Tunneling anisotropic magnetoresistance and spin-orbit coupling in Fe/GaAs/Au tunnel junctions

Tuning Rashba-Dresselhaus effect with ferroelectric polarization at asymmetric heterostructural interface

The spin-orbit interaction (SOI) plays an essential role in materials properties, and controlling its intensity has great potential in the design of materials. In this work, asymmetric [(La0.7Sr0.3MnO3)8/(BaTiO3)t/(SrTiO3)2]8 superlattices were fabricated on (001) SrTiO3 substrate with SrO or TiO2 termination, labelled as SrO-SL and TiO2-SL, respectively. The in-plane angular magnetoresistance of the superlattices shows a combination of two- and four-fold symmetry components. The coefficient of two-fold symmetry component has opposite sign with current I along [100] and [110] directions for TiO2-SL, while it has the same sign for SrO-SL. Detailed study shows that the asymmetric cation inter-mixing and ferroelectricity-modulated electronic charge transfer induce asymmetric electronic potential for SrO-SL with dominating Rashba SOI, and symmetric electronic potential for TiO2-SL with dominating Dresselhaus SOI induced by BaTiO3. This work shows that the Rashba and Dresselhaus SOIs are sensitive to the ferroelectric polarization in the asymmetric structure.

The tunable anisotropic Rashba spin-orbit coupling effect in Pb-adsorbed Janus monolayer WSeTe

The spin-splitting properties of Pb-adsorbed monolayer Janus WSeTe are investigated based on first-principles calculations. The adsorbed system shows large Rashba splitting (the Rashba parameter is up to 0.75 eV Å), and we find that different adsorption layers (Te/Se adsorption layers) exhibit different significant features under spin-orbit coupling. Zeeman splitting and Rashba splitting co-exist at the high symmetry Γ point of the Te adsorption layer, while the Se adsorption layer exhibits anisotropic Rashba spin-orbit coupling. It was determined using k·p perturbation theory that Pb atom adsorption reduces the initial symmetry of the 2H-WSeTe monolayer and induces a strong spin-orbit coupling effect, so as to induce the anisotropic Rashba effect. Furthermore, the tunability of Rashba splitting was demonstrated by varying the adsorption concentration, adjusting the adsorption distance, and applying biaxial strain. This predicted adsorption system has potential value in spintronic devices.

Spin-Resolved Imaging of Antiferromagnetic Order in Fe4 Se5 Ultrathin Films on SrTiO3

Unraveling the magnetic order in iron chalcogenides and pnictides at atomic scale is pivotal for understanding their unconventional superconducting pairing mechanism, but is experimentally challenging. Here, by utilizing spin-polarized scanning tunneling microscopy, real-space spin contrasts are successfully resolved to exhibit atomically unidirectional stripes in Fe₄ Se₅ ultrathin films, the plausible closely related compound of bulk FeSe with ordered Fe-vacancies, which are grown by molecular beam epitaxy. As is substantiated by the first-principles electronic structure calculations, the spin contrast originates from a pair-checkerboard antiferromagnetic ground state with in-plane magnetization, which is modulated by a spin-lattice coupling. These measurements further identify three types of nanoscale antiferromagnetic domains with distinguishable spin contrasts, which are subject to thermal fluctuations into short-ranged patches at elevated temperatures. This work provides promising opportunities in understanding the emergent magnetic order and the electronic phase diagram for FeSe-derived superconductors.

Rashba effect on finite temperature magnetotransport in a dissipative quantum dot transistor with electronic and polaronic interactions

The Rashba spin-orbit coupling induced quantum transport through a quantum dot embedded in a two-arm quantum loop of a quantum dot transistor is studied at finite temperature in the presence of electron-phonon and Hubbard interactions, an external magnetic field and quantum dissipation. The Anderson-Holstein-Caldeira-Leggett-Rashba model is used to describe the system and several unitary transformations are employed to decouple some of the interactions and the transport properties are calculated using the Keldysh technique. It is shown that the Rashba coupling alone separates the spin-up and spin-down currents causing zero-field spin-polarization. The gap between the up and down-spin currents and conductances can be changed by tuning the Rashba strength. In the absence of a field, the spin-up and spin-down currents show an opposite behaviour with respect to spin-orbit interaction phase. The spin-polarization increases with increasing electron-phonon interaction at zero magnetic field. In the presence of a magnetic field, the tunneling conductance and spin-polarization change differently with the polaronic interaction, spin-orbit interaction and dissipation in different temperature regimes. This study predicts that for a given Rashba strength and magnetic field, the maximum spin-polarization in a quantum dot based device occurs at zero temperature.

