Skyrmionics in correlated oxides

While chiral magnets, metal-based magnetic multilayers, or Heusler compounds have been considered as the material workhorses in the field of skyrmionics, oxides are now emerging as promising alternatives, as they host special correlations between the spin-orbital-charge-lattice degrees of freedom and/or coupled ferroic order parameters. These interactions open new possibilities for practically exploiting skyrmionics. In this article, we review the recent advances in the observation and control of topological spin textures in various oxide systems. We start with the discovery of skyrmions and related quasiparticles in bulk and heterostructure ferromagnetic oxides. Next, we emphasize the shortcomings of implementing ferromagnetic textures, which have led to the recent explorations of ferrimagnetic and antiferromagnetic oxide counterparts, with higher Curie temperatures, stray-field immunity, low Gilbert damping, ultrafast magnetic dynamics, and/or absence of skyrmion deflection. Then, we highlight the development of novel pathways to control the stability, motion, and detection of topological textures using electric fields and currents. Finally, we present the outstanding challenges that need to be overcome to achieve all-electrical, nonvolatile, low-power oxide skyrmionic devices.


Introduction
Skyrmionics is a burgeoning field in spintronics that aims to exploit real-space whirling topological magnetic textures as mobile information bits ('0' and '1') in beyond-Moore computing paradigms. [1] Herein, textures such as skyrmions, bimerons, merons and others, illustrated in Figure 1, are composed of spins winding in a specific sense endowing them topological protection, and allowing them to effectively behave like quasi-particles that can be controlled and processed electrically. Skyrmionic topological racetrack memory, akin to magnetic tunnel junction based random access memory, [2] brings the benefits of fast access and eliminates mechanical moving parts, markedly improving upon the state-of-the-art hard disk drives. Moreover, in the bit control process, in contrast to regular ferromagnetic domain switching or domain wall (DW) motion driven by spin torques, [3] skyrmionic platforms allow the reduction of threshold current density (JC) by up to five orders-of-magnitude, afforded by skyrmions evading defect pinning because of their topological protection. [4][5][6][7] Due to these unique advantages, skyrmionics could open a promising pathway to build fast, dense and energy-efficient non-volatile computing.
Various chiral topological textures can be classified by their unique topological charge, helicity, and orientation of background spins, see Table 1. The topological charge (̂) quantifies the integrated solid angle spanned by the spatially varying local order parameter ̂, which corresponds to the magnetization ̂ in ferromagnetic (FM) or ferrimagnetic (FiM) systems and the Néel vector ̂ in the antiferromagnetic (AFM) counterparts. Topological textures are stabilized by a negative DW energy, [8,9] that can be achieved by the Dzyaloshinskii-Moriya Interaction (DMI) involving a broken spatial inversion symmetry associated with the Dn, T or O (for Bloch skrymions), Cnv (for Néel skyrmions) and D2d (for antiskyrmions) point group symmetries, or through geometrical frustration. [10][11][12] In the absence of a DW energy-lowering agent, the dipolar /demagnetization field may also stabilize multichiral magnetic textures. Most recently, the Kibble-Zurek mechanism, [13,14] which exploits magnetic phase transitions to nucleate multichiral topological textures, has also joined this list. Figure 1 illustrates various magnetic textures found thus far, albeit non-exhaustively, and indicates the corresponding stabilizing mechanisms. Typically, nucleation of these textures is assisted by thermal excitations, usually not found at the ground state, when the competing terms of exchange, anisotropy, DMI/frustration, and external magnetic field are present in an effective magnetic Hamiltonian. With increasing magnetic field, several phase transitions can be seen from stripes, to skyrmion lattice (SkL) before saturating into a trivial collinear magnetic state. [15] By tuning the strength of DMI relative to exchange and anisotropy it is possible to go from thermodynamically stable topological lattices or spin spirals in the strong DMI regime above a critical threshold, to isolated metastable topological quasiparticles in the intermediate/weaker DMI regime. The latter scenario is practically more relevant as it enables these textures to serve as individually addressable bits in racetrack implementations. [16,17]

