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Oxide spin-orbitronics: spin–charge interconversion and topological spin textures | Nature Reviews Materials
Abstract . Oxide materials possess a vast range of functional properties, ranging from superconductivity to multiferroicity, that stem from the interplay between the lattice, charge, spin and orbital degrees of freedom, and electron correlations often play an important role in defining such properties. Historically, spin–orbit coupling was rarely a dominant energy scale in oxides. However, it recently became the focus of intense interest and was exploited to realize various exotic phenomena connected with real-space and reciprocal-space topology that may be harnessed in spintronics applications. In this Review, we survey the recent advances in the new field of oxide spin-orbitronics, with a special focus on spin–charge interconversion through the direct and inverse spin Hall and Edelstein effects, and on the generation and observation of topological spin textures, such as skyrmions. We also highlight the control of spin–orbit-driven effects by ferroelectricity and discuss the future perspectives for the field. You have full access to this article via your institution. Download PDF Download PDF Introduction . The coupling between the electron spin and its charge by the spin–orbit interaction lies at the core of multiple phenomena in condensed matter physics. The presence of a large spin–orbit interaction in materials in which inversion symmetry is broken enables a plethora of intriguing phenomena, such as spin-momentum locking, spin–orbit torque and topologically non-trivial spin textures arising from antisymmetrical magnetic exchange interaction. Collectively, this broad and rapidly emerging area of research is known as spin-orbitronics 1 . The advantage of spin-orbitronics over conventional spintronics, where ferromagnetic elements have traditionally been employed to generate and detect spin currents, lies in the efficient spin–charge interconversion through the spin–orbit coupling (SOC), which can be achieved without the need for magnetic materials. The spin–orbit interaction is also key to the existence of topological spin textures such as skyrmions, which have been proposed as nanoscale magnetic bits for information storage 2 . Although spin-orbitronics was first considered in metals and semiconductors, it is now quickly entering the field of oxide heterostructures 3 , which endows it with a number of unique characteristics. Oxide interfaces have been at the centre of attention in recent years, owing to the intimate coupling between the spin, charge and lattice degrees of freedom occurring at such interfaces, which, consequently, serve as a basis for a variety of emergent phenomena 4 . In particular, oxide interfaces provide an exciting test bed for studying and harnessing the spin–orbit interaction through the Rashba effect 5 and Dzyaloshinskii–Moriya interaction (DMI) and, thus, represent a versatile platform to generate, control and detect spin currents or magnetic textures. Moreover, oxide interfaces can, nowadays, be grown with exquisite precision 6 and ultrasharp interfaces, which has opened the door to their use for spin-orbitronics 7 . The significance of oxides for spin-orbitronics lies also in their broad range of functional material properties, which is often much richer than in traditional materials. One of these material properties, ferroelectricity, is, for instance, commonly found in oxides but is absent from most other material families. In recent years, ferroelectricity has entered the stage as a new degree of freedom to control spin–orbit-driven effects. In this context, recent important advances in oxide spin-orbitronics include the demonstration of a giant spin-to-charge conversion efficiency in SrTiO 3 -based 2D electron gases (2DEGs) 8 , its control by ferroelectricity 9 , the observation of magnetic skyrmions tunable by ferroelectricity in ultrathin oxide heterostructures 10 and the realization of skyrmion embryos at room temperature in multiferroics 11 . These achievements have not gone unnoticed, and several major companies, including Intel, IBM and Thales, have inaugurated their own research activities on oxide spin-orbitronics. Here, we review recent advances in the emerging field of oxide spin-orbitronics. In the first part of the Review, we cover spin–charge interconversion using oxide materials through the direct and inverse spin Hall and Edelstein effects realized in the prominent oxide platform SrTiO 3 , as well as in ruthenates and iridates. We also overview the ferroelectric control of spin–charge interconversion. In the second part of the Review, we discuss chiral magnetism and skyrmionic structures in oxide systems. Herein, we survey non-centrosymmetrical magnetic oxides, the generation and observation of skyrmions and skyrmion bubbles in oxide heterostructures and, lastly, the electrical control of skyrmions. Spin–charge interconversion with oxides . SrTiO 3 -based 2DEGs . Origin of the electron gas . The 2DEG based on the perovskite SrTiO 3 was first discovered in 2004 by Akira Ohtomo and Harold Hwang 12 at the LaAlO 3 /SrTiO 3 (LAO/STO) (001) interface, for LAO thicknesses of at least four unit cells 13 , 14 , 15 , 16 , 17 . The interest towards the LAO/STO system then grew rapidly. This interest was due, on the one hand, to the prospects of developing oxide-based electronic applications 4 , 18 , from field-effect resistance control 19 , 20 to solar cells 21 , and, on the other hand, to unexpected properties of the LAO/STO interface, such as the low-temperature (co)existence of superconductivity and magnetism 22 , 23 , 24 , 25 and the manifestation of an unconventional quantum Hall effect 26 . The initial explanation for the appearance of the 2DEG at the LAO/STO interface was based on the so-called polar catastrophe model 18 , 27 . LAO can be viewed as consisting of alternating charged planes of LaO + and \({{\rm{A}}{\rm{l}}{\rm{O}}}_{2}^{-}\) , which results in a polar discontinuity at the interface with the nonpolar STO. When the diverging potential due to this polar discontinuity becomes large enough, an electronic reconstruction spontaneously occurs, and half an electron per 2D unit cell is transferred from the LAO valence band at the surface to the STO conduction band at the interface (Fig.? 1a ). Fig. 1: SrTiO 3 -based 2D electron gas: origin and spin-dependent band structure. a Sketch illustrating the polar catastrophe. Atomic layers are considered as charged planes, with the net charge (in units of electrons per surface unit cell) given by ionic formal charges. The z axis corresponds to the [001] direction. The potential, V , diverges with increasing LaAlO 3 (LAO) thickness (left). When the potential becomes sufficiently large (right), an electronic reconstruction leads to the appearance of an electron gas at the interface. b Band structure of t 2 g orbitals in bulk SrTiO 3 (STO) calculated by density functional theory (DFT) and tight-binding methods 55 , exhibiting the heavy ( yz ) and light ( xy , zx ) bands. c Electronic structure of the LAO/STO 2D electron gas along the [010] direction 54 . The magnified view reveals a weak Rashba-type spin splitting around the band bottom, which becomes enhanced by approximately one order of magnitude at the crossings of the light and heavy sub-bands. d Calculated Fermi surface and spin expectation values (direction given by the arrows) for a Fermi level near the band inversion region, and zoom-in on a zone with enhanced spin splitting 8 . The numbers denote the bands in energetically ascending order. The colour scale shows the absolute spin expectation value. e Spin-to-charge conversion efficiency (inverse Edelstein length λ IEE ) as a function of the back-gate voltage in a NiFe/Al/STO sample, measured through spin pumping ferromagnetic resonance experiments 8 . The conversion efficiency depends on the Fermi level position and can be controlled both in amplitude and in sign. SOC, spin–orbit coupling. Panel a reprinted with permission from ref. 15 , IOP. Panel b reprinted with permission from ref. 55 , APS. Panel c reprinted from ref. 54 , Springer Nature Limited. Panels d and e reprinted from ref. 8 , Springer Nature Limited. Full size image Although this model explains why the 2DEG only appears for LAO thicknesses greater than four unit cells, it has been challenged by several observations. In particular, the polar catastrophe model fails to explain the appearance of a 2DEG when amorphous oxide overlayers are deposited on STO 28 , 29 , 30 , as well as the detection of Ti 3 d -like states