Unconventional Rashba Spin-Orbit Coupling on the Charge Conductance and Spin Polarization of a Ferromagnetic/Insulator/Ferromagnetic Rashba Metal Junction

A ferromagnetic/insulator/ferromagnetic Rashba metal junction (FM/I/FRM) with both Rashba spin-orbit coupling (RSOC) and exchange energy splitting was studied theoretically. Two kinds of interactions in FRM generate the three metallic states in a FRM; the Rashba ring metal (RRM) state, the anomalous Rashba metal (ARM) state and the normal Rashba metal (NRM) state. The scattering method and the free-electron model are used to describe the transport properties of particles and to calculate the conductance spectrum and the spin polarization of current in the junction. The conductance spectrum in the applied voltage shows the prominent features at the boundaries not only for the three states of the FRM but also in the ARM state. In addition, the conductance in the RRM and ARM states is strongly influenced by both the thickness and barrier height of the insulator layer. We also found that the spin polarization obtains a high value in the ARM state and is not affected by the qualities of the insulator, unlike the RRM and NRM states. Obtaining high-spin polarization from FRM material can be useful to produce spintronic devices in future devices.

Spin-orbit enabled all-electrical readout of chiral spin-textures

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since the electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of respectively one- and two-dimensional magnetic states of matter. It is linear with spin-orbit coupling in contrast to the quadratic dependence associated with the unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport effects are systematized on various non-collinear magnetic states – spin-spirals and skyrmions – and compared to the uncovered spin-orbit-independent multi-site magnetoresistances. Owing to their simple implementation in readily available reading devices, the proposed magnetoresistances offer exciting and decisive ingredients to explore with all-electrical means the rich physics of topological and chiral magnetic objects.

One challenge for encoding information in chiral spin textures is how to read the information electrically. Here, Lima Fernandes et al. show that chiral spin textures exhibit a magnetoresistance signature which could allow for efficient electric readout of the chirality and helicity.

Recent developments on the magnetic and electrical transport properties of FeRh- and Rh-based heterostructures

It is fascinating how the binary alloy FeRh has been the subject of a vast number of studies almost solely for a single-phase transition. This is, however, reasonable, considering how various degrees of freedom are intertwined around this phase transition. Furthermore, the tunability of this phase transition-the large response to tuning parameters, such as electric field and strain-endows FeRh huge potential in applications. Compared to the bulk counterpart, FeRh in the thin-film form is superior in many aspects: materials in thin-film form are often more technologically relevant in the first place; in addition, the substrates add extra dimensions to the tunability, especially when the substrate itself is multiferroic. Here we review recent developments on the magnetic and transport properties of heterostructures based on FeRh and its end-member Rh, with the latter providing a new route to exploiting spin-orbit interactions in functional spintronic heterostructures other than the more often employed 5dmetals. The methods utilized in the investigation of the physical properties in these systems, and the design principles employed in the engineering thereof may conceivably be extended to similar phase transitions to other magnetic materials.

Evidence for anisotropic spin-triplet Andreev reflection at the 2D van der Waals ferromagnet/superconductor interface

Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which provides the possible experimental evidence for the spin-triplet Andreev reflection and induced spin-triplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling. The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spin-triplet Andreev reflection. This discovery, together with the impressive advances in two-dimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.

Strain-Controlled Superconductivity in Few-Layer NbSe2

The controlled tunability of superconductivity in low-dimensional materials may enable new quantum devices. Particularly in triplet or topological superconductors, tunneling devices such as Josephson junctions, etc., can demonstrate exotic functionalities. The tunnel barrier, an insulating or normal material layer separating two superconductors, is a key component for the junctions. Thin layers of NbSe₂ have been shown as a superconductor with strong spin orbit coupling, which can give rise to topological superconductivity if driven by a large magnetic exchange field. Here we demonstrate the superconductor-insulator transitions in epitaxially grown few-layer NbSe₂ with wafer-scale uniformity on insulating substrates. We provide the electrical transport, Raman spectroscopy, cross-sectional transmission electron microscopy, and X-ray diffraction characterizations of the insulating phase. We show that the superconductor-insulator transition is driven by strain, which also causes characteristic energy shifts of the Raman modes. Our observation paves the way for high-quality heterojunction tunnel barriers to be seamlessly built into epitaxial NbSe₂ itself, thereby enabling highly scalable tunneling devices for superconductor-based quantum electronics.

