Materials challenges for SrRuO3: from conventional to quantum electronics

The need for faster and more miniaturised electronics is challenging scientists to develop novel forms of electronics based on quantum degrees of freedom different from electron charge. In this fast-developing field, often referred to as quantum electronics, the metal-oxide perovskite SrRuO3 can play an important role thanks to its diverse physical properties, which have been intensively investigated, mostly for conventional electronics. In addition to being chemically stable, easy to fabricate with high quality and to grow epitaxially onto many oxides - these are all desirable properties also for conventional electronics - SrRuO3 has interesting properties for quantum electronics like itinerant ferromagnetism and metallic behaviour, strong correlation between magnetic anisotropy and spin-orbit coupling, strain-tuneable magnetisation, anomalous Hall and Berry effects. In this Research Update, after describing the main phenomena emerging from the interplay between spin, orbital, lattice and topological quantum degrees of freedom in SrRuO3, we discuss the challenges still open to achieve control over these phenomena. We then provide our perspectives on the most promising applications of SrRuO3 for devices for conventional and quantum electronics. We suggest new device configurations and discuss the materials challenges for their realisation. For conventional electronics, we single out applications where SrRuO3 devices can bring competitive advantages over existing ones. For quantum electronics, we propose devices that can help gain a deeper understanding of quantum effects in SrRuO3 to exploit them for quantum technologies. We finally give an outlook about properties of SrRuO3 still waiting for discovery and applications that may stem from them.


Introduction
The interest of the research community in SrRuO3 has been kept high for almost 60 years 1,2 , as result of the coexistence of its fascinating physical properties with the easiness of its fabrication and integration in oxide heterostructures and devices.
Despite the intense research activity done on SrRuO3 and SrRuO3-based heterostructures, new physical properties and applications of SrRuO3 are continuously being discovered. SrRuO3 combines a range of interesting properties including good metallic conductivity at low temperatures (Ts), magnetic ordering with perpendicular magnetic anisotropy, narrow domain walls, strong spin-orbit coupling strength 2 . In addition to this rich physics, another advantage of SrRuO3 for device applications is that most of the SrRuO3 properties can be modulated. The possibilities to tune these properties are many and include changes in the SrRuO3 thickness and stoichiometry, strain application and interfacing of SrRuO3 to other oxides in heterostructures and superlattices 2 .
Several review articles have been written on SrRuO3 over the years including a very comprehensive review 2 on SrRuO3 properties and applications. In addition to several papers 3 -6 summarizing the main results reported in the literature on the anomalous Hall effect (AHE) and topological Hall effect (THE) in SrRuO3, we are aware of another review article 7 recently published which describes the main applications of SrRuO3-based heterostructures.
The aim of this work is to put the results obtained to date on SrRuO3 in perspectives and discuss which materials challenges have to be addressed to realise SrRuO3-based devices with better performance and novel functionalities compared to existing ones. In addition to analysing these challenges, we propose specific examples of electronic devices with corresponding geometries that have never been realised to date. The fabrication and testing of these devices can serve as a stimulus to the research community not only from an applicationrelated perspective, but also to gain a better understanding of quantum phenomena recently discovered in SrRuO3. We propose, for example, devices that would allow to differentiate between real-space or momentum-space contributions to the SrRuO3 Berry curvature.
Differentiating between these contributions is a key step to engineer future quantum devices exploiting AHEs and THEs in SrRuO3 for their functioning.
In section 1 of this review, we describe the main physical properties of SrRuO3, and we report the deposition techniques and methodologies that can be used to fabricate SrRuO3 devices for technological applications. We highlight in particular techniques that are not only suitable to produce devices with optimal properties but also with high reproducibility and scalability. After discussing the structural parameters and mechanisms that mostly affect the physical properties of SrRuO3, we review progress made on the fabrication of free-standing SrRuO3 structures. We also review how SrRuO3 properties change when the SrRuO3 dimensionality is lowered from the three-dimensional (3D) to the zero-dimensional (0D) regime and quantum effects become increasingly more relevant.
In section 2, we consider the most promising applications of SrRuO3 for both conventional and quantum electronics and propose possible devices that can be made for each type of applications. Whilst describing these electronic devices and discussing possible layouts for their realization, we also outline the materials challenges that have to be addressed for their realization.