below four unit cells of LAO by photoemission spectroscopy 31 , 32 , 33 , 34 . Whereas cation intermixing seems to have been ruled out as the source of interface conductivity, these experimental observations point towards oxygen vacancies as the source of interfacial charge carriers, in particular, in samples that have not been annealed in oxygen after deposition. Although the question is still open, it appears that both the polar catastrophe and oxygen vacancies can contribute to 2DEG formation 14 . However, at high deposition temperatures and oxygen pressures, electronic reconstruction should be the dominant effect. Several other STO-based heterointerfaces have been found to display metallic 2DEGs, for instance, when STO is in contact with LaFeO 3 (ref. 35 ), KTaO 3 (refs 36 , 37 ), LaTiO 3 (refs 38 , 39 ), LaGaO 3 (ref. 40 ), LaVO 3 (ref. 41 ), KNbO 3 (ref. 37 ), NaNbO 3 (ref. 37 ), GdTiO 3 (ref. 42 ), LaVO 3 (ref. 43 ), NdGaO 3 (ref. 44 ), PrAlO 3 (refs 44 , 45 ), NdGaO 3 (refs 44 , 45 ), NdAlO 3 (ref. 45 ) or γ -Al 2 O 3 (ref. 46 ). Interestingly, various studies showed that oxygen vacancies may provide mobile carriers and result in a 2DEG even if STO is not in hard contact with a material. A metallic gas can, thus, be obtained at the vacuum-cleaved surface of STO, independently of the STO bulk carrier density, which has been tuned over more than seven orders of magnitude 47 . The carrier density of the gas appearing at a bare STO surface can be controlled through exposure of the surface to intense ultraviolet light 48 . The use of epitaxially grown oxide heterostructures and of bare surfaces might be impractical for mass production, mostly because of contacting, deposition temperature and reproducibility issues. A way to overcome this technical challenge was solved by the demonstration that 2DEGs can also be realized when a thin layer of an elementary reducing agent, such as Al, is deposited at the surface of STO 49 . This breakthrough discovery represents an important step towards the development of low-cost oxide-based applications. Angle-resolved photoemission spectroscopy (ARPES) and transport experiments have, furthermore, shown that the deposition of a ferromagnetic material above such a reducing layer preserves the 2DEG 8 , 9 , 50 . Band structure and spin–charge interconversion . With low-temperature mobility values comparable with or larger than that of silicon 51 , and the possibility to tune the transport properties using a back gate 20 , 52 , STO-based 2DEGs are promising for electronic applications. For spintronics, the interest of STO-based 2DEGs lies in their peculiar band structure that gives rise to unparalleled high spin-to-charge conversion efficiencies 8 , 9 , 53 . This band structure has been studied both experimentally, using ARPES 8 , 54 , and theoretically 54 , 55 , 56 in different systems (LAO/STO, metals/STO, vacuum/STO). In all cases, the interface band structure observed in ARPES is related to the bulk STO band structure, with 2DEG wave functions spreading across several STO atomic layers 56 . Bulk STO is a band insulator with unoccupied Ti 3 d t 2 g ( d yz , d zx , d xy ) bands (in the absence of SOC). The t 2 g band structure calculated by density functional theory displays a small energy dispersion for the heavy d yz band and light d xy and d zy bands (Fig.? 1b ). For STO-based heterointerfaces, the quantum well extends 200–300?meV below the Fermi level 8 , 54 (Fig.? 1c ). The confinement in the 2DEG leads to the creation of sub-bands, so that the band structure is comprised of several light states having dominantly d xy orbital character, with corresponding concentric circular Fermi surfaces, and of heavy states deriving from d xy/yz orbitals, with Fermi surfaces ellipsoidal along the (010) and (100) directions. As the inversion symmetry is broken, the SOC lifts the spin degeneracy of the 2DEG. Band inversion and orbital mixing lead to a spin splitting that is enhanced in certain k -space points, in particular, at trivial and topologically non-trivial avoided band crossings 8 (Fig.? 1b , c ). These features of the band structure have two major implications for spintronics applications. First, the enhancement of the Rashba-like splitting can lead to highly spin-dependent transport properties. Second, these properties depend on the position of the Fermi level in the band structure and can, thus, be tuned by electric fields from a gate. The possibility of modifying the magnitude of the Rashba spin–orbit interaction by using gate voltages was first explored in refs 57 , 58 . Beyond this magnetoresistance control, the existence of tunable SOC effects in STO-based 2DEGs offers a new degree of freedom, which does not exist for the spin Hall effect (SHE) in heavy metals and, thus, provides an exciting way to control several spin-orbitronic effects. The possibility to tune the efficiency of the spin-to-charge conversion by the inverse Rashba–Edelstein effect (Box? 1 ) has been demonstrated using spin-pumping techniques 8 , 53 . The figure of merit of the conversion, the inverse Edelstein length ( λ IEE ), is very large at low temperatures ( T ?≈?10?K), reaching λ IEE ?=?7?nm in LAO/STO 53 and λ IEE ?=?20?nm in Al/STO 8 (the spin–charge interconversion efficiencies of several oxide systems are summarized in Table? 1 ). For comparison, the product of the spin Hall angle (the figure of merit of the spin-to-charge conversion efficiency in the SHE) by the spin diffusion length is equal to approximately 0.2?nm for Pt. These values of λ IEE in STO-based 2DEGs are higher than those observed in topological insulators or at Rashba interfaces with very high SOC, which has been attributed to the long carrier relaxation lifetime in STO 59 , 60 and to the spin-splitting enhancement due to orbital mixing at the vicinity of avoided band crossings 8 (Fig.? 1d ). It is, however, important to note that the value of the inverse Edelstein length decreases to around 0.5?nm at room temperature 8 , 61 . Both the sign of the conversion and its amplitude vary spectacularly with the gate voltage (Fig.? 1e ). These variations are qualitatively close to what can be theoretically predicted from the band structure 8 . Additionally to the gate voltage, the conversion might be controlled using strain 62 . Beyond these spin-pumping experiments, attempts have also been made to detect the conversion using electrical spin injection from La 0.7 Sr 0.3 MnO 3 (LSMO) to the LAO/STO 2DEG 63 . Table 1 Spin–charge interconversion efficiencies of oxides Full size table Whereas the spin-to-charge conversion could find applications in magnetoelectric spin–orbit devices 64 , the charge-to-spin conversion could be used to manipulate the magnetization by spin–orbit torques 65 , 66 , leading to new reconfigurable spin–orbit torque memories and logic gates, enabling skyrmions or domain wall manipulation and allowing the development of agile THz emitters and spin-wave logic architectures 67 , 68 . The charge-to-spin conversion has been observed in CoFeB/LAO/STO, using the spin-torque ferromagnetic resonance technique 69 , with a spin/charge current ratio at room temperature of 0.6?nm ?1 . This ratio was found to decrease as the temperature was reduced, an observation explained by the suppression of inelastic tunnelling at lower temperatures, which should effectively prevent the spin accumulation to access the ferromagnet. In LSMO/LAO/STO, planar Hall effect measurements also indicate that an in-plane current creates an effective in-plane field exerted on the magnetization, orthogonal to the current direction 70 . The spin–charge interconversion can also be realized by the 2D SHE 71 (Box? 1 ), which leads to a pure spin current transverse to the applied current with an out-of-plane spin polarization. The electrical generation and detection of this spin current through the direct and inverse 2D SHE have been demonstrated experimentally 72 in LAO/STO nanoscale devices 73 . Moreover, both the spin diffusion length and the conversion efficiency were demonstrated to be largely tunable by a back-gate voltage 73 . Beyond the spin-to-charge conversion, the symmetry breaking at the LAO/STO interface, combined with an externally applied magnetic field, leads to the appearance of non-reciprocal transport phenomena 74 , such as a large unidirectional magnetoresistance, often coined the bilinear magnetoresistance 75 , 76 , 77 , 78 , because it varies linearly with both the applied current and the applied field. Because this magnetoresistance is a consequence of the spin–orbit interaction, it has been shown that it can be likewise tuned using a back-gate voltage 76 , 77 . Importantly, the amplitude of the bilinear magnetoresistance can be used to extract the Rashba coefficient, with a good agreement with values deduced from weak antilocalization — but over a broader range of carrier densities — and with theory 76 . Box 1 Rashba–Edelstein effect and 2D spin Hall effect . The presence of finite spin–orbit coupling in a 2D electron gas induces a spin splitting, which, in a simple free-electron picture with parabolic dispersion, results in two concentric circular Fermi?contours with opposite spin chiralities. In these Fermi contours, the spins are locked perpendicularly to the momentum (left schematic in the figure). This gives rise to two different spin-to-charge conversion mechanisms. The first is the direct Edelstein effect (top-right schematic), where a current injected along the x direction induces a shift of Δ k x of the Fermi contour, generating a spin accumulation \(\delta s=\delta s\uparrow -\delta s\downarrow \) along the y direction. This spin accumulation can diffuse towards a neighbouring ferromagnetic layer, thus generating a spin current and, eventually, spin–orbit torques. The inverse Edelstein effect corresponds to the reciprocal mechanism: an incoming spin current generates a spin accumulation, spin-polarized along y and, thus, a charge current along x . The second charge-to-spin conversion mechanism is the direct 2D spin Hall effect (bottom-right schematic). When the Fermi contours are displaced by Δ k , the spins are not exactly perpendicular to k and start to precess around the local Rashba field, ultimately acquiring a finite component along + z for k y ?>?0 and ? z for k y ?charge current applied along x , thus, results in the motion of electrons with opposite spins in opposite directions, that is, in a pure spin current with a spin polarization along z . The reciprocal effect, the inverse 2D spin Hall effect, is also possible: in this case, a spin current is converted into a charge current. Figure reprinted with permission from ref. 73 , ACS. Other oxide-based 2DEGs and interfaces . KTaO 3 -based 2DEGs . Recently, another perovskite oxide, KTaO 3 , has attracted the attention of the research community. Similarly to SrTiO 3 , when KTaO 3 is interfaced with other oxide thin films, such as LaTiO 3 (ref. 79 ), amorphous LaAlO 3 (ref. 80 ), EuO (ref. 81 ) or LaVO 3 (ref. 82 ), a 2DEG appears at the interface. However, unlike SrTiO 3 , KTaO 3 contains the 5 d heavy element tantalum, which results in a strong band splitting due to a SOC of 400?meV (refs 83 , 84 , 85 ). Owing to this large SOC, the 2DEG displays clear signatures of weak antilocalization at low temperatures 82 . Moreover, when in proximity with the ferromagnet EuO, the 2DEG exhibits hysteretic magnetoresistance up to a temperature of 25?K (ref. 81 ). Based on these properties, KTaO 3 -based 2DEGs hold great potential as a robust platform for spin-to-charge interconversion experiments. Indeed, a charge current of ~1?nA was demonstrated at 10?K at the EuO/KTaO 3 interface 86 , generated through the inverse Edelstein effect by thermally injecting a spin current from EuO. A recent study also demonstrated both spin–charge and charge–spin conversion in KTaO 3 2DEGs defined by the deposition of a thin Al film 87 . Finally, we note that (111)-oriented KTaO 3 2DEGs were recently shown to display superconductivity at 2?K, a temperature one order of magnitude higher than the superconducting critical temperature in STO 2DEGs 88 , 89 . BaSnO 3 -based 2DEGs . The promising transparent conductor BaSnO 3 represents yet another system that has attracted a great deal of attention in recent years. When covered with LaInO 3 (refs 90 , 91 ), the near-interface region of BaSnO 3 shows a 2DEG character. The most attractive feature of this 2DEG system is its excellent room-temperature conductivity, owing to the combination of a very large electron mobility (~300?cm 2 ?Vs ?1 ) 92 , exceeding that found in SrTiO 3 by two orders of magnitude 51 , and a high carrier concentration (~10 20 ?cm ?3 ). Thanks to these unparalleled room-temperature transport properties, this 2DEG system is expected to hold great potential for applications. Nonetheless, it is yet to be investigated as a possible spin–charge interconversion platform. ZnO-based 2DEGs . Moving beyond perovskite systems, several other oxide-based 2DEGs have been studied. The most prominent example is the high-mobility interface between Mg x Zn 1? x O and ZnO (ref. 93 ). For this 2DEG system, the carrier density and mobility vary greatly with the amount of magnesium substitution ( x ). For x ?=?0.15 and x ?=?0.2, sheet carrier densities of n s ?~?0.66?×?10 12 and 3.7?×?10 12 ?cm ?2 , with corresponding electron mobilities of μ ?~?5,500 and 2,700?cm 2 ?Vs ?1 , respectively, were demonstrated at 1?K. These relatively large mobility values, combined with the value of the electron mass in ZnO, 0.3?m e , allowed the first demonstrations of the quantum Hall effect 93 and of the fractional quantum Hall effect 94 in an oxide material, in samples grown by molecular beam epitaxy. These observations underline the cleanliness and extreme smoothness of the MgZnO/ZnO interface. Nonetheless, this 2DEG system only displays a moderately small Rashba SOC strength of 0.7?meV?? (ref. 95 ), and, therefore, has not yet served as the basis of any spin–charge interconversion experiments. Ruthenates, iridates and other oxide systems . Apart from the interfacial 2DEGs covered up to this point, a large variety of bulk conductive oxides have recently emerged as promising systems for spintronics applications based on the SHE. The first experimental demonstration of a detectable spin-to-charge conversion in a conductive oxide was realized in indium tin oxide (ITO) 96 . These results paved the way for the possibility to use all-oxide systems in spintronics, with a ferromagnetic oxide as the spin current source and an oxide as the detector. Nonetheless, in ITO, the spin-to-charge current conversion efficiency — the spin Hall angle ( θ SHE ) — is one order of magnitude smaller than that found in heavy metals 97 (Table? 1 ). This limitation can be circumvented by using other conducting oxides containing heavy elements. One such oxide is IrO 2 , which possesses a very high spin Hall conductivity, nearly ten times larger than that of Pt, which makes it an excellent spin detector 98 . This large spin Hall conductivity is accompanied by a low conductivity; thus, the spin Hall angle is smaller than that of Pt and is θ SHE ?=?4%. However, recent spin-torque measurements have indicated a θ SHE ?=?9% 99 , with a spin diffusion length λ S ?=?1.7?nm. Spin Seebeck measurements yielded a product θ SHE ?×? λ S ?=?0.15?nm, consistent with these results 100 . The high spin Hall conductivity is connected with the presence of exotic features in the band structure of IrO 2 , known as Dirac nodal lines. In the presence of SOC, these Dirac nodal lines can induce a large intrinsic SHE 101 . In SrIrO 3 , similar topologically non-trivial states were also predicted 102 , 103 and observed using ARPES 104 , 105 . Based on calculations of the spin Berry curvature 106 , the amplitude of the intrinsic spin Hall conductivity in SrIrO 3 is expected to be giant. One additional characteristic of the SHE in SrIrO 3 is that it is sensitive to oxygen octahedra tilting and to the lattice symmetry, which offers the possibility to tune the SHE with thickness 107 . This giant SHE was probed by several experimental methods 107 , 108 , 109 and can lead to current-induced magnetization switching, which could be used, for example, for memory applications 110 (Fig.? 2a ). Fig. 2: Spin-to-charge conversion in iridates and ruthenates. a Current-induced magnetization switching in SrIrO 3 /SrRuO 3 bilayers grown on SrTiO 3 (STO). The top schematic shows the set-up for current ( I )-induced magnetization ( M ) switching. The magnetic easy axis is tilted away from the z axis with an angle θ EA . The bottom schematic illustrates the spin torque switching behaviour observed when θ EA ?