Large room-temperature tunneling anisotropic magnetoresistance and electroresistance in single ferromagnet/Nb:SrTiO3 Schottky devices

There is a large effort in research and development to realize electronic devices capable of storing information in new ways - for instance devices which simultaneously exhibit electro and magnetoresistance. However it remains a challenge to create devices in which both effects coexist. In this work we show that the well-known electroresistance in noble metal-Nb:SrTiO₃ Schottky junctions can be augmented by a magnetoresistance effect in the same junction. This is realized by replacing the noble metal electrode with ferromagnetic Co. This magnetoresistance manifests as a room temperature tunneling anisotropic magnetoresistance (TAMR). The maximum room temperature TAMR (1.6%) is significantly larger and robuster with bias than observed earlier, not using Nb:SrTiO₃. In a different set of devices, a thin amorphous AlO_x interlayer inserted between Co and Nb:SrTiO₃, reduces the TAMR by more than 2 orders of magnitude. This points to the importance of intimate contact between the Co and Nb:SrTiO₃ for the TAMR effect. This is explained by electric field enhanced spin-orbit coupling of the interfacial Co layer in contact with Nb:SrTiO₃. We propose that the large TAMR likely has its origin in the 3d orbital derived conduction band and large relative permittivity of Nb:SrTiO₃ and discuss ways to further enhance the TAMR.

Anisotropic sensor and memory device with a ferromagnetic tunnel barrier as the only magnetic element

Multiple spin functionalities are probed on Pt/La₂Co_0.8Mn_1.2O₆/Nb:SrTiO₃, a device composed by a ferromagnetic insulating barrier sandwiched between non-magnetic electrodes. Uniquely, La₂Co_0.8Mn_1.2O₆ thin films present strong perpendicular magnetic anisotropy of magnetocrystalline origin, property of major interest for spintronics. The junction has an estimated spin-filtering efficiency of 99.7% and tunneling anisotropic magnetoresistance (TAMR) values up to 30% at low temperatures. This remarkable angular dependence of the magnetoresistance is associated with the magnetic anisotropy whose origin lies in the large spin-orbit interaction of Co²⁺ which is additionally tuned by the strain of the crystal lattice. Furthermore, we found that the junction can operate as an electrically readable magnetic memory device. The findings of this work demonstrate that a single ferromagnetic insulating barrier with strong magnetocrystalline anisotropy is sufficient for realizing sensor and memory functionalities in a tunneling device based on TAMR.

Relativistic torques induced by currents in magnetic materials: physics and experiments

In this review article, an insight of the physics that explains the phenomenon of torques induced by currents in systems comprising ferromagnetic (FM)–non-magnetic (NM) materials has been provided with particular emphasis on experiments that concern the observation of such torques. An important requirement of systems that enables observation of such relativistic torques is that the material needs to possess large spin–orbit coupling (SOC). In addition, the FM/NM interface should be of high quality so that spin angular momentum can be transferred across the interface. Under such conditions, the magnetization of a magnetic material experiences a torque, and can be reversed, thanks to the phenomenon of the spin Hall effect in the NM layer with large SOC. A reciprocal process also occurs, in which a changing magnetization orientation can produce spin current, i.e. current that supports spin angular momentum. It is important to know how these processes occur which often tells us about the close connection between magnetization and spin transport. This paves the way to transform technologies that process information via magnetization direction, namely in magnetic recording industry. This field of physics being relatively young much remains to be understood and explored. Through this review we have attempted to provide a glimpse of existing understanding of current induced torques in ferromagnetic thin film heterostructures along with some future challenges and opportunities of this evolving area of spintronics. Specifically, we have discussed the state-of-the art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of magnetic memory devices.

The article focuses on the physics that explains the phenomenon of torques induced by currents in systems comprising ferromagnetic–non-magnetic materials with particular emphasis on experiments that concern the observation of such torques.

Tunneling anisotropic magnetoresistance driven by magnetic phase transition

The independent control of two magnetic electrodes and spin-coherent transport in magnetic tunnel junctions are strictly required for tunneling magnetoresistance, while junctions with only one ferromagnetic electrode exhibit tunneling anisotropic magnetoresistance dependent on the anisotropic density of states with no room temperature performance so far. Here, we report an alternative approach to obtaining tunneling anisotropic magnetoresistance in α′-FeRh-based junctions driven by the magnetic phase transition of α′-FeRh and resultantly large variation of the density of states in the vicinity of MgO tunneling barrier, referred to as phase transition tunneling anisotropic magnetoresistance. The junctions with only one α′-FeRh magnetic electrode show a magnetoresistance ratio up to 20% at room temperature. Both the polarity and magnitude of the phase transition tunneling anisotropic magnetoresistance can be modulated by interfacial engineering at the α′-FeRh/MgO interface. Besides the fundamental significance, our finding might add a different dimension to magnetic random access memory and antiferromagnet spintronics.

Tunneling anisotropic magnetoresistance is promising for next generation memory devices but limited by the low efficiency and functioning temperature. Here the authors achieved 20% tunneling anisotropic magnetoresistance at room temperature in magnetic tunnel junctions with one α′-FeRh magnetic electrode.