For conventional electronics, we focus on applications for which SrRuO3-based devices would offer a competitive advantage over existing devices. The first class of applications include room-T spintronic devices and cryogenic memories, where two distinct properties of SrRuO3 namely its high spin-orbit coupling and narrow domain walls are used, respectively, to make devices that can offer better performance than existing ones. For the second class of applications, we suggest exploiting the properties of freestanding SrRuO3 membranes under strain to realise nanoelectromechanical systems with unprecedentedly high figures of merit.
For quantum electronics, we focus on effects related to the non-trivial Berry curvature of SrRuO3 and suggest the realization of novel devices, where real-space and momentum-space contributions to Hall signals can be differentiated and separately manipulated. We also propose new schemes of superconducting devices, where SrRuO3 is coupled to a superconductor. The SrRuO3-based superconducting devices that we suggest can host topological superconductivity or spin-polarised superconducting currentswhich can be reversibly modulated by tuning the SrRuO3 Berry curvature.

Main properties and growth techniques
In this section, we review the main physical properties of SrRuO3 including its structural, electronic transport and magnetic properties. We list some parameters and typical values that can be used as benchmark comparison to evaluate the degree of quality of SrRuO3 samples.
We then discuss which growth techniques appear most promising to date for the reliable fabrication of SrRuO3 thin films with optimal parameter values (i.e., close to bulk) and over large scale. The growth of SrRuO3 thin films with properties identical to bulk is essential to investigate emergent phenomena and discover new quantum effects in SrRuO3. A high scalability in making optimal SrRuO3 thin films is in turn crucial for the development of device applications exploiting such effects and phenomena.
SrRuO3 is a layered oxide perovskite of the ABO3 type belonging to the Ruddlesden-Popper series of ruthanates, Srn+1RunO3n+1, with number of layers n = ∞. As for several other ABO3 perovskites, the unit cell of bulk SrRuO3 has an orthorhombic crystal symmetry at room T (space group Pbnm). In bulk single-crystal form, SrRuO3 undergoes a structural transition first into a tetragonal phase (space group I4 / mcm) as T is increased to 547 °C and then into a cubic phase (space group Pm3m) as T is further increased up to 677 °C (ref. 2 ).
In the unstrained orthorhombic phase at room T, the Ru-O bond is about 2 times shorter in length than the Sr-O bond which introduces a distortion of the RuO6 octahedra. The distortion of the RuO6 octahedra, which can be manipulated via strain engineering, is a key structural parameter affecting some of the SrRuO3 physical properties, as further discussed below in this review. The lattice parameters of the orthorhombic cell (space group Pbnm) are 2,8 aor = 5.57 Ȧ, bor = 5.53 Ȧ, and cor = 7.85 Ȧ. The orthorhombic unit cell consists of four units of the ideal cubic perovskite structure, which results in a pseudocubic lattice constant 2 apc = 3.93 Ȧ (Fig. 1). We note that throughout the review we use the subscripts 'or' and 'pc' to refer to the orthorhombic and pseudocubic unit cell parameters, respectively.
SrRuO3 was reported as the first oxide exhibiting ferromagnetism 1 due to itinerant electrons below a Curie temperature (TCurie) of ~ 160 K (ref. 2), it has a relatively high saturation moment of 1.6 μΒ/Ru atom 9,10 at T = 0 (μΒ = 9.27 x 10 -24 J • T -1 being the Bohr magneton) and it usually exhibits perpendicular magnetic anisotropy when epitaxially grown as thin film under compressive strain onto a (001) SrTiO3 substrate 2 . This magnetic anisotropy, however, can change depending on substrate-induced strain and orientation (see also section 1.2). The Tdependence of the SrRuO3 electronic transport properties also shows that SrRuO3 has very good metallicity at low Ts due to its Fermi liquid behavior 11 for T < 10 K (metallicity is defined from the slope dρ/dT of the resistivity ρ versus T curve). As T is increased and approaches room T, metallicity in SrRuO3 progressively gets worse 12 .