Imaging and Detection techniques
To date, significant advances have been made in skyrmionics thanks to a plethora of microscopic imaging and detection techniques, which harness neutrons, photons, electrons or stray magnetic fields. This includes neutron scattering, [18] magneto-optical Kerr effect (MOKE), [19] magnetic force microscopy (MFM), [17] spin-polarized scanning tunnelling microscopy (Sp-STM), [20] Lorentz transmission (LTEM), [21] and dichroic photoemission electron microscopy (PEEM), [22] scanning transmission X-ray microscopy (STXM), [23] nitrogen-vacancy (NV) magnetometry. [24] Among these, X-ray techniques offer the unique advantage of resonant element-specific imaging, thereby, providing an unambiguous picture of the underlying textures. Furthermore, electrical detection via the anomalous topological contributions to the Hall effect (THE) has also served as a promising technique. [25] However, THE only provides a tell-tale sign of the existence of chiral textures, without definitively confirming if they are topological quasiparticles. Lastly, the tunnelling non-collinear magnetoresistance (TNcMR) effect, where the tunnelling current across a multi-layer junction depends on the non-collinearity of spins in the racetrack layer, also promises electrical detection. [26] Future development of skyrmion racetrack memory is expected to employ some form of TNcMR for all-electrical readout of topological textures.

Why Correlated Oxides?
To harness topological textures practically, it is important to develop materials that can stabilize these textures across a wide range of temperatures including room temperature, and develop all-electrical pathways to nucleate, move, read and destroy them in patterned tracks.
A large family of topological textures and control mechanisms have been reported in magnetic metal-based heterostructures, or chiral magnets such as Heusler compounds, and B20 systems, [1] making them favourites for developing skyrmionics. However, correlated oxide magnets have also drawn considerable interest as they offer the following distinctive opportunities. (i) They host coupled ferroic order parameters (e.g., magneto-electric or multiferroic) [27,28]  This review is dedicated to the two overarching thrusts in the field of oxide skyrmionics -i.e., the development of materials and control mechanisms -that could help to pave the way toward practical oxide devices.

Materials development
The quest for magnetic textures in oxides began as early as the 1970s, in orthoferrites, [29] garnet-ferrites, [30,31] and hexaferrites [32,33] during the bubble memory era, and more recently in the 2010s in manganites [34][35][36][37][38][39] where the materials were prepared as thin plates to satisfy the stability conditions imposed by dipolar interaction. Imaging was performed by magneto-optical Microscopy, and more recently by LTEM. Hence various textures, including trivial bubbles, [38,39] (counter)clockwise Bloch skyrmions [38] and compound textures such as biskyrmions [36] or complex multi-ring skyrmions [33] were found to exist across different parts of the parameter space. Many of these textures are illustrated in Figure 1.
La1.37Sr1.63Mn2O7 was one of the celebrated examples that hosted a dense biskyrmion lattice (Figure 2a-b) and recorded promisingly low threshold JC of ~10 7 A/m 2 for their electrically driven motion. Almost concurrently, bulk Cu2OSeO3 crystal was found to host Bloch-type SkL as it possesses bulk DMI similar to B20 compounds, due to the T symmetry. [40] In contrast, the lacunar spinel VOSe2O5 was found to stabilize Néel-type SkL and incommensurate (IC) spin-crystal neighbouring phases as verified by neutron scattering. [41] Its polar crystal structure was found to play the crucial role of providing the C4v symmetry, although no sharp material interface was involved. These discoveries in bulk systems, inspired further investigations into oxide thin films.