≠?0 and a current is applied to switch the magnetization, which is tilted in the x direction, without the need for an external magnetic field. τ AD is the spin transfer torque and the dashed green line indicates the magnetic hard axis. The plot shows the anomalous Hall resistance, R H , as a function of current, showing current-induced magnetization switching 110 . b Inverse spin Hall effect measured using spin pumping by ferromagnetic resonance in La 0.7 Sr 0.3 MnO 3 (LSMO)/SrRuO 3 (SRO) at room temperature (right, top). When the SRO layer is absent, the effect disappears (right, centre). The bottom-right panel shows the same experiment replacing SRO with Pt, indicating a higher efficiency in the SRO case. At the ferromagnetic resonance, the magnetization M of the LSMO precess, leading to the injection of a spin current j s from the LSMO towards SRO. The spin current is then converted into a charge current j c and a measurable voltage 115 . Panel a adapted from ref. 110 , Springer Nature Limited. Panel b adapted from ref. 115 , CC BY 4.0 . Full size image The presence of Dirac nodal lines in the band structure of conductive oxides is not limited to iridates and was also predicted in RuO 2 (ref. 101 ), whose associated large spin Hall angle was further confirmed through spin Seebeck effect measurements, in which the output voltage was, after material optimization through annealing, larger than that of Pt (ref. 111 ). Another ruthenate that attracted much attention recently is SrRuO 3 , a conductive oxide with a ferromagnetic transition below 160?K. Although several reports evidence the existence of the SHE in SrRuO 3 (refs 112 , 113 ), only a few experiments quantitatively estimated the conversion efficiency. These results evidence that SrRuO 3 possesses a short spin diffusion length 114 and a large spin Hall angle, comparable with that of Pt (ref. 115 ) (Fig.? 2b ; Table? 1 ). Similarly to SrIrO 3 , the degree of oxygen octahedra tilting plays an important role in the intensity of the SHE 116 . Following the recent rise of interest for the use of ferromagnets as efficient SHE materials 117 , one can expect that SrRuO 3 will attract attention in the near future as a platform to study the interplay between magnetism and the SHE in oxide systems. The effect of the ferromagnetic transition is still not fully understood, and contradictory results have been reported 115 , 116 . Recent work also showed a substantial charge–spin conversion effect in ultrathin films of the delafossite oxide Rashba ferromagnet PdCoO 2 (ref. 118 ), which in the bulk exhibits a giant surface Rashba splitting 119 . In oxide systems, a high spin–charge interconversion is not limited solely to the bulk or to the presence of a 2DEG but can also occur at interfaces, similarly to the case of the Ag/Bi Rashba interface 120 . The use of a metallic interlayer can lead to a substantial enhancement of the conversion efficiency in Ag/ITO compared with the bare ITO film 121 . Interestingly, the use of such a multilayer structure to harness the spin-to-charge conversion at an interface is applicable also to insulating oxides such as Cu/Bi 2 O 3 (refs 122 , 123 ). These results provide evidence that, in addition to the bulk properties or the presence of a 2DEG, the interface plays a critical role in the spin-to-charge conversion in oxides. Interestingly, iridates and ruthenates are also widely studied in combination, as skyrmionic structures arise in SrIrO 3 /SrRuO 3 bilayers. This topic is discussed in more detail in the section on chiral magnetism and skyrmionic structures. Ferroelectric control of the spin–charge interconversion . The polar nature of ferroelectrics makes them prime candidates to harbour a Rashba SOC, which can have the additional advantage of being switchable by an electric field. The past few years have seen efforts towards the identification of single-phase ferroelectric Rashba semiconductors (FERSCs) 124 , with the focus mainly directed towards GeTe, a low-bandgap semiconductor and ferroelectric with a Curie temperature of 700?K. GeTe has been predicted to be a bulk Rashba material 125 in which polarization switching causes a full reversal of the spin texture of the Rashba-split Fermi contours. Experimentally, because of high leakage, indications of ferroelectricity have only been provided in thin films using piezoresponse force microscopy 126 . The surface band structure of GeTe has been mapped by ARPES, which provided evidence of a strong Rashba splitting that depends on the ferroelectric polarization state (in two different samples 127 or on the same sample poled in situ 128 ). However, early spin-to-charge conversion experiments in GeTe-based structures have shown a low efficiency 129 . In parallel, a switchable Rashba SOC has been predicted in compounds from the perovskite family that includes BiAlO 3 (ref. 130 ), strained KTaO 3 (ref. 131 ), strained SrBiO 3 (ref. 132 ) and PbTiO 3 (ref. 133 ). Importantly, it has been argued that the coexistence of a large spontaneous polarization and a sizeable SOC is not sufficient to have strong Rashba effects, which is why simple ferroelectric oxide perovskites with transition metal at the B-site are typically not ideal candidates for FERSCs, which require bands with a large and electrically switchable Rashba splitting at the conduction band minimum (CBM) 134 . Indeed, in several oxide FERSCs, the Rashba-split bands are higher in energy than the CBM, implying that, when the Fermi level is positioned to intersect them, other, non-Rashba-split bands also contribute to the transport, diminishing the ensuing direct or inverse Edelstein effect (note, however, that this is also the case in STO 2DEGs, that, nevertheless, show a very strong inverse Edelstein effect, as we discussed 8 ). Instead, an Aurivillius compound, Bi 2 WO 6 , was proposed as a possible FERSC in which a different and larger crystal field causes the Rashba-split bands to lie at the CBM 134 . Regarding interfacial systems, perhaps the first prediction of a ferroelectric control of the Rashba SOC was reported by Jürgen Henk and colleagues for Bi/BaTiO 3 interfaces 135 , a system that was later probed experimentally 136 . The variation of the Rashba coefficient was modest, but other studies have also calculated a large (0.1–0.7?eV??) and fully switchable Rashba coefficient in various types of perovskite interfaces combining BaTiO 3 with BaRuO 3 , BaIrO 3 or BaOsO 3 (ref. 137 ). Experimental demonstrations of the ferroelectric control of the spin–charge interconversion were provided only very recently 9 . Under high electric fields, the ferroelectric-like behaviour developing in STO — a feature that had been previously reported 138 — was harnessed to control the inverse Edelstein effect by ferroelectricity in STO 2DEGs 9 . In NiFe/Al/STO samples, it was shown that both the electrical conductivity and the spin-to-charge conversion display a hysteretic dependence on the gate voltage (Fig.? 3 ). The conversion is very large, with a record inverse Edelstein length of around 60?nm, but also bipolar, as the sign of the current changes with the ferroelectric polarization state. This bipolar property of the conversion shows electrical remanence up to T ? ?50?K, which corresponds to the ferroelectric Curie temperature. By applying positive or negative voltage pulses across the STO substrate, the conversion current obtained in spin-pumping experiments was fully reversed and remained stable for several hours. Fig. 3: Non-volatile electrical control of spin-to-charge conversion in SrTiO 3 -based 2D electron gases. Gate-voltage-dependence of the normalized current produced by the inverse Edelstein effect in the sample sketched in the inset, evidencing a non-volatile control of spin-to-charge conversion (left). Magnetic-field-dependence of the normalized current produced in spin-pumping experiments for different values of the gate voltage as marked on the left graph (right). A dominant symmetrical response corresponding to spin-to-charge conversion is obtained at all gate voltages; it changes sign with the gate and shows two opposite remanent states (C and E). H res is the ferromagnetic resonance field in the spin-pumping experiment 9 . 