Several growth techniques have been used over the years to grow SrRuO3 with the abovelisted properties. The vast majority of the studies to characterise these properties of SrRuO3 has been carried out on SrRuO3 thin films. Bulk single crystals of SrRuO3 are difficult to grow, and this is the main reason why the physical properties of SrRuO3 have been mostly investigated in its thin film form 2 . The growth of bulk single crystals of SrRuO3 by the floating zone technique, which is the preferred method to synthesize single crystals with low levels of disorder, is made difficult by the large amount of RuO2 that evaporates during the SrRuO3 growth. In general, obtaining good-quality single crystals is challenging for any ruthenates infrared light in the molten zone, which makes the growth extremely unstable 29 . This is the main reason why, although the floating zone technique has been routinely used to grow highquality crystals of other compounds in the Srn+1RunO3n+1 Ruddlesden-Popper series 30,31 like the unconventional superconductor Sr2RuO4 (n = 1) and the metamagnet Sr3Ru2O7 (n = 2), it has not been extensively used for SrRuO3 (n = ∞) single crystals. Other factors are also crucial to get good-quality SrRuO3 single crystals, which contribute to make the growth process very challenging. These crucial factors include the high quality of the feed rod and the excess RuO2 amount, which has to be added to the rod before growth to compensate for Ru losses.
SrRuO3 single crystals of good quality grown by the floating zone technique have been obtained thanks to the installation of a cold trap 29 . The cold trap allows the evaporated RuO2 to collect onto the trap surface other than on the walls of the quartz tube.
Unlike for single crystals, the growth of epitaxial SrRuO3 thin films onto lattice-matched substrates is relatively easy to carry out and SrRuO3 thin films of very high quality have been obtained by many groups using a variety of chemical and physical deposition techniques 32 .
SrRuO3 thin films epitaxially grown with the above techniques usually have different lattice parameters compared to bulk because of epitaxial strain induced by the substrate. As recently observed in ref. 49 , SrRuO3 thin films with RRR higher than 50 have mostly been obtained on growth substrates having a small lattice mismatch with SrRuO3 such as (001) SrTiO3 (refs. 13,35,[48][49][50][51][52] ) and (110) DySrO3 (refs. 53,54 ). The lattice mismatch for SrRuO3 is of ~ -0.6% with (001) SrTiO3 and of ~ 0.4% with (110) DySrO3. We note here that epitaxial SrRuO3 thin films grown onto a (001) SrTiO3 substrate usually have a tetragonal structure (4mmm space group) for small thicknesses (up to 4-6 nm), and a monoclinic structure (P21/m space group) for larger thicknesses 55,56 . Following the conventional notation, in the literature this monoclinic structure with the angle γ (close to 90°) between the [100]or and [001]or axes is also denoted as orthorhombic 55 .
The structural transition from tetragonal to orthorhombic is correlated to a change in the RuO6 octahedra tilting (see section 1.2), although the origin of this change with thickness remains unclear 49 . Using low-energy electron diffraction and high-resolution scanning transmission electron microscopy, it has been shown 57 that, unlike for other oxide perovskites, the RuO6 octahedra tilting is already present in one-unit-cell-thick SrRuO3 on (001) SrTiO3.
In addition to a very high RRR 51,52,58 (> 50), there are several other physical properties that can be regarded as hallmark signatures of high quality for SrRuO3 thin films. Indications of high SrRuO3 thin film quality include low residual ρ at liquid helium T (~ 4.2 K), a high TCurie, a strong perpendicular magnetic anisotropy (for thin films grown under compressive strain), and a low in-plane mosaic spread.
Low residual ρ is an indication of low concentration of defects and of a good stoichiometry.
Ultra-high quality SrRuO3 thin films have residual resistivity lower than 3 μΩ cm at T = 4.2 K, which is consistent with their very high RRR values 13,48,49,51,52 . A high TCurie is also a signature of good stoichiometry, since Ru deficiencies are one of the main reasons for a decrease in TCurie (see section 1.2). The highest TCurie reported for SrRuO3 thin films deposited on (001) SrTiO3 is of ~ 152 K (ref. 53 ). For tensile-strained SrRuO3 thin films grown on (110) DySrO3 substrates, TCurie as high as 169 K have been instead measured 35,54 .