Unconventional magnetic anisotropy in one-dimensional Rashba system realized by adsorbing Gd atom on zigzag graphene nanoribbons

The Rashba effect, a spin splitting in electronic band structures, attracts much attention for potential applications in spintronics with no requirement of an external magnetic field. Realizing a one-dimensional (1D) Rashba system is a big challenge due to the difficulties of growing high-quality heavy-metal nanowires or introducing strong spin-orbit coupling (SOC) and broken inversion symmetry in flexible materials. Here, based on first-principles calculations, we propose a pathway to realize the Rashba spin-split by adsorbing Gd atom on zigzag graphene nanoribbons (Gd-ZGNR) and further investigate the magnetic anisotropy energy (MAE). Perpendicular MAE and unconventional MAE contributions in k-space are found in the self-assembled Gd-ZGNR system, which presents a remarkable Rashba effect (the estimated strength is 1.89 eV Å) due to the strong SOC (∼65.6 meV) and the asymmetric adsorption sites at the nanoribbon edge. Moreover, first-order MAE is connected to the intrinsic Rashba effect beyond the traditional second-order MAE, which is confirmed based on the analysis of electronic structures perturbed with SOC in comparison with metastable Gd-ZGNR at the central symmetric adsorption site. The dependence on the ribbon width of the first-order MAE and the Rashba effect on Gd-ZGNRs are also examined. This work not only opens a new gate for designing the 1D Rashba system but also provides insight into the unconventional MAE due to the intrinsic Rashba effect, which would be of great significance for searching Majorana fermions and promoting potential applications in spintronics.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Observation of spontaneous spin-splitting in the band structure of an n-type zinc-blende ferromagnetic semiconductor

Large spin-splitting in the conduction band and valence band of ferromagnetic semiconductors, predicted by the influential mean-field Zener model and assumed in many spintronic device proposals, has never been observed in the mainstream p-type Mn-doped ferromagnetic semiconductors. Here, using tunnelling spectroscopy in Esaki-diode structures, we report the observation of such a large spontaneous spin-splitting energy (31.7–50 meV) in the conduction band bottom of n-type ferromagnetic semiconductor (In,Fe)As, which is surprising considering the very weak s-d exchange interaction reported in several zinc-blende type semiconductors. The mean-field Zener model also fails to explain consistently the ferromagnetism and the spin-splitting energy of (In,Fe)As, because we found that the Curie temperature values calculated using the observed spin-splitting energies are much lower than the experimental ones by a factor of 400. These results urge the need for a more sophisticated theory of ferromagnetic semiconductors.

A large spin-splitting is essential for spintronic devices. Here, the authors observe a spontaneous spin-splitting energy of between 31.7 and 50 millielectronvolts in n-type indium iron arsenide at temperatures up to several tens of Kelvin, challenging the conventional theory of ferromagnetic semiconductors.

Robust spin-orbit torque and spin-galvanic effect at the Fe/GaAs (001) interface at room temperature

Interfacial spin-orbit torques (SOTs) enable the manipulation of the magnetization through in-plane charge currents, which has drawn increasing attention for spintronic applications. The search for material systems providing efficient SOTs, has been focused on polycrystalline ferromagnetic metal/non-magnetic metal bilayers. In these systems, currents flowing in the non-magnetic layer generate—due to strong spin–orbit interaction—spin currents via the spin Hall effect and induce a torque at the interface to the ferromagnet. Here we report the observation of robust SOT occuring at a single crystalline Fe/GaAs (001) interface at room temperature. We find that the magnitude of the interfacial SOT, caused by the reduced symmetry at the interface, is comparably strong as in ferromagnetic metal/non-magnetic metal systems. The large spin-orbit fields at the interface also enable spin-to-charge current conversion at the interface, known as spin-galvanic effect. The results suggest that single crystalline Fe/GaAs interfaces may enable efficient electrical magnetization manipulation.

Interfacial spin-orbit torque allows electrical manipulation of magnetization, but this has been shown mostly in polycrystalline metal bilayers. Here the authors show robust spin-orbit torque in single crystalline Fe/GaAs interface at room temperature, observing conversion between spin and charge current.

Theory of Spin Loss at Metallic Interfaces

Interfacial spin-flip scattering plays an important role in magnetoelectronic devices. Spin loss at metallic interfaces is usually quantified by matching the magnetoresistance data for multilayers to the Valet-Fert model, while treating each interface as a fictitious bulk layer whose thickness is δ times the spin-diffusion length. By employing the properly generalized circuit theory and the scattering matrix approaches, we derive the relation of the parameter δ to the spin-flip transmission and reflection probabilities at an individual interface. It is found that δ is proportional to the square root of the probability of spin-flip scattering. We calculate the spin-flip scattering probabilities for flat and rough Cu/Pd interfaces using the Landauer-Büttiker method based on the first-principles electronic structure and find δ to be in reasonable agreement with experiment.