Ferromagnetic textures
Over the last few decades, various layer-by-layer or step-flow oxide growth techniques have emerged which have enabled the creation of high quality interfaces for novel heterostructure design. Such capability has opened doors for stabilizing Néel-type skyrmions by engineering interfacial DMI. For instance, in ferromagnetic SrRuO3 thin films, Ru 4+ 4d t2g 4 eg 0 electronic configuration is known to endow several interesting properties, such as the minority-spin double exchange and the unquenched orbital angular momentum (L = 1)allowing large spin-orbit coupling (SOC) and perpendicular magnetic anisotropy (PMA). The partially filled t2g orbitals also form bands with various k-space Chern numbers, [42,43] producing a large anomalous Hall effect (AHE). Subsequently, via first-principles calculations and half-integer x-ray Bragg diffraction, [44] the monoclinic and tetragonal phases of SrRuO3 can be distinguished especially in the sign of dominant AHE conductivity. On the other hand, in semi-metallic SrIrO3, the Ir 4+ 5d Jeff = 1/2 band near Fermi level (EF) is also understood to have Dirac-like band dispersion due to its strong SOC. [45] Hence, (001)-oriented SrIrO3/SrRuO3 interfaces were explored for topological textures where strong DMI could be expected due to interfacial inversion symmetry breaking. Indeed, THE signals were found in the ultrathin, low Curie temperature regime hinting at the existence of magnetic skyrmions. [46] This THE signature, usually appearing as hump-shaped anomalies in the Hall transport measurements, emerges from the deflection of mobile spin-polarized electrons as they accumulate a Berry phase while traversing the emergent magnetic field from the non-coplanar magnetic moments constituting the topological textures. [25,47] This Berry phase, which is a geometric phase accumulated in the wavefunction of the mobile electrons, results from the sizable exchange interaction between the mobile spins and the spatially varying local moments.
Subsequently, similar THE-like signals were also discovered in single-layer ultrathin SrRuO3 [48] and ferroelectric/SrRuO3 heterostructures. [49] However, an alternative interpretation of THE soon arose, where the hump-shaped Hall features were reproduced by two overlapping AHE loops, with Langevin function shapes of opposite signs. [43,50] Here, AHE refers to the Karplus-Luttinger intrinsic mechanism that must involve SOC directly in driving electron deflection, [51] unlike the geometrical THE where a scalar moment chirality is needed, but not SOC. This implied the presence of trivial magnetic domain inhomogeneities, most likely a coexistence of monoclinic and tetragonal phases of SrRuO3, and hence bringing into question the existence of genuine topologically protected magnetic skyrmions. In particular, magnetic states in the aforementioned SrIrO3/SrRuO3 bilayers [46,52] and the atomic terrace-engineered ultrathin SrRuO3 films [53] were found to be distinct, when measured by low-temperature MFM. Skyrmion-like bubbles were imaged in the former cases [52] (Figure 2c-d), while the latter showed straight domains segregated along the atomic terraces, [53] albeit hump-shaped THE features were present in both systems. Hence, the debate around THE has demanded further support from highresolution magnetic imaging to unambiguously confirm the topological origin for each case.
More recently, MFM imaging of SrRuO3/PbTiO3(001) with Fourier transform revealed a "square-lattice IC-phase" formed by two perpendicularly propagating cycloids. [54] Such ICphase is similar to those in bulk GaV4S8 and VOSe2O5, also with C3,4v symmetries. [41,55] Hence, the mentioned Hall humps were concluded as true THE due to the scalar moment chirality present in the IC-phase. Meanwhile, the interfacial 3d-5d cationic charge-transfer scheme [58] became an insightful concept for achieving t2g-dominated and topologically nontrivial valence band in manganites. The large PMA and AHE in SrMnO3/SrIrO3 [59,60] and CaMnO3/CaRuO3 [61] superlattices are very similar, and also resemble the double-perovskites A2BʹBʹʹO6 studied earlier [62] where the inter-B-site super-exchange and ferro-/ferrimagnetism is absent when the parent materials are separated. Furthermore, the incorporation of 5d Ir 4+ at sharp interfaces opens the possibility of creating large SOC and interfacial DMI. Subsequently, as an effort to extend skyrmion search into antiferromagnets, obvious THE signals were found in LaMnO3/SrIrO3 superlattices [63] and CaMnO3/CaIrO3/CaMnO3 trilayer (Figure 2e). [56] respectively. In the former system, the distinct cationic oxidation states (La 3+ Mn 3+ and Sr 2+ Ir 4+ ) were discussed as the source of interfacial broken inversion symmetry. While in the latter, random stacking faults were found at the bottom CaIrO3/CaMnO3 interface of the trilayer for avoiding DMI cancellation. On the other hand, the lightly Ce 4+ -doped CaMnO3 single-layer thin film was realized as a good candidate for stabilizing magnetic bubbles by dipolar interaction, [57] confirmed by low-temperature MFM. Here, a giant THE signal was reported that diverged with reducing carrier density, which is consistent with a correlation-enhanced THE model (Figure 2f). [64] While FM topological textures have significant promise for skyrmionics, they suffer from some critical drawbacks. They typically require external magnetic fields for their stabilization. [49,57] Next, they exhibit undesired sideway deflection when driven by lateral currents (known as skyrmion Hall effect). [19,23]

Ferrimagnetic textures
A tell-tale sign for the presence of chiral textures in FiM oxide films was initially obtained by