2DEG, 2D electron gas. Reprinted from ref. 9 , Springer Nature Limited. Full size image The exact role of the induced ferroelectric state on the band structure and its influence on the position of the Fermi level within the band structure remain to be elucidated. A change of ferroelectric polarization, and of the associated electric field, at the interface with the 2DEGs can lead to the reversal of the chirality of the Fermi contours. Nonetheless, the peculiar avoided crossing points in the band structure are known to play an important role in determining the intensity and the sign of the produced charge current 8 . The precise role of ferroelectricity is still an open question, but the data suggest that the ferroelectric state and its associated additional internal electric field increase the Rashba field, leading to higher conversion efficiencies. Soon after the publication of these results, two groups showed that, by minute Ca substitution for Sr in STO (Ca-STO) — known to make STO ferroelectric 139 — and by depositing a reactive metal like Al (ref. 140 ) or an epitaxial LAO thin film 141 , it is possible to tune the electrical conductivity of the 2DEGs through the ferroelectric state of Ca-STO 140 , 141 . Whereas in Al/STO samples 9 the ferroelectric state disappears at around 50?K, Ca-STO exhibits a transition temperature of 28?K. An open question is whether the 2DEG is ferroelectric by itself or if its vicinity to a ferroelectric material only tunes its carrier density. Indeed, with large doping values and quite extended 2DEGs, the electric field might be quickly screened in the 2DEG. More recently, a ferroelectric control of spin-to-charge conversion at room temperature was demonstrated with GeTe-based structures, with an efficiency comparable with that of Pt (ref. 142 ). This remanent control of the spin–charge interconversion is highly interesting for spintronics applications, because it enables storage of the information in the ferroelectric state, rather than in a ferromagnetic state. Beyond spin–orbit torques, the spin-to-charge conversion could, for instance, be used in devices derived from the magnetoelectric spin–orbit transistor proposed recently by Intel 64 . Spin transfer and spin–orbit torque are fast ways to switch the magnetic state, but still require substantial energy, typically in the 10–100 femtojoule range, whereas attojoule switching energy can be achieved for a ferroelectric state 143 . This low-energy switching might enable ultralow-power spintronic devices with non-volatile, ultralow-energy switching capabilities. Chiral magnetism and skyrmionic structures . Recent years have seen a renewal of interest for non-collinear spin structures, both in the oxide world — many multiferroics are oxides and display spiral or cycloidal spin states — and in metal-based systems. In most cases, SOC is a key ingredient for the stabilization of non-collinear spin textures. Although for both oxide and metallic systems most early work focused on bulk materials, thin-film heterostructures are now under intense scrutiny and bring additional functionalities in terms of design and control. Non-collinear spin order in oxides . Several mechanisms can lead to non-collinear magnetic order 144 . Let us first distinguish between systems with inversion symmetry and systems with broken inversion symmetry, in which antisymmetrical exchange (the DMI, which depends linearly on the strength of the spin–orbit interaction) leads to non-chiral spin textures. In centrosymmetrical systems, non-collinear spin order can simply arise from the geometry of the spin lattice. A typical example is that of a triangular lattice of spins coupled by antiferromagnetic interactions. The impossibility to achieve an antiparallel alignment between all neighbouring spins leads to magnetic frustration and to a non-collinear spin arrangement corresponding to, for instance, spins aligned along the edges of the triangles or pointing towards their centre (whilst maintaining a zero net magnetization). A similar situation occurs for spins arranged at the corners of tetrahedra, which leads to a rich variety of spin arrangements within and between tetrahedra with (almost) degenerate energies (see, for example, the review on magnetic pyrochlores in ref. 145 ). Non-collinear magnetism can also arise when different magnetic interactions coexist and compete. In a system with two magnetic sublattices, at least three magnetic interactions are present, within each sublattice and between spins on different sublattices. If the strengths of these interactions are comparable, the ground state may be not a collinear ferrimagnetic or ferromagnetic state but a non-collinear state. This is the situation in some spinel ferrites 146 , in which the spins are canted according to the Yafet–Kittel model 147 . SrFeO 3 and CaFeO 3 are two rare examples of perovskite oxides with a spiral spin order. In these negative charge-transfer compounds, the magnetic order has been proposed to arise from the competition between ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour interactions 148 or owing to double exchange in the peculiar case of negative charge-transfer systems 149 . Upon increasing temperature and/or applying a large magnetic field, additional helical phases can be stabilized. Remarkably, some of these phases lead to the observation of a topological Hall effect (THE), suggestive of a topological character for the spin texture, in analogy with the situation in the celebrated B20 alloys 150 . The competition between magnetic anisotropies can promote non-collinear magnetic states. A typical situation is that of thin films with a uniaxial anisotropy, for instance, a perpendicular anisotropy (induced by epitaxial strain or interface anisotropy) that favours out-of-plane spins, competing with shape anisotropy, favouring spins lying in the film plane. Structural distortions can be another source of uniaxial anisotropy. This mechanism has been successfully used to engineer topological spin textures in oxides, as we see in the following section. The oxide family also hosts several non-centrosymmetrical magnetic oxides that present non-collinear spin textures 151 . These compounds are usually insulating and their non-collinear spin order often leads to (or is associated with) ferroelectricity, making them multiferroic 152 . A famous example is that of BiFeO 3 (BFO), one of the very few room-temperature multiferroics. In the bulk, it displays a non-collinear antiferromagnetic state with a long-period (≈?62?nm) cycloidal modulation 153 . The cycloid order arises from a Dzyaloshinskii–Moriya-like interaction caused by the magnetoelectric coupling between the large ferroelectric polarization and the spins carried by the Fe ions. An additional DMI due to the rotations of the FeO 6 octahedra induces a periodic canting of the spins, leading to a weak ferromagnetic moment and to a spin density wave with the same periodicity as the cycloid 154 . In epitaxial thin films, the cycloid state can see its period or propagation direction modified by strain 155 , 156 , 157 ; very large strain even destroys it, inducing a transition to a weak ferromagnetic state. The spin textures are also sensitive to the ferroelectric domain configurations (the cycloid propagation vector depends on the polarization direction) and, at ferroelectric domain walls, interesting bubble-shaped chiral spin textures that are possible skyrmion embryos 11 have been observed (Fig.? 4 ). Engineering antiferromagnetic skyrmions in BFO heterostructures would open exciting possibilities, given the superiority of antiferromagnetic skyrmions 158 over ferromagnetic ones in terms of operation frequency and displacement speed 159 , for example, and owing to the possibility to control them by electric field at low power. Fig. 4: Chiral magnetic textures at ferroelectric domain walls in a BiFeO 3 thin film. a Scanning nitrogen-vacancy magnetometry image (left) evidencing the presence of two cycloids, together with a rectangular array of magnetic bubbles at ferroelectric domain walls, and simulation of the stray field generated by the spin texture (right), showing very good agreement with the microscopy image. b Magnetic simulations showing the cycloidal spin textures within the ferroelectric stripe domains and at the domain walls. Every second wall, the polarization (black arrows) rotates along a long winding consistent with the chirality measured for the ferroelectric order. Reprinted from ref. 11 , Springer Nature Limited. Full size image In addition to BFO, several other multiferroic oxides display non-collinear magnetic order. This is the case of rare-earth manganite perovskites such as TbMnO 3 (ref. 160 ) and more complicated compounds such as TbMn 2 O 5 (ref. 161 ). Unlike in BFO, where ferroelectricity is caused by the lone-pair mechanism, leading to an off-centring of the Bi ions, in these materials, the ferroelectric state is a consequence of the non-collinear (cycloidal) spin order (spin-driven ferroelectricity 162 ). The description of their rich physics goes beyond the scope of this Review and we refer the reader to the 2016 review by Manfred Fiebig and colleagues 163 . Despite the obvious potential for skyrmion physics in multiferroics and efforts in this direction 164 , only Cu 2 OSeO 3 and related compounds have been shown to exhibit skyrmions 165 . Skyrmions and skyrmion bubbles in oxide heterostructures . Manganites . Mixed-valence manganites 166 display rich phase diagrams where hole doping (by, for example, Sr or Ca) into the parent compound LaMnO 3 , an antiferromagnetic insulator, results first in charge-ordered and orbital-ordered ferromagnetic and insulating phases, and