Effect of Orbital Hybridization on Spin-Polarized Tunneling across Co/C60 Interfaces

The interaction between ferromagnetic surfaces and organic semiconductors leads to the formation of hybrid interfacial states. As a consequence, the local magnetic moment is altered, a hybrid interfacial density of states (DOS) is formed, and spin-dependent shifts of energy levels occur. Here, we show that this hybridization affects spin transport across the interface significantly. We report spin-dependent electronic transport measurements for tunnel junctions comprising C₆₀ molecular thin films grown on top of face-centered-cubic (fcc) epitaxial Co electrodes, an AlO_x tunnel barrier, and an Al counter electrode. Since only one ferromagnetic electrode (Co) is present, spin-polarized transport is due to tunneling anisotropic magnetoresistance (TAMR). An in-plane TAMR ratio of approximately 0.7% has been measured at 5 K under application of a magnetic field of 800 mT. The magnetic switching behavior shows some remarkable features, which are attributed to the rotation of interfacial magnetic moments. This behavior can be ascribed to the magnetic coupling between the Co thin films and the newly formed Co/C₆₀ hybridized interfacial states. Using the Tedrow-Meservey technique, the tunnel spin polarization of the Co/C₆₀ interface was found to be 43%.

Anisotropic Polar Magneto-Optic Kerr Effect of Ultrathin Fe/GaAs(001) Layers due to Interfacial Spin-Orbit Interaction

We report the observation of the anisotropic polar magneto-optical Kerr effect in thin layers of epitaxial Fe/GaAs(001) at room temperature. A clear twofold symmetry of the Kerr rotation angle depending on the orientation of the linear polarization of the probing laser beam with respect to the crystallographic directions of the sample is detected for ultrathin magnetic films saturated out of the film plane. The amplitude of the anisotropy decreases with increasing Fe film thickness, suggesting that the interfacial region is the origin of the anisotropy. The twofold symmetry is fully reproduced by model calculations based on an interference of interfacial Bychkov-Rashba and Dresselhaus spin-orbit coupling.

Dynamic detection of electron spin accumulation in ferromagnet-semiconductor devices by ferromagnetic resonance

A distinguishing feature of spin accumulation in ferromagnet-semiconductor devices is its precession in a magnetic field. This is the basis for detection techniques such as the Hanle effect, but these approaches become ineffective as the spin lifetime in the semiconductor decreases. For this reason, no electrical Hanle measurement has been demonstrated in GaAs at room temperature. We show here that by forcing the magnetization in the ferromagnet to precess at resonance instead of relying only on the Larmor precession of the spin accumulation in the semiconductor, an electrically generated spin accumulation can be detected up to 300 K. The injection bias and temperature dependence of the measured spin signal agree with those obtained using traditional methods. We further show that this approach enables a measurement of short spin lifetimes (<100 ps), a regime that is not accessible in semiconductors using traditional Hanle techniques.

Magnetoanisotropic Andreev reflection in ferromagnet-superconductor junctions

Andreev reflection spectroscopy of ferromagnet-superconductor (FS) junctions [corrected] is an important probe of spin polarization. We theoretically investigate spin-polarized transport in FS junctions in the presence of Rashba and Dresselhaus interfacial spin-orbit fields and show that Andreev reflection can be controlled by changing the magnetization orientation. We predict a giant in- and out-of-plane magnetoanisotropy of the junction conductance. If the ferromagnet is highly spin polarized-in the half-metal limit-the magnetoanisotropic Andreev reflection depends universally on the spin-orbit fields only. Our results show that Andreev reflection spectroscopy can be used for sensitive probing of interfacial spin-orbit fields in a FS junction.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Tunneling Anomalous and Spin Hall Effects

We predict, theoretically, the existence of the anomalous Hall effect when a tunneling current flows through a tunnel junction in which only one of the electrodes is magnetic. The interfacial spin-orbit coupling present in the barrier region induces a spin-dependent momentum filtering in the directions perpendicular to the tunneling current, resulting in a skew tunneling even in the absence of impurities. This produces an anomalous Hall conductance and spin Hall currents in the nonmagnetic electrode when a bias voltage is applied across the tunneling heterojunction. If the barrier is composed of a noncentrosymmetric material, the anomalous Hall conductance and spin Hall currents become anisotropic with respect to both the magnetization and crystallographic directions, allowing us to separate this interfacial phenomenon from the bulk anomalous and spin Hall contributions. The proposed effect should be useful for proving and quantifying the interfacial spin-orbit fields in metallic and metal-semiconductor systems.