Apart from being desirable for spintronics applications, strong perpendicular magnetic anisotropy is also a signature of high crystallinity in compressive-strained epitaxial SrRuO3 thin films, since it is normally lowered by grain boundaries and other defects 59,60 . The SrRuO3 thin film in ref. 48 do not only have the highest RRR (~ 86) reported to date, but they are also the first to show single-domain perpendicular magnetization. The single-domain perpendicular magnetization of the thin films in ref. 48 is evidenced by the fact that their remanent magnetization to saturation magnetization ratio (i.e., squareness) is of ~ 0.97. Single-domain perpendicular magnetization in SrRuO3 is a desirable property for spintronics 61 , and its recent realization in ref. 48 will certainly contribute to further applications of SrRuO3 in oxide spintronics at cryogenic Ts.
Low in-plane mosaic spread is also a good indication of high thin film quality. The in-plane mosaic spread can be estimated for SrRuO3 by measuring the full width at half maximum, FWHM, for the rocking curves of the (001)pc or (002)pc peaks. In Fig. 2b, we reproduce a figure from ref. 32 , where the authors compare the FWHM of the (001)pc and (002)pc peaks of SrRuO3 thin films grown with different deposition techniques and substrates. The data in Fig. 2b show that SrRuO3 thin films with very low amount of in-plane mosaic spread (i.e., FWHM ≤ 0.01°) have been obtained by several groups using either PLD or MBE growth.
Apart from targeting the above-listed parameter values, which are good indicators of high SrRuO3 thin film quality, another main challenge to address for future applications of SrRuO3 in conventional and quantum electronics is to understand how to scale up SrRuO3 thin films and in turn devices based on them. The scaling up therefore implies not only growing epitaxial SrRuO3 thin films with optimal physical properties, but also doing this over large areas and pattern then the films into devices with reliable functioning.
Optimising the growth of high-quality epitaxial SrRuO3 thin films on Si, the material at the core of complementary metal-oxide semiconductor (CMOS) technology, over areas comparable to the size of Si wafers used by the semiconductor industry (> 4'' in diameter) can lead, for example, to the integration of the fabrication of SrRuO3-based devices into the industrial processes and fabs of the semiconductor industry 32 . Until recently, most of the attempts done at growing SrRuO3 thin films on Si have resulted in thin films of poor quality both from a structural and an electronic transport point of view.
The formation of an amorphous SiO2 layer directly onto Si during the growth of SrRuO3 usually impedes epitaxial growth 32 and results in polycrystalline SrRuO3 thin films with a poor RRR of ~ 3 at most 62 . To achieve epitaxial growth, a multi-step deposition is necessary, where a thin epitaxial buffer layer (e.g., SrTiO3 (001)) is first deposited on Si, which is then followed by the deposition of an epitaxial SrRuO3 thin film onto the buffer layer. This two-step process, however, requires breaking vacuum between the two depositions and hence exposing the surface of the buffer layer to air, which eventually also leads to thin films of poor quality.
Recently, a single-step process has been successfully developed by Wang and co-workers 32 , where both the SrTiO3 buffer layer and the SrRuO3 thin films are grown in the same MBE chamber on 2'' commercial Si wafers without breaking vacuum. This approach has resulted in epitaxial SrRuO3 thin films on Si with excellent structural, magnetic and transport properties.
Reflection high-energy electron diffraction (RHEED) patterns acquired along the [100]pc and [110]pc azimuths of the SrRuO3 thin films and X-ray diffraction ϕ scans demonstrate epitaxial growth of the SrRuO3 thin films with the [100]pc direction of SrRuO3 oriented along the [110] axis of the (001) Si substrate 32 . The RRR of the SrRuO3 thin films reported in this study 32 is of ~ 11this is comparable to that of other SrRuO3 thin films grown on single-crystal oxide substrates by PLD 32,[40][41][42] (Fig. 2a). It is worth nothing that MBE is nowadays used also to manufacture semiconductor devices 63 , which makes the process reported in ref. 32 appealing for the large-scale production of SrRuO3 devices on Si using the same nanofabrication processes of the CMOS industry.
More recently, machine-learning models have been combined with the MBE technique to quickly determine the growth conditions for high-quality SrRuO3 thin films. Wakabayashi et al., for example, have adopted Bayesian optimization during the MBE growth of SrRuO3 thin films 58 . Their approach consists in applying Bayesian optimization to one growth parameter at a time, whilst keeping all the other growth parameters fixed 58 . Following this procedure, all the MBE growth parameters (e.g., Ru flux rate, growth T, and O3-noozle-to-substrate distance) were optimized after only 24 MBE growth runs, and SrRuO3 thin films with a RRR ~ 50 were obtained 58 . Machine-learning-assisted MBE with Bayesian optimization has been reproduced also in other studies 48,49,51,58 , and it has yielded SrRuO3 thin films with RRR of ~ 80 and 86 after 35 and 44 MBE optimization runs, respectively 51,64 .