Antiferromagnetic textures
While textures in FM and FiM materials can be visualized and controlled readily by standard magnetic techniques, it is difficult to directly translate these approaches to AFM counterparts due to the compensation of constituent magnetic sublattices. The first problem of imaging the AFM order parameter (i.e. the Néel vector), can be tackled via synchrotron-based linear dichroic X-ray imaging, [81] where combining angle-dependent images has been used to generate Néel vector phase-maps. [82,83] However, the second problem of generating AFM topological textures has been a hard nut to crack, as AFMs respond poorly to external magnetic field -one of the standard ingredients for generating FM skyrmions. To overcome this, inspiration was drawn from a half-century-old idea of cosmic string formation, called the Kibble-Zurek mechanism, [13,14] where a phase transition was suggested to generate topological defects under specific constraints, for instance U(1)-like symmetry. [82] Such a constraint is approximately satisfied in the earth-abundant layered-AFM oxide -α-Fe2O3 -across the Morin transition temperature (TM) where the Néel vectors reorient from out-of-plane to in-plane. This approach has enabled the recent breakthrough [22] of reversible and field-free generation of a family of topological AFM textures, including Néel and Bloch AFM merons, antimerons, and bimerons, Figure 1 and 3c, that are stable in the in-plane state at and above room temperatures. Here, (anti)merons and bimerons are equivalent to halfskyrmions and in-plane-rotated skyrmions, respectively, with their core dimensions directly tunable through temperature, [22] chemical/ionic doping, [84] strain, [85] or heterostructure design. [82,86] In the latter case, coupling α-Fe2O3 with a Co FM layer resulted in flat AFM (anti)vortices coupled to FM (anti)merons. [82,86]   Another material of interest is the AFM oxide α-Cr2O3, which was found to exhibit THE signals near and above the Néel ordering temperature, when its thin films were interfaced with a Pt over-layer. [87] As α-Cr2O3 is magnetoelectric, [73] this could open an interesting pathway to electrically control AFM topological textures. However, it must be noted that while SH-THE assisted transport signals hint at the presence of chiral spin textures, further imaging studies in tandem are required to unequivocally confirm their topological origin.
Finally, in analogy with synthetic antiferromagnets (SAF) made of metallic multilayers using Ruderman-Kittel-Kasuya-Yosida interaction, [88] oxide-SAF have been achieved using the interlayer-exchange coupling in La0.7Ca0.3MnO3/CaRu0.5Ti0.5O3 superlattice, where the Mn 4+ /Ru 4+ coupling is antiferromagnetic. [89] By controlling the superlattice repetitions, the magnetization at zero-field can be tuned between FM/AFM orientations. Hence, this could be also become a potential system for exploring SAF-based topological textures.

Control mechanisms
To enable practical topological racetracks, three crucial prerequisites need to be met: (i) control over the stability landscape for texture generation/annihilation, (ii) control of texture motion, and (iii) the readout mechanism that detects topological textures. These features have to be integrated into an all-electrical platform. To this end, oxides offer several advantages not found in other materials.

Controlling the stability landscape of topological textures
To precisely generate/annihilate skyrmions with low power consumption, a zero-current, magnetic-field-free, non-volatile electric field controlled magnetic landscape is highly desirable. This can be achieved either with systems possessing coupled ferroic orders, either intrinsically or via interfacial interactions. In metallic skyrmion platforms, the state-of-the-art approaches involve skyrmion nucleation via current-based spin-orbit torques [90] or the voltage-controlled magnetic anisotropy (VCMA) by carrier density modulation. [91] Hence, coupling to the ferroelectric order in oxides offers a new advantageous scheme providing a non-volatile field control.
Among oxide bulk crystals, Cu2OSeO3 is a celebrated compound for its multiferroic functionality. Besides housing a Bloch-type SkL, its d-p hybridization allows magnetoelectric coupling between the electric polarization and magnetic moment. [92] Using alternating field (AC) magnetometry with an applied magnetic field H[111] to obtain a SkL, the magnetoelectric coupling was observed by a depression in the real-part of AC-susceptibility with concomitant enhancement in polarization P [111]. [93,94] Subsequently, numerous other characterizations for multiferroic SkL followed. Particularly, using microwave resonance of the skyrmion rotation and breathing modes, a non-reciprocal directional dichroism effect was observed. [95] Besides, a magnetoelectric cooling process was demonstrated (Figure 4a-b), where the skyrmion phase space is systematically enlarged by cooling with an electric field. A sweeping electric field also produced hysteresis in the AC-susceptibility, as an evidence of tuning the magnetic phases. [96] It has been shown that preparing thin plates can enlarge the skyrmion phase-space. [93] However, using Cu2OSeO3 for practical developments has remained challenging due to the low Curie temperature and difficulty of thin-film growth. Hence, it would be interesting to search for topological textures in room temperature multiferroic or magneto-electric systems than can be readily grown via standard approaches. In oxide heterostructures such as SrRuO3/titanate ferroelectric (FE) interfaces in (001)orientation, the tetragonal distortion has been discussed to propagate into a thin layer of SrRuO3 resulting in an interfacial DMI with C4v symmetry for stabilizing Néel-type skyrmions. In a recent breakthrough exploiting ultrathin BaTiO3/SrRuO3 heterostructures, [49] electric field applied through a sharp tip was used to locally switch the BaTiO3 polarization at room temperature in a Hall bar channel, which tuned the interfacial DMI and thereby the topological properties, Figure 4c. Changes to THE signals and MFM images were measured at low temperatures, and correlated to the percentage of switched FE domains (Figure 4c-d).
However, several caveats can be noted: with the bottom SrRuO3 being obscured by the top BaTiO3, quantifying the changes in DMI by MFM is difficult due to the weaker signal. Besides, BaTiO3 is known to undergo several structural phase transitions upon cooling, [97] which could result in a change of the FE polarization easy-axis. Hence, it is preferable to perform the electrical switching and magnetic imaging experiments isothermally to make unambiguous correlations.
These developments, harnessing the ferroelectric order in natural/artificial multiferroic oxides, have opened non-volatile pathways to tune topological stability. Next, it will be crucial to realize this electric field control over topological textures in FiM/AFM materials at room temperature.