Emergence of spin-orbit fields in magnetotransport of quasi-two-dimensional iron on gallium arsenide

The desire for higher information capacities drives the components of electronic devices to ever smaller dimensions so that device properties are determined increasingly more by interfaces than by the bulk structure of the constituent materials. Spintronic devices, especially, benefit from the presence of interfaces—the reduced structural symmetry creates emergent spin–orbit fields that offer novel possibilities to control device functionalities. But where does the bulk end, and the interface begin? Here we trace the interface-to-bulk transition, and follow the emergence of the interfacial spin–orbit fields, in the conducting states of a few monolayers of iron on top of gallium arsenide. We observe the transition from the interface- to bulk-induced lateral crystalline magnetoanisotropy, each having a characteristic symmetry pattern, as the epitaxially grown iron channel increases from four to eight monolayers. Setting the upper limit on the width of the interface-imprinted conducting channel is an important step towards an active control of interfacial spin–orbit fields.

Broken symmetry at material interfaces allows for novel spintronic functionality via emergent spin–orbit effects. Here, Hupfauer et al. follow the interface-to-bulk transition of ultra-thin epitaxial iron films on gallium arsenide via anisotropic magnetoresistance measurements and first-principle calculations.

Anisotropic magnetoresistance in an antiferromagnetic semiconductor

Recent studies in devices comprising metal antiferromagnets have demonstrated the feasibility of a novel spintronic concept in which spin-dependent phenomena are governed by an antiferromagnet instead of a ferromagnet. Here we report experimental observation of the anisotropic magnetoresistance in an antiferromagnetic semiconductor Sr2IrO4. Based on ab initio calculations, we associate the origin of the phenomenon with large anisotropies in the relativistic electronic structure. The antiferromagnet film is exchange coupled to a ferromagnet, which allows us to reorient the antiferromagnet spin-axis in applied magnetic fields via the exchange spring effect. We demonstrate that the semiconducting nature of our AFM electrode allows us to perform anisotropic magnetoresistance measurements in the current-perpendicular-to-plane geometry without introducing a tunnel barrier into the stack. Temperature-dependent measurements of the resistance and anisotropic magnetoresistance highlight the large, entangled tunabilities of the ordinary charge and spin-dependent transport in a spintronic device utilizing the antiferromagnet semiconductor.

Room-temperature antiferromagnetic memory resistor

The bistability of ordered spin states in ferromagnets provides the basis for magnetic memory functionality. The latest generation of magnetic random access memories rely on an efficient approach in which magnetic fields are replaced by electrical means for writing and reading the information in ferromagnets. This concept may eventually reduce the sensitivity of ferromagnets to magnetic field perturbations to being a weakness for data retention and the ferromagnetic stray fields to an obstacle for high-density memory integration. Here we report a room-temperature bistable antiferromagnetic (AFM) memory that produces negligible stray fields and is insensitive to strong magnetic fields. We use a resistor made of a FeRh AFM, which orders ferromagnetically roughly 100 K above room temperature, and therefore allows us to set different collective directions for the Fe moments by applied magnetic field. On cooling to room temperature, AFM order sets in with the direction of the AFM moments predetermined by the field and moment direction in the high-temperature ferromagnetic state. For electrical reading, we use an AFM analogue of the anisotropic magnetoresistance. Our microscopic theory modelling confirms that this archetypical spintronic effect, discovered more than 150 years ago in ferromagnets, is also present in AFMs. Our work demonstrates the feasibility of fabricating room-temperature spintronic memories with AFMs, which in turn expands the base of available magnetic materials for devices with properties that cannot be achieved with ferromagnets.

Magnetic control of spin-orbit fields: a first-principles study of Fe/GaAs junctions

The microscopic structure of spin-orbit fields for the technologically important Fe/GaAs interface is uncovered from first principles. A symmetry based method allows us to obtain the spin-orbit fields-both their magnitude and orientation-for a generic Bloch state, from the electronic band structure for any in-plane magnetization orientation. It is demonstrated that the spin-orbit fields depend not only on the electric field across the interface, but also surprisingly strongly on the Fe magnetization orientation, opening prospects for their magnetic control. These results give important clues in searching for spin-orbit transport and optical phenomena in ferromagnet/nonmagnet heterostructures.