It is clear to us that growth optimization of SrRuO3 thin films assisted by machine learning approaches such as Bayesian optimization will eventually replace the typical growth optimization based on a trial-and-error approach. The traditional trial-and-error approach is in fact time consuming and costly, and it ultimately depends on the skills of the researcher carrying out the process.
The ultra-high quality SrRuO3 thin films grown by machine-learning-assisted MBE have also led to the discovery of novel quantum phenomena in SrRuO3. Performing transport measurements on SrRuO3 thin films grown by machine-learning-assisted MBE, Takiguchi and co-workers have shown 51 evidence for Weyl nodes in the electronic band structure of SrRuO3 the existence of Weyl nodes had only been predicted 65 theoretically in 2013. Weyl nodes are of both fundamental and practical interest because they are tuneable in an applied magnetic field and can provide high-mobility two-dimensional carriers. The two-dimensional nature of these high-mobility carriers stem from Fermi arcs that connect the surface projection of Weyl nodes with opposite chirality. Two recent studies 66,67 have shown evidence for high-mobility two-dimensional carriers from surface Fermi arcs in untwined ultra-high quality SrRuO3 thin films.
Based on the example studies reported above, it is clear that MBE, and in particular machine-learning-assisted MBE, is currently the most reliable technique to produce ultrahighquality SrRuO3 thin films. The ultrahigh quality is an essential prerequisite to get access to quantum phenomena recently discovered in SrRuO3 and to develop quantum electronic applications based on transport of Weyl nodes and high-mobility two-dimensional carriers.
MBE, and in particular machine-leaning-assisted MBE, appears therefore as the most promising growth techniques to realize SrRuO3 thin films and devices for quantum electronics.
Recent studies 32 have shown that MBE is also suitable for large-scale growth of high-quality SrRuO3 thin films on Siwhich is an essential requirement for the integration of SrRuO3 devices with conventional CMOS electronics. In addition to MBE, we believe that other growth techniques are equally promising and should be tested in the future for high-throughput growth of high-quality epitaxial SrRuO3 thin films on Si. These techniques are radiofrequency (RF) magnetron sputtering in a multi-target sputtering chamber equipped with substrate heater and continuous compositional-spread PLD 43 with synchronised translation of the substrate heater with the pulsing of the excimer laser.

Structural parameters and experimental tools to control physical properties
In the previous section, we have described the main physical properties of SrRuO3, the values of the measurable parameters attesting high quality of SrRuO3 thin films, and the growth techniques that can be used to produce such high-quality films. Here, we review the main structural parameters affecting the physical properties of SrRuO3 thin films and we also discuss the experimental tools that can be exploited to control these properties. Achieving fine control over the physical properties of SrRuO3 is in fact another essential ingredient for the development of conventional and quantum electronics applications based on SrRuO3.
As for other perovskite compounds, the physical properties of SrRuO3 depend on a number of structural parameters 2 including the degree of off-stoichiometry, substrate-induced strain, structural disorder, thickness etc. Some properties like the magnetic properties are more sensitive than others in SrRuO3 to any variations in these structural parameters.
Changes in the nominal stoichiometry of SrRuO3 thin films are either due to ruthenium or to oxygen vacancies 45 . The stoichiometry of the SrRuO3 thin films is extremely dependent on the oxygen activity during deposition, which is set by the amounts of atomic and molecular oxygen present during growth 45 . In SrRuO3 thin films made by MBE, nominal stoichiometry is easier to achieve because the fluxes of molecular and atomic oxygen can be controlled independently (also from the Ru and Sr supplied). Atomic oxygen, for example, can be generated in an MBE chamber using a microwave plasma source and its pressure can be tuned by adjusting the oxygen flow supplied to the plasma source and the generator power 45 . At low oxygen activity, in SrRuO3 thin films made by MBE, stoichiometry is mostly set by the amounts of Sr and Ru supplied during growth. At oxygen activities much higher than those suitable for good stoichiometry, Ru vacancies become unavoidable and independent on the amount of Sr and Ru supplied. The increase in Ru vacancies is most likely due to the formation of the volatile compound RuO4, whose concentration increases at higher oxygen activity 45,68 .
