magnetotransport that the dephasing length L(φ) and spin relaxation length L(so) of carriers can be effectively modulated with gate bias. As a direct result, SOI-induced weak antilocalization (WAL), together with a crossover from WAL to weak localization (WL), was observed at near-zero magnetic field. Interestingly, among existing localization models, only the Iordanskii-Lyanda-Geller-Pikus theory can successfully reproduce the obtained magnetoconductance well, serving as evidence for gate tuning of the weak but distinct SOI in graphene. Realization of SOI and its large tunability in the trilayer graphene EDLTs provides us with a possibility to electrically manipulate spin precession in graphene systems without ferromagnetics.

Gate-controlled spin injection at LaAlO3/SrTiO3 interfaces

We report results of electrical spin injection at the high-mobility quasi-two-dimensional electron system (2-DES) that forms at the LaAlO3/SrTiO3 interface. In a nonlocal, three-terminal measurement geometry, we analyze the voltage variation associated with the precession of the injected spin accumulation driven by perpendicular or transverse magnetic fields (Hanle and inverted Hanle effect). The influence of bias and back-gate voltages reveals that the spin accumulation signal is amplified by resonant tunneling through localized states in the LaAlO3 strongly coupled to the 2-DES by tunneling transfer.

Topological superconductivity in bilayer Rashba system

We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the heterostructures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given.

Superconducting and ferromagnetic phases in SrTiO3/LaAlO3 oxide interface structures: possibility of finite momentum pairing

We introduce a model to explain the observed ferromagnetism and superconductivity in LAO/STO oxide interface structures. Because of the polar catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface layer. We argue that this charge localizes and orders ferromagnetically via exchange with the conduction electrons. Ordinarily, this ferromagnetism would destroy superconductivity, but, due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming a Fulde-Ferrell-Larkin-Ovchinikov-type condensate of Cooper pairs at finite momentum, which is surprisingly robust in the presence of strong disorder.

Emergent phenomena at oxide interfaces

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

Electrolyte gate-controlled Kondo effect in SrTiO3

We report low-temperature, high-field magnetotransport measurements of SrTiO(3) gated by an ionic gel electrolyte. A saturating resistance upturn and negative magnetoresistance that signal the emergence of the Kondo effect appear for higher applied gate voltages. This observation, enabled by the wide tunability of the ionic gel-applied electric field, promotes the interpretation of the electric field-effect-induced 2D electron system in SrTiO(3) as an admixture of magnetic Ti(3+) ions, i.e., localized and unpaired electrons, and delocalized electrons that partially fill the Ti 3d conduction band.

Persistent spin oscillations in a spin-orbit-coupled superconductor

Quasi-two-dimensional superconductors with tunable spin-orbit coupling are very interesting systems with properties that are also potentially useful for applications. In this Letter we demonstrate that these systems exhibit undamped collective spin oscillations that can be excited by the application of a supercurrent. We propose to use these collective excitations to realize persistent spin oscillators operating in the frequency range of 10 GHz-1 THz.

Coexistence of superconductivity and ferromagnetism in two dimensions

Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO(3) (LAO) and SrTiO(3) (STO), a system that has been studied intensively recently. Magnetoresistance, Hall, and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field makes this a fascinating system for the study of the interplay between superconductivity and magnetism.

Spontaneous 2-dimensional carrier confinement at the n-type SrTiO3/LaAlO3 interface

We describe the intrinsic mechanism of 2-dimensional electron confinement at the n-type SrTiO3/LaAlO3 interface as a function of the sheet carrier density n(s) via advanced first-principles calculations. Electrons localize spontaneously in Ti 3d(xy) levels within a thin (≲2  nm) interface-adjacent SrTiO3 region for n(s) lower than a threshold value n(c)∼10(14)  cm(-2). For n(s)>n(c) a portion of charge flows into Ti 3d(xz)-d(yz) levels extending farther from the interface. This intrinsic confinement can be attributed to the interface-induced symmetry breaking and localized nature of Ti 3d t(2g) states. The sheet carrier density directly controls the binding energy and the spatial extension of the conductive region. A direct, quantitative relation of these quantities with n(s) is provided.

Two-dimensional electron gas with universal subbands at the surface of SrTiO(3)

As silicon is the basis of conventional electronics, so strontium titanate (SrTiO(3)) is the foundation of the emerging field of oxide electronics. SrTiO(3) is the preferred template for the creation of exotic, two-dimensional (2D) phases of electron matter at oxide interfaces that have metal-insulator transitions, superconductivity or large negative magnetoresistance. However, the physical nature of the electronic structure underlying these 2D electron gases (2DEGs), which is crucial to understanding their remarkable properties, remains elusive. Here we show, using angle-resolved photoemission spectroscopy, that there is a highly metallic universal 2DEG at the vacuum-cleaved surface of SrTiO(3) (including the non-doped insulating material) independently of bulk carrier densities over more than seven decades. This 2DEG is confined within a region of about five unit cells and has a sheet carrier density of ∼0.33 electrons per square lattice parameter. The electronic structure consists of multiple subbands of heavy and light electrons. The similarity of this 2DEG to those reported in SrTiO(3)-based heterostructures and field-effect transistors suggests that different forms of electron confinement at the surface of SrTiO(3) lead to essentially the same 2DEG. Our discovery provides a model system for the study of the electronic structure of 2DEGs in SrTiO(3)-based devices and a novel means of generating 2DEGs at the surfaces of transition-metal oxides.

Two-dimensional quantum oscillations of the conductance at LaAlO3/SrTiO3 interfaces

We report on a study of magnetotransport in LaAlO3 /SrTiO3 interfaces characterized by mobilities of the order of several thousands cm2/V s. We observe Shubnikov-de Haas oscillations whose period depends only on the perpendicular component of the magnetic field. This observation directly indicates the formation of a two-dimensional electron gas originating from quantum confinement at the interface. From the temperature dependence of the oscillation amplitude we extract an effective carrier mass m* ≃ 1.45 m(e). An electric field applied in the back-gate geometry increases the mobility, the carrier density, and the oscillation frequency.

Shubnikov-de Haas oscillations in SrTiO3/LaAlO3 interface

Quantum magnetic oscillations in SrTiO3/LaAlO3 interface are observed in the magnetoresistance. We study their frequency as a function of gate voltage and the evolution of their amplitude with temperature. The data are consistent with the Shubnikov-de Haas theory. The Hall resistivity ρ(xy) is nonlinear at low magnetic fields. ρ(xy) is fitted assuming multiple carrier contributions. We infer the density of the mobile charge carriers from the oscillations frequency and from Hall measurements. The comparison between these densities suggests multiple valley and spin degeneracy. The small amplitude of the oscillation is discussed in the framework of the multiple band scenario.