Tunneling anisotropic magnetoresistance at the single-atom limit

The tunneling anisotropic magnetoresistance (TAMR) of single Co atoms adsorbed on a double-layer Fe film on W(110) is observed by scanning tunneling spectroscopy. Without applying an external magnetic field the TAMR is found by comparing spectra of atoms that are adsorbed on the domains and domain walls of the Fe film. The TAMR can be as large as 12% and repeatedly changes sign as a function of bias voltage. First-principles calculations show that the hybridization between Co d states of different orbital symmetries depends on the magnetization direction via spin-orbit coupling. This leads to an anisotropy of the density of states and thus induces a TAMR.

Room-temperature perpendicular exchange coupling and tunneling anisotropic magnetoresistance in an antiferromagnet-based tunnel junction

We investigate the exchange coupling between perpendicular anisotropy (PMA) Co/Pt and IrMn in-plane antiferromagnets (AFMs), as well as tunneling anisotropic magnetoresistance (TAMR) in [Pt/Co]/IrMn/AlO_{x}/Pt tunnel junctions, where Co/Pt magnetization drives rotation of AFM moments with the formation of exchange-spring twisting. When coupled with a PMA ferromagnet, the AFM moments partially rotate with out-of-plane magnetic fields, in contrast with being pinned along the easy direction of IrMn for in-plane fields. Because of the superior thermal tolerance of perpendicular exchange coupling and the stability of moments in ~6 nm-thick IrMn, TAMR gets significantly enhanced up to room temperature. Their use would advance the process towards practical AFM spintronics.

Tunnelling anisotropic magnetoresistance of Fe/GaAs/Ag(001) junctions from first principles: effect of hybridized interface resonances

Results of first-principles calculations of the Fe/GaAs/Ag(001) epitaxial tunnel junctions reveal that hybridization of interface resonances formed at both interfaces can enhance the tunnelling anisotropic magnetoresistance (TAMR) of the systems. This mechanism is manifested by a non-monotonic dependence of the TAMR effect on the thickness of the tunnel barrier, with a maximum for intermediate thicknesses. A detailed scan of k([parallel])-resolved transmissions over the two-dimensional Brillouin zone proves an interplay between a few hybridization-induced hot spots and a contribution to the tunnelling from the vicinity of the Γ[combining overline] point. This interpretation is supported by calculated properties of a simple tight-binding model of the junction, which reproduce qualitatively most of the features of the first-principles theory.

Detection of electrically modulated inverse spin hall effect in an Fe/GaAs microdevice

We report the detection of the inverse spin Hall effect (ISHE) in n-gallium arsenide (n-GaAs) combined with electrical injection and modulation of the spin current. We use epitaxial ultrathin-Fe/GaAs injection contacts with strong in-plane magnetic anisotropy. This allows us to simultaneously perform Hanle spin-precession measurements on an Fe detection electrode and ISHE measurements in an applied in-plane hard-axis magnetic field. In this geometry, we can experimentally separate the ordinary from the spin-Hall signals. Electrical spin injection and detection are combined in our microdevice with an applied electrical drift current to modulate the spin distribution and spin current in the channel. The magnitudes and external field dependencies of the signals are quantitatively modeled by solving drift-diffusion and Hall-cross response equations.

Tunnel anisotropic magnetoresistance in graphene with Rashba spin-orbit interaction

Ballistic transport in a graphene-based normal/ferromagnetic barrier/normal junction in the presence of Rashba-type spin-orbit interaction (RSOI) is investigated by the non-equilibrium Green's function approach. It is found that due to the interplay between ferromagnetic exchange coupling and RSOI, the energy dispersion in the ferromagnetic barrier depends on the magnetization direction. The conductance changes by varying the magnetization direction, resulting in a tunnel anisotropic magnetoresistance (TAMR). The predicted TAMR effect oscillates with the RSOI strength or on-site energy, which is efficiently controllable by the gate voltage, making this junction very promising in spintronics applications.

Current-induced spin-orbit torques

The ability to reverse the magnetization of nanomagnets by current injection has attracted increased attention ever since the spin-transfer torque mechanism was predicted in 1996. In this paper, we review the basic theoretical and experimental arguments supporting a novel current-induced spin torque mechanism taking place in ferromagnetic (FM) materials. This effect, hereafter named spin-orbit (SO) torque, is produced by the flow of an electric current in a crystalline structure lacking inversion symmetry, which transfers orbital angular momentum from the lattice to the spin system owing to the combined action of SO and exchange coupling. SO torques are found to be prominent in both FM metal and semiconducting systems, allowing for great flexibility in adjusting their orientation and magnitude by proper material engineering. Further directions of research in this field are briefly outlined.