For SrRuO3 thin films grown by PLD other than MBE, it has been observed that they tend to be normally Ru deficient because a (high) atomic oxygen pressure already exists within the plume, and very little can be done to avoid this 2,45 . This is one of the reasons why, although PLD allows to grow SrRuO3 thin films of consistently good quality, PLD-grown SrRuO3 thin films have normally lower RRR compared to thin films of similar thickness deposited by MBE, where the fluxes of molecular and atomic oxygen can be independently controlled during growth 2,45 . A good crystallinity in SrRuO3 thin films grown by PLD, however, can still be achieved, even in the presence of Ru vacancies 45 . Now we discuss the effect that off-stoichiometry has on the SrRuO3 thin film properties. Ru vacancies induce an expansion in the SrRuO3 unit cell and this is mechanism responsible for a reduction in the TCurie, which can be of up to several tens of Kelvin degrees from its bulk value of ~ 160 K (refs. 45,69 ). As the amount of Ru vacancies increases, the ratio between the pseudocubic apc and cpc-axis lattice parameters (cpc/apc) becomes lower than 1, and the saturation magnetisation of SrRuO3 increases up to 2.4 μΒ/Ru atom 69 . This suggests that the high spin configuration of half d filled Ru 4 ions stabilises 69 , as the crystal structure is distorted from cpc/apc > 1 to cpc/apc < 1 by the increase in Ru vacancies.
Oxygen vacancies on their hand cannot be distinguished by Ru vacancies on the basis of lattice parameters 2 . It has been reported, however, that variation in the oxygen stoichiometry of the thin films achieved by varying the oxygen partial pressure, P(O2), during growth, can influence the RuO6 octahedra rotation and tilting. Like thin films with Ru vacancies, also SrRuO3 thin films with oxygen vacancies exhibit an increase of the cpc-axis lattice constant.
The increase in the cpc-axis lattice constant leads to a deformation of the unit cell from orthorhombic to tetragonal 70,71 . Missing oxygen ions at the octahedral apexes due to oxygen vacancies increase the Ru-Ru repulsion along the cpc-axis, which suppresses the rotation of the RuO6 octahedra along the apc-and bpc-axes and stabilizes the tetragonal phase 72,73 . These SrRuO3 thin films with a tetragonal structure usually exhibit different electronic transport properties compared to thin films with an orthorhombic unit cell. The different physical properties are also related to differences in the RuO6 octahedra tilting and rotationwhich are known to have significant effect on the SrRuO3 properties (as further discussed below).
For thin films grown by PLD, as P(O2) during growth is reduced, the Sr/Ru ration increases and the structure stabilises into the tetragonal phase 72 . Compared to orthorhombic thin films grown in the same conditions but at higher P(O2), tetragonal SrRuO3 thin films show an increase in their room-T ρ, most likely due to a reduced hybridization between the Ru 4d and O 2p orbitals in the tetragonal phase compared to the orthorhombic one 72 . In addition to the electrical properties, also magnetic properties, and in particular magnetic anisotropy, change as result of the structural phase transition into the tetragonal phase introduced by oxygen vacancies. In a study carried out by W. Lu et al. 70 , for example, they show that SrRuO3 thin films with a thickness larger than 50 nm and tetragonal structure have perpendicular magnetic anisotropy, whilst thin films with the same thickness and orthorhombic structure exhibit inplane magnetic anisotropy 70 . These results also suggest that stochiometric control is a possible route to stabilize the tetragonal phase and the corresponding magnetic anisotropy in SrRuO3 thin films, in addition to varying epitaxial strain or reducing the film thickness 70 .