then in ferromagnetic and metallic phases, owing to the onset of double-exchange interaction. At optimal doping (around 0.33), the Curie temperature is maximized, reaching 360?K in La 0.67 Sr 0.33 MnO 3 . This compound is a half-metal 167 that has been widely used in spintronic devices such as magnetic tunnel junctions or spin filters 168 . At high doping, manganites typically display insulating behaviour and antiferromagnetism, but, in some compounds, slight electron doping from the other end member (SrMnO 3 or CaMnO 3 ) produces a metallic phase with weak ferromagnetism 169 , 170 . Mixed-valence manganites are centrosymmetrical systems in which a uniaxial anisotropy can arise at structural phase transitions or be engineered through epitaxial strain in thin films. Most compounds have Curie temperatures below 300?K, which makes the direct observation of nanoscale spin textures challenging compared with magnetic multilayers based on Co or Fe. Nevertheless, magnetic bubbles have been imaged by Lorentz microscopy in bulk manganite specimens 171 , 172 , 173 , 174 , 175 . Despite being formed in the absence of a DMI (but through long-range dipolar interactions), these bubbles, 100–200?nm in diameter, can possess a topological character and carry a finite topological charge, albeit with different chiralities (Box? 2 ). In manganite thin films, compressive strain promotes perpendicular anisotropy, which led to attempts to generate and observe topological bubbles and skyrmions. Ca 0.96 Ce 0.04 MnO 3 is a canted ferromagnet with a magnetization of ~0.8 μ B /Mn that develops a strong perpendicular magnetic anisotropy when grown on YAlO 3 substrates 176 . Hall measurements below the Curie temperature (~110?K) revealed the presence of a hump associated with the THE 177 (Fig.? 5a , top). Magnetic force microscopy (MFM) showed the presence of bubble-like features, whose density is maximum at the peak of the THE as a function of magnetic field. Interestingly, the amplitude of the THE strongly increases with decreasing carrier density in Ca 1? x Ce x MnO 3 with various doping levels, possibly owing to enhanced electron correlations upon approaching the charge-transfer insulating state of the parent compound CaMnO 3 (refs 178 , 179 ) (Fig.? 5a , bottom). A sizeable THE was also observed in La 0.7 Sr 0.3 Mn 0.95 Ru 0.05 O 3 thin films with tailored perpendicular anisotropy (Fig.? 5b ); the effect was ascribed to the presence of topological spin textures observed by both MFM and Lorentz microscopy. A variety of skyrmions were found, as illustrated in the lower part of Fig.? 5b . Fig. 5: Topological Hall effect in manganite heterostructures. a Hall effect at 15?K in a Ca 0.96 Ce 0.04 MnO 3 thin film (top). In addition to the usual anomalous Hall effect, a peak is present in the data, corresponding to the topological Hall effect (THE). The inset shows a magnetic force microscopy (MFM) image evidencing bubbles whose density depends on the magnetic field and is maximum at the THE peak. The relationship between the THE and the carrier density for various Ca 1? x Ce x MnO 3 thin films suggests that the THE is enhanced by correlations (bottom) 177 . The grey and black lines correspond to a model in two different coupling regimes. b THE at 10?K for a La 0.7 Sr 0.3 Mn 0.95 Ru 0.05 O 3 thin film (top). The MFM and Lorentz microscopy images are measured at the same temperature and at 70?mT (corresponding to the marker in the top graph); the bottom images show the result of the transport-of-intensity equation analyses for the Lorentz transmission electron microscopy image in the two areas labelled a and b. Domain a is a single skyrmion with skyrmion number N ?=?1 and domain b is a biskyrmion with N ?=?2 (ref. 235 ). ρ THE , THE resistivity. Panel a adapted from ref. 177 , Springer Nature Limited. Panel b reprinted with permission from ref. 235 , JPS. Full size image Even in the absence of a DMI induced by interfacing with materials containing heavy elements, skyrmions and THEs have, thus, been observed in manganites. However, there have also been attempts to stabilize skyrmions in bilayers combining manganites with iridates — where the interface breaks the inversion symmetry 180 , 181 — in part motivated by theoretical predictions 182 . For instance, in ref. 180 , LaMnO 3 was combined with SrIrO 3 to craft chiral spin textures producing a THE signal. In spite of such efforts, unambiguous signatures of skyrmions in such heterostructures remain elusive. Box 2 Skyrmions and magnetic bubbles . Skyrmions and magnetic bubbles can be classified as topological if they possess a non-zero value of the topological charge, which is given by the quantity \(\int d{r}^{2}{\bf{m}}\cdot ({\partial }_{x}{\bf{m}}\times {\partial }_{y}{\bf{m}})\) , where m represents the magnetization vector. The in-plane component of the magnetization takes on a Néel-type configuration for interface-driven Dzyaloshinskii–Moriya interaction (DMI), whereas Bloch-type configurations are favoured by bulk DMI, dipolar interactions or both. Competing interactions can result in mixed Néel–Bloch states, whereas non-topological bubbles possess a mixture of opposite chiralities, as shown in the figure. Skyrmion states are favoured when the DMI dominates over dipolar interactions, and are characterized by a compact core with a peak-like variation in the polar angle of the magnetization, θ ( r ), as a function of the radial distance r from the core centre. Magnetic bubbles are favoured when the dipolar interaction is dominant, and are characterized by a smooth plateau in θ ( r ) at their centre. Skyrmions are homochiral, whereas bubbles can be either homochiral if the DMI is sufficiently large or heterochiral or achiral if the DMI is small or non-existent. SrRuO 3 . The case of SrRuO 3 (SRO) is perhaps the most complex. SRO is an itinerant ferromagnet with a Curie temperature of 160?K. It can be grown as epitaxial thin films of very high structural quality, notably on SrTiO 3 substrates 183 , and generally displays strong perpendicular magnetic anisotropy. In 2016, Masashi Kawasaki and colleagues reported the observation of a topological effect in bilayers combining SRO and SrIrO 3 (SIO), interpreted as resulting from the presence of 10-nm-sized Néel skyrmions 184 (Fig.? 6a ). Just as in metallic multilayers, a heavy-metal-based layer — here, the SIO — was used to generate a DMI and induce skyrmions in the ferromagnet, SRO. These results were reproduced by other groups 185 , 186 , 187 , 188 , but a similar THE was also found in SRO single films 189 , 190 , 191 , not interfaced with a layer with strong SOC, such as SIO. This observation started to raise questions on the origin of the THE. Five years after the seminal paper on SRO/SIO 184 , subsequent work has coalesced into two main lines of interpretation. Fig. 6: Topological Hall effect in SrRuO 3 heterostructures. a Hall effect at 80?K in a SrRuO 3 (5?u.c.)/SrIrO 3 (2?u.c.) sample. The red curve shows the total Hall signal, whereas the green curve corresponds to the anomalous Hall effect (AHE) and the blue curve to the topological Hall effect (THE, characterized by a peak in the Hall trace). The inset is a magnetic force microscopy image measured at 0.2?T. The dashed square highlights a possible skyrmion 184 . b Model (left) illustrating how the addition of two AHE contributions with opposite sign (green and purple) can generate a signal resembling a THE (pink), and illustration (right) showing the opposite spin accumulation of the two individual AHE contributions 198 . c Anomalous Hall resistance ( R AHE ) curves of SrRuO 3 films with thickness increasing from 4 to 5 u.c. The light grey curves are linear combinations of the AHE curves of individual 4-u.c. and 5-u.c. SrRuO 3 films 191 . u.c., unit cell. Panel a adapted with permission from ref. 184 , AAAS. Panel b reprinted from ref. 191 , CC BY 4.0 . Panel c reprinted with permission from ref. 191 , ACS. Full size image A first set of works argue that the THE in SRO heterostructures is caused by topological spin textures. Several groups have performed MFM as a function of temperature and/or magnetic field and observed contrast interpreted as bubbles or skyrmions 10 , 184 , 186 . Jun-Sik Lee and colleagues also detected Néel-type chiral spin textures using resonant X-ray scattering 192 . Based on MFM data, Lukas Eng and colleagues concluded that the detected features could not account for the observed THE 193 . By contrast, Marin Alexe and colleagues observed chiral objects arising from the intersection of two spin cycloids, appearing in a magnetic field range consistent with the observation of the THE 194 . In