A spin-valve-like magnetoresistance of an antiferromagnet-based tunnel junction

A spin valve is a microelectronic device in which high- and low-resistance states are realized by using both the charge and spin of carriers. Spin-valve structures used in modern hard-drive read heads and magnetic random access memoriescomprise two ferromagnetic electrodes whose relative magnetization orientations can be switched between parallel and antiparallel configurations, yielding the desired giant or tunnelling magnetoresistance effect. Here we demonstrate more than 100% spin-valve-like signal in a NiFe/IrMn/MgO/Pt stack with an antiferromagnet on one side and a non-magnetic metal on the other side of the tunnel barrier. Ferromagneticmoments in NiFe are reversed by external fields of approximately 50  mT or less, and the exchange-spring effect of NiFe on IrMn induces rotation of antiferromagnetic moments in IrMn, which is detected by the measured tunnelling anisotropic magnetoresistance. Our work demonstrates a spintronic element whose transport characteristics are governed by an antiferromagnet. It demonstrates that sensitivity to low magnetic fields can be combined with large, spin-orbit-coupling-induced magnetotransport anisotropy using a single magnetic electrode. The antiferromagnetic tunnelling anisotropic magnetoresistance provides a means to study magnetic characteristics of antiferromagnetic films by an electronic-transport measurement.

Electrical measurement of the direct spin hall effect in Fe/InxGa(1-x)As heterostructures

We report on an all-electrical measurement of the spin Hall effect in epitaxial Fe/InxGa(1-x)As heterostructures with n-type (Si) channel doping and highly doped Schottky tunnel barriers. A transverse spin current generated by an ordinary charge current flowing in the InxGa(1-x)As is detected by measuring the spin accumulation at the edges of the channel. The spin accumulation is identified through the observation of a Hanle effect in the voltage measured by pairs of ferromagnetic Hall contacts. We investigate the bias and temperature dependence of the resulting Hanle signal and determine the skew and side-jump contributions to the total spin Hall conductivity.

Electric field control of magnetoresistance in InP nanowires with ferromagnetic contacts

We demonstrate electric field control of sign and magnitude of the magnetoresistance in InP nanowires with ferromagnetic contacts. The sign change in the magnetoresistance is directly correlated with a sign change in the transconductance. Additionally, the magnetoresistance is shown to persist at such a high bias that Coulomb blockade has been lifted. We also observe the magnetoresistance when one of the ferromagnets is replaced by a nonmagnetic metal. We conclude that it must be induced by a single ferromagnetic contact, and that spin transport can be ruled out as the origin. Our results emphasize the importance of a systematic investigation of spin-valve devices in order to discriminate between ambiguous interpretations.

Large voltage-induced magnetic anisotropy change in a few atomic layers of iron

In the field of spintronics, researchers have manipulated magnetization using spin-polarized currents. Another option is to use a voltage-induced symmetry change in a ferromagnetic material to cause changes in magnetization or in magnetic anisotropy. However, a significant improvement in efficiency is needed before this approach can be used in memory devices with ultralow power consumption. Here, we show that a relatively small electric field (less than 100 mV nm(-1)) can cause a large change (approximately 40%) in the magnetic anisotropy of a bcc Fe(001)/MgO(001) junction. The effect is tentatively attributed to the change in the relative occupation of 3d orbitals of Fe atoms adjacent to the MgO barrier. Simulations confirm that voltage-controlled magnetization switching in magnetic tunnel junctions is possible using the anisotropy change demonstrated here, which could be of use in the development of low-power logic devices and non-volatile memory cells.

Tunneling anisotropic magnetoresistance in Co/AlOx/Au tunnel junctions

We observe spin-valve-like effects in nanoscaled thermally evaporated Co/AlOx/Au tunnel junctions. The tunneling magnetoresistance is anisotropic and depends on the relative orientation of the magnetization direction of the Co electrode with respect to the current direction. We attribute this effect to a two-step magnetization reversal and an anisotropic density of states resulting from spin-orbit interaction. The results of this study points to future applications of novel spintronics devices involving only one ferromagnetic layer.

Tunneling anisotropic magnetoresistance in multilayer-(Co/Pt)/AlO_(x)/Pt structures

We report observations of tunneling anisotropic magnetoresitance (TAMR) in vertical tunnel devices with a ferromagnetic multilayer-(Co/Pt) electrode and a nonmagnetic Pt counterelectrode separated by an AlOx barrier. In stacks with the ferromagnetic electrode terminated by a Co film the TAMR magnitude saturates at 0.15% beyond which it shows only weak dependence on the magnetic field strength, bias voltage, and temperature. For ferromagnetic electrodes terminated by two monolayers of Pt we observe order(s) of magnitude enhancement of the TAMR and a strong dependence on field, temperature and bias. The discussion of experiments is based on relativistic ab initio calculations of magnetization orientation dependent densities of states of Co and Co/Pt model systems.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.