Substrate-induced strain is another parameter that can be tuned to obtain SrRuO3 thin films with desired physical properties for conventional and quantum electronics. Epitaxial strain in stoichiometric SrRuO3 thin films can have a similar effect on magnetism as Ru vacancies in off-stochiometric films, meaning that strain can also induce suppression in TCurie (ref. 34 ). The correlation between the structural and physical properties of SrRuO3 with substrate-induced strain has been the subject of several studies 2,34,[74][75][76][77][78] . From a structural point of view, there is general agreement that SrRuO3 thin films under substrate-induced tensile strain tend to have a tetragonal structure 41,78 , whilst SrRuO3 thin films under substrate-induced compressive strain have an orthorhombic structure 76 . For a fixed growth substrate, strain can also change depending on several growth parameters including the SrRuO3 thin film thickness. SrRuO3 thin films under tensile strain on (110) GdScO3 substrates, for example, show an orthorhombic structure up to a certain thickness (~ 16 nm), beyond which these SrRuO3 thin films assume a tetragonal structure 41 .
In general, strain imposed by the substrate, changes the Ru-O and Ru-O-Ru bond lengths, as result of the different rotation of the RuO6 octahedra. In the orthorhombic phase, the RuO6 octahedra rotate out-of-phase about the [010]pc ( [1][2][3][4][5][6][7][8][9][10]or), which is the magnetic easy axis, and in-phase about the [100]pc ([001]or) direction, which is the magnetic hard axis 70 . The rotations along these two orthogonal in-plane directions, however, is suppressed in the tetragonal phase 70 , meaning that in-plane symmetry breaking is different between the orthorhombic and tetragonal phases. This difference in in-plane symmetry breaking is considered to be the reason for the different magnetic anisotropies observed in orthorhombic and tetragonal SrRuO3 thin films 70,78 (see also above).
Twinning can also have a profound effect on the magnetocrystalline properties of SrRuO3 thin films and introduce anisotropy axes that are different from those of thin films of optimal quality. In the paramagnetic state above TCurie, epitaxial SrRuO3 thin films on (001) SrTiO3 which are free of twin-plane defects and with ideal stoichiometry exhibit uniaxial magnetocrystalline anisotropy with an easy axis coinciding with the orthorhombic bor-axis 79,80 (i.e., the [010]or axis of the orthorhombic unit cell). We note that epitaxial SrRuO3 thin films grown on (001) SrTiO3 substrates are oriented with the pseudocubic [001]pc axis (equivalent to the orthorhombic [110]or axis) perpendicular to the substrate surface, so that the bor-axis is at 45° out of the plane of the film. The uniaxial nature of the magnetocrystalline anisotropy in SrRuO3 has been demonstrated using Lorentz force microscopy 81 as well as through measurements of the magnetic susceptibility χ around TCurie. χ shows an increase along the boraxis, as T is decreased from room T down to TCurie, by several orders of magnitude compared to its value measured along the aor-axis 79 . Below TCurie, the easy magnetization axis deviates from the bor-axis due to an orientational transition 82 occurring as is decreased, so that the angle that the easy axis forms with the surface normal, meaning the [001]pc-(or [110]or-) axis, decreases progressively from ~ 45° to ~ 30° (ref. 10 ). Deviations of the angle formed by the magnetic easy axis with the [001]pc ( [110]or) axis in this films from these values have also been reported, which depend on the presence of intertwined crystal nanodomains 83 or on the crystallographic orientation or on the type of growth mode (e.g., step flow or two dimensional) of the SrRuO3 thin film 80 . In general, changes in the orientation of the magnetic easy axis in SrRuO3 thin films are due to structural deformations of the orthorhombic unit cell 8 (e.g., due to strain). Structural deformations are in turn associated with changes in the rotation and tilt of the RuO6 octahedra 3,84 . As discussed above, when the strain in SrRuO3 thin films changes, the magnetic easy axis of the films can switch from having an out-of-plane to an in-plane orientation 70,84,85 .This implies that there exists a strong correlation between spin-orbit interactions in SrRuO3 and its magnetocrystalline anisotropy (ref. 2 ).
Variations in the physical properties of SrRuO3 thin films as a function of film thickness have also been intensively investigated. An evolution from a metallic to an insulating behaviour in the electronic transport properties has been observed as the thin film thickness is decreased below a critical value, dc, of a few unit cells (u.c.) [86][87][88] . The smallest dc reported to date 89 corresponds to 2 u.c. for bare SrRuO3 thin films, although similar low-T conductivity values to ref. 89 have been obtained for SrRuO3/SrTiO3 superlattices with SrRuO3 thickness of 1 u.c.