a second body of results, it is argued that the THE is just the sum of two anomalous Hall effect (AHE) terms with opposite signs, in regions of the sample with different coercivity 191 , 193 , 195 , 196 , 197 , 198 . This scenario is illustrated in Fig.? 6b . Indeed, in SRO, the AHE is known to have an intrinsic, band-structure-driven origin and to change sign with temperature or when SRO is alloyed with CaRuO 3 , which both modify the magnetization 199 . Andrea Caviglia and colleagues 198 provided a theoretical explanation for the existence of sign-competing anomalous channels, whose origin they attribute to bands with a non-trivial topological character associated with non-zero Chern numbers; this scenario explains their and others’ experimental data. One striking result is the very strong thickness dependence of the AHE in SRO single films at very low thickness: the AHE is positive at 4 unit cells but negative at 5 unit cells (Fig.? 6c ). For intermediate, non-integer thicknesses, the Hall signal displays a clear hump, usually interpreted as a THE, which can, however, be reproduced rather well by a simple interpolation between the 4-unit-cell and 5-unit-cell AHE traces (grey lines in Fig.? 6c ). MFM on a 4.5-unit-cell sample revealed an inhomogeneous magnetic response, with two types of regions having distinct coercive fields, leading to a bimodal distribution 199 . In summary, in SrRuO 3 , clear-cut evidence of skyrmions with an unambiguous topological character — that could be ascertained by Lorentz microscopy — has not been provided yet. In fact, the latest results tend to suggest that the observed THE may, instead, reflect reciprocal space-based mechanisms combined with magnetic disorder. More efforts are needed to disentangle this complicated problem. Ferrites . Heterostructures involving ferrimagnetic insulators, such as yttrium iron garnet, Y 3 Fe 5 O 12 (YIG), thulium iron garnet, Tm 3 Fe 5 O 12 (TmIG), and terbium iron garnet, Tb 3 F 5 O 12 (TbIG), have recently been shown to possess the requisite properties for hosting topological spin textures such as skyrmions. The key advantage compared with other ferromagnetic oxides is the high Curie temperature of these compounds, in the 500?K range. TmIG, in particular, exhibits perpendicular magnetic anisotropy as a result of tensile strain when grown on (111)-oriented gadolinium gallium garnet (Gd 3 Ga 5 O 12 , GGG) or its substituted variants (sGGG), which are commonly used substrates for such materials. When combined with a heavy-metal overlayer, such as platinum or tungsten, spin–orbit torques and interfacial DMIs can be induced in the magnetic insulator in an analogous fashion to all-metallic systems, such as Pt/Co-based systems 200 , 201 , 202 . As a result, a renewed focus on phenomena such as chiral domain wall motion under spin–orbit torques and skyrmion bubble formation has been brought about by such garnet-based heterostructures. Following observations of current-driven magnetization dynamics in YIG/Pt systems 203 , 204 , 205 , magnetization switching due to spin–orbit torques in TmIG was reported in 2017 with Pt overlayers 206 and in 2018 with W overlayers 207 . Harmonic Hall effect measurements performed on these systems indicate that the strength of the spin–orbit torques is comparable with that observed in earlier work on YIG/Pt (ref. 206 ). Such torques have also been exploited to study current-driven domain wall motion in TmIG/Pt (refs 208 , 209 ) and TbIG/Pt (ref. 209 ), where the observed high velocities, reaching up to 800?m?s ?1 , can be attributed to the interfacial DMI, which pushes the Walker transition to higher fields under field-driven motion and suppresses it entirely under pure SHE-driven motion 200 . The homochiral Néel character of the domain walls has been deduced from the way the wall velocities vary in the presence of in-plane-applied magnetic fields and from nitrogen-vacancy centre magnetometry measurements 208 , which suggest that the DMI induced at the TmIG/Pt interface is of opposite sign to that at the sGGG/TmIG interface. The chiral magnetic order in TmIG heterostructures exhibiting the THE has also been probed. Fengyuan Yang and colleagues 210 and Kang Wang and colleagues 211 have revealed clear signatures of an additional topological contribution to the Hall effect in TmIG/Pt films, which appears over a temperature range around and above room temperature (depending on the TmIG film thickness) and for applied perpendicular fields up to about 0.5?T. The temperatures explored remain below but approach the Curie temperature of TmIG, which is about 560?K for bulk samples. The THE signal is attributed to the presence of magnetic skyrmions, and it is argued that the transition between a perpendicular magnetic anisotropy and an in-plane anisotropy, which occurs at a temperature coinciding with the appearance of the THE signal 211 , favours the formation of a skyrmion lattice by reducing the domain wall energy. Because current only flows through the Pt overlayer, the topological spin structure induced in the TmIG film is probed indirectly. Yang and colleagues suggest that the THE signal arises from spin-torque interactions at the TmIG/Pt interface, leading to a phenomenon dubbed the spin Hall THE 210 . Wang and colleagues suggest, instead, that the THE arises from an imprinted spin structure in the Pt through the proximity effect 212 . Both of these viewpoints appear to be consistent with more recent experiments in which the THE signal disappears with the inclusion of an additional Cu buffer layer 213 , because both the proximity effect and the spin-torque interactions would be suppressed when adding the buffer. Although a direct correlation between the observed THE and spin structures is still lacking, separate studies have provided clear evidence of skyrmion states in TmIG films. Besides the observation of chiral domain walls mentioned above, Kerr microscopy has been used to reveal bubble-like states in TmIG/Pt films 214 , which have been subsequently studied in greater detail in experiments involving scanning transmission X-ray microscopy 215 . Complementary measurements with photoemission electron microscopy revealed a variety of topological and non-topological configurations in the bubbles (Box? 2 ), whose diameter was found to be in the sub-micrometre range 215 . The origin of the DMI in such garnet heterostructures remains a subject of debate. Evidence for the garnet/garnet interface being the primary source of the DMI has been presented in ref. 208 , which showed that chiral domain walls in sGGG/TmIG transition from a pure Néel state to a mixed Bloch–Néel state with the addition of a Pt overlayer. This observation is corroborated by the similar DMI values found for GGG/TbIG/Pt and GGG/TbIG/Cu/Pt (refs 209 , 216 ), where the insertion of a Cu spacer would be expected to suppress any DMI at the TbIG/Pt interface, and is also consistent with the finding that the DMI strength varies little with the Pt film thickness and with different capping layers 217 . Detailed experiments on current-driven domain wall motion suggest that the DMI arises primarily from the strong SOC in the rare-earth garnet itself, induced by broken inversion symmetry at an interface, rather than in the substrate or heavy metal overlayer 216 (although the latter does give a finite contribution). It can be noted that frequency nonreciprocity of spin wave propagation in GGG/YIG has also been reported and attributed to an induced DMI at the garnet/garnet interface 218 . The symmetry breaking at surfaces was also shown to enhance the DMI in BFO, for example 219 . Other studies suggest that the TmIG/Pt interface is the most important for the DMI. For example, ref. 220 shows that the inclusion of a Y 3 Sc 2 Al 3 O 12 (YSAG) buffer layer between the GGG substrate and TmIG or YIG does not suppress the THE when Pt overlayers are present, from which the authors conclude that the DMI at the TmIG/Pt and YIG/Pt interfaces is sufficiently large to promote chiral spin textures. This observation is interpreted by the absence of f -band electrons in YSAG, which, thereby, minimizes the induced DMI at the YSAG/TmIG and YSAG/YIG interfaces. Ultimately, THE signals do not probe the existence of chiral interactions directly but, rather, the presence of topological spin structures like skyrmions that may be stabilized by them. Skyrmionic textures have also been reported in other ferrite compounds. A recent example involving a topological insulator is BaFe 12 O 19 /Bi 2 Se 3 , in which low-temperature signatures of the THE can be attributed to the presence of skyrmions 221 . Here, it is argued that the