Moving and detecting topological textures
For moving topological textures, three underlying mechanisms have been identified, namely the thermal effect, spin-transfer torque (STT) and spin-orbit torque (SOT).
Firstly, in thin Cu2OSeO3 plates, a local temperature imbalance was found to produce magnon current components propagating parallel and perpendicular to the temperature gradient. These magnon currents are deflected by the emergent magnetic field of the topological SkL due to spin torques, and in return the skyrmions experience a reaction force resulting in their motion. Radial thermal gradients have produced ratchet-like rotations of a laterally constricted SkL. [98] Whereas, for lateral thermal gradients, unconfined skyrmions were found to move while experiencing the skyrmion Hall effect. [99] Although exciting, thermal effects may be difficult to use practically.
Secondly, in the case of the biskyrmion-hosting La1.37Sr1.63Mn2O7 system, currentbased STTs generated by low JC ~10 7 A/m 2 triggered the lateral motion of SkLs. [36] This STT effect emerges from spin-polarized charge current transferring a net angular momentum to the localized spins, effectively resulting in skyrmion motion. Moreover, the low JC is likely a result of high crystalline quality of the oxide samples minimizing defect pinning. [16] Subsequently, although SOT driven motion of skyrmions is yet to be directly confirmed in oxides, recent studies have used SOTs to displace chiral FiM DWs. Particularly, in Pt/garnetferrite heterostructures, [100] lateral charge currents in the Pt layer resulted in pure spin currents normal to the interface, due to spin Hall effect. [101] These spin currents exerts a damping-like SOT and push the chiral DWs into motion, with ultrafast speeds on the order ~km/s, thanks to the low Gilbert damping. [72] At these speeds, magnetic textures start to reach the speed-limit of magnons thereby reproducing spintronic analogues of relativistic physics (e.g., Lorentz contraction). It is expected that similar processes should be able to drive skyrmions and other topological textures in an ultrafast manner via SOTs in Pt-capped AFM oxides. [71] Meanwhile, for detection of topological textures, the TNcMR effect has emerged to be very promising. It is electrically sensitive to the magnetic textures through local variations in the electronic density of states (DOS). For instance, a collinear magnetic background (representing bit value '0') would register a larger tunnelling current in comparison to the case when a topological texture (representing '1') is present. This effect can be harnessed by integrating tunnel junctions onto topological racetracks making them scalable. Thus far, the TNcMR effect has been realized only in magnetic metallic heterostructures via ultrasharp STM tips. [26,102] Moreover, its experimental demonstration in skyrmion hosting oxides is also pending. Nonetheless, in strongly correlated metallic oxides with d-electron dominated conduction the electronic bands are usually narrow in the energy spread with large DOS, which is closely related to the local magnetic arrangement. Hence, one could expect the TNcMR effect to be enhanced in the case of correlated oxides. To detect textures in insulating AFM oxides, one could harness interfacial exchange interactions to couple the topological AFM order to an adjacent magnetic metal, [82,86] which could in turn be read-out via TNcMR.

Outlook
Given that a wide variety of topological textures and control pathways have already been demonstrated in oxides, the stage is now set to explore oxide skyrmionics. Imminent steps are to stabilize topological textures in FiM or AFM oxides that are coupled to a ferroelectric order, enabling non-volatile control over the topological stability landscape, at room temperature and above. This can be facilitated by careful heterostructure designing of emergent phenomena.
Subsequently, it is important to harness current-based SOTs to realize ultrafast motion of textures along racetracks. Finally, incorporation of tunnel junctions to detect topological textures via TNcMR will allow scalable read out of bits. Integrating all these aspects in a single device would enable practical exploitation of oxides for low-power multifunctional skyrmionics.