strong spin-momentum locking of the topological insulator Bi 2 Se 3 induces a large DMI at the interface with BaFe 12 O 19 , where scattering of the surface states through an equilibrium or nonequilibrium proximity effect results in the observed THE signal. Simulations predict a window of applied magnetic field in which the skyrmion states should appear, which is found to correlate well with the appearance of the THE signal in experiment. Another example is α -Fe 2 O 3 (haematite), an insulating antiferromagnetic oxide of trigonal corundum structure that is composed of antiparallel aligned planes of ferromagnetic spins along the crystallographic c axis. The magnetocrystalline anisotropy changes sign at the Morin temperature T m , whereby the Néel vector characterizing the antiferromagnetic order reorients from the out-of-plane direction for T ?? T m . By examining the antiferromagnetic order with linear magnetic dichroism in photoemission electron microscopy, it was shown that temperature variations about T m can produce a variety of meron states, possessing half-skyrmion charges, which grow out of domain wall structures as the reorientation transition takes place 222 . Despite the presence of a Pt capping layer, the overall DMI is not sufficiently strong to impose the favoured chirality on all states, and both Néel-type and Bloch-type merons are observed, along with antimerons, bimerons and topologically trivial coupled meron states. However, the system may be promising for future studies of the electrical control of such states through spin Hall effects. Electrical control of skyrmions in oxide systems . For potential devices based on skyrmions, the ability to generate and displace these topological objects by electrical means is paramount. As discussed above, their electrical detection can be achieved through the THE, which can be much larger in oxides compared with 3 d metal-based systems, or through the AHE 223 . In metallic systems, skyrmions can be generated and displaced by charge currents through spin-transfer torques, and the literature abounds with examples in metallic multilayers 224 , 225 . An electric field can also be used, but then the material must be insulating, or the electric field must be applied across a gate oxide by which the interfacial anisotropy can be tuned 226 . In oxides, both current-based and voltage-based approaches have been used to manipulate skyrmions. The response of non-collinear spin textures comprising both stripes and biskyrmions to the application of a current was investigated in the layered manganite La 1.37 Sr 1.63 Mn 2 O 7 . Upon increasing the current, Lorentz images of the stripes and biskyrmions progressively become blurred (Fig.? 7a ), which the authors interpret as reflecting a dynamical motion faster than the microscope frame rate 172 . In garnets such as TmIG, controlled nucleation of the bubbles is possible with applied current pulses flowing in the Pt overlayer, but the absence of correlation between the bubble motion and current polarity suggests that Joule heating is the primary driving mechanism. This observation is consistent with the finding that bubble density increases with increasing repetitions of applied laser pulses 215 . Fig. 7: Electrical control of skyrmions and topological Hall effect in oxide systems. a Changes in magnetic configurations with increasing current (from 4.8?×?10 7 to 9.0?×?10 7 ?A?m ?2 ), obtained under a magnetic field of 0.3?T applied normal to the (001)-plane device plate at 20?K in a La 1.37 Sr 1.63 Mn 2 O 7 sample 172 . b Top: schematic illustration of the reversible transition of the spin texture from the helical phase to the skyrmion phase upon the application of an electric field in Cu 2 OSeO 3 . Bottom: corresponding Lorentz transmission electron microscopy images measured at 24.7?K (ref. 228 ). c Left: schematic diagram of the experimental set-up for ferroelectric domain switching and Hall measurements. A SrRuO 3 /BaTiO 3 is patterned into a Hall bar in order to detect the topological Hall effect (THE) electrically. An atomic force microscopy tip (shown in orange) is used to write ferroelectric domains into the BaTiO 3 layer and, thereby, affect the THE response. Centre: piezoresponse force microscopy phase images (top) and corresponding Hall and extracted topological Hall curves (bottom) for a SrRuO 3 /BaTiO 3 sample for different ferroelectric poling states: the amplitude of the THE is tuned by the ferroelectric domain configuration. Right: difference in magnetic force microscopy contrast between images taken at two different magnetic fields, evidencing the nucleation of magnetic bubbles induced by ferroelectric poling 10 . ρ AHE , resistivity of the anomalous Hall effect; ρ THE , resistivity of the THE; ρ xy , Hall resistivity. Panel a adapted from ref. 172 , Springer Nature Limited. Panel b adapted with permission from ref. 228 , ACS. Panel c reprinted from ref. 10 , Springer Nature Limited. Full size image In the magnetoelectric skyrmion system Cu 2 OSeO 3 (ref. 165 ), the application of an electric field was found to influence the skyrmion lattice, making it rotate, as evidenced by neutron diffraction measurements 227 . In the same compound, a voltage-induced transition between a stripe phase and a skyrmion lattice (Fig.? 7b ) was also reported 228 . Thin-film heterostructures enable the application of larger electric fields and also make it possible to combine skyrmion-hosting layers with ferroelectrics, which allow for a non-volatile electrical control of properties, such as the skyrmion density. By working with SrRuO 3 /SrIrO 3 bilayers grown on STO, it was shown that a back-gate voltage can be applied to tune the topological and AHEs 229 . Finally, SrRuO 3 was combined with ferroelectric BaTiO 3 to control the amplitude of the THE, associated with the presence of skyrmions in these heterostructures (see Fig.? 7c and, in particular, the MFM image at the far right) 10 . This latter approach is particularly interesting, as it takes advantage of a specific characteristic of oxides — here, the epitaxial combination with a ferroelectric material — to suggest routes for future functional architectures harnessing spin–orbit properties in oxide materials. Outlook . The field of oxide spin-orbitronics is still in its infancy but has already pointed to exciting new research directions arising from the combination of spin–orbit interactions with the numerous coupled degrees of freedom present in oxide systems. Sizeable spin–charge interconversion effects have been observed, both through the spin Hall effect in thin films of, for example, IrO 2 or SrRuO 3 , and in interface systems such as STO 2DEGs. The oxide family harbours many metals based on heavy elements, such as SrMoO 3 or doped BaSnO 3 , and efforts should be made to characterize their spin-to-charge conversion properties 230 . STO 2DEGs show very efficient spin-to-charge conversion and a complex gate dependence linked to their peculiar band structure. KTaO 3 2DEGs share a number of similarities with STO 2DEGs and could potentially display even stronger responses; yet, their spin-conversion properties have barely been studied. In STO 2DEGs, most studies have focused on spin-to-charge conversion, with only a handful of papers exploring charge-to-spin conversion. The recently discovered bilinear magnetoresistance now provides a convenient method to explore this effect, even allowing for a quantitative estimation of the Rashba coefficient, provided an appropriate formalism is used 76 . Efforts should also be directed at spin-torque measurements and magnetization switching experiments, in line with the work by Jingsheng Chen and colleagues on SrIrO 3 (ref. 110 ). As recently highlighted 9 , bringing ferroelectricity as a new ingredient into spin-orbitronics opens many opportunities to design low-power devices operating on spin, whose non-volatility would derive from ferroelectricity rather than from ferromagnetism. An important challenge is now to demonstrate this type of control at room temperature. More generally, the interplay between ferroelectricity and the transport properties of 2DEGs emerges as an interesting topic, in particular, in light of the enhanced superconducting T c in related systems 231 . As described in the second part of this Review, SOC may also bestow oxides with non-collinear spin textures, some of which have a topological character. Some ambiguities in the interpretation of topological Hall signatures should be lifted by performing experiments able to directly assess the topological character of the spin structures. 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