(ref. 90 ). Earlier studies ascribed the thickness dependent of the metal-to-insulator transition (MIT) to several extrinsic mechanisms like disorder, defects, surface electronic reconstruction 86,87,91-92 etc. which become more significant as the SrRuO3 film thickness is reduced and that can lead to an enhancement in weak localization effects 86 . Nonetheless, the atomic-scale precision currently achieved in the growth of ultrathin SrRuO3 thin films rules out extrinsic mechanisms as the origin of the MIT, since a MIT is still observed in ultrathin SrRuO3 grown with state-of-the-art deposition techniques for a thickness below 2 u.c. One of the intrinsic mechanisms that could be responsible for the MIT is the ratio between the Coulomb interaction and the Ru 4d bandwidth resulting from the hybridizations between the Ru 4d and O 2p orbitals 93 . This hybridization is strong and anisotropic in thicker SrRuO3 films generally due to substrate-induced strain, but it becomes weaker in the ultrathin limit leading to Ru-O bonds with an ionic nature and localised Ru 4d orbitals.
The MIT in the electronic transport is also accompanied by a suppression in ferromagnetism, which disappears at a critical thickness below 3 and 4 u.c. in bare SrRuO3 thin films 88,89 .
Exchange bias has also been observed in SrRuO3 thin films of thickness smaller than 3 u.c., which points to the possible presence of antiferromagnetic regions in contact with ferromagnetic ones 88 . In a theoretical study 91 , it was suggested that ferromagnetism should even persist in thin films of 2 u.c. and that only SrRuO3 thin films with a thickness of 1 u.c.
should be non-ferromagnetic due to surface-driven effects. Based on this suggestion, it was recently found 90 that one-unit-cell-thick SrRuO3 films embedded in a SrTiO3/SrRuO3 superlattice, where surface effects are non-existent, are indeed ferromagnetic with a magnetic moment of approximately 0.2 μΒ/Ru atom. This magnetic moment in one-unit-cell-thick SrRuO3 was measured by scanning superconducting quantum interference device (SQUID) microscopy 90  There exist in fact significant differences between the magnetic properties of all these ARuO3type compounds. Studying the physical mechanisms behind these differences can help better understand ferromagnetism in SrRuO3 and how to manipulate its TCurie.
Although both SrRuO3 and CaRuO3, for example, have an orthorhombic structure with Pbnm space group, evidence for ferromagnetic ordering in CaRuO3 has not been found. Several studies 95,96 , however, suggest that CaRuO3 is on the verge of ferromagnetic ordering. Unlike SrRuO3, BaRuO3 has a cubic structure with space group Pm-3m and it shows ferromagnetic ordering with TCurie ~ 60 K (ref. 97 ). The saturation magnetization of BaRuO3 (measured at T = 5 K in an applied H of 5 Tesla) is of ~ 0.8 μB/Ru atom 97 , which is significantly lower than the saturation magnetization of ~ 1.6 μB/Ru atom measured in SrRuO3.
Earlier studies on Sr1-xCaxRuO3 suggested that the suppression of magnetism in CaxRuO3 is due to a decrease in the Ru-O-Ru bond angle happening for increasing Ca concentration x (the bond angle decreases from 163° in SrRuO3 to 148° in CaRuO3). Theoretical calculations of the band structure of Sr1-xCaxRuO3 compounds also showed that, as the Ru-O-Ru bond angle reduces, the band degeneracy at the Fermi level decreases until the Stoner criterion is no longer verified, and magnetism is suppressed 98 . This explanation, however, cannot account for the reduced TCurie of BaRuO3 compared to SrRuO3 (the Ru-O-Ru bond angle is 180° in BaRuO3), even if size variance effects (induced by Ca and Ba doping) are considered. It should be finally noted that Sr1-yBayRuO3 compounds show typical Curie-Weiss (CW) behavior for T > TCurie and critical fluctuations 99 near TCurie, whereas Sr1-xCaxRuO3 compounds exhibit an unusual χ -1 (T) dependence as TCurie is approached 97 .
C. Q. Jin and co-workers 97 have recently argued that the reduction in TCurie for Sr1-yBayRuO3 for increasing Ba concentration y is caused by band broadening induced by Ba doping, since CW behavior persists for T > TCurie. This is in contrast with Sr1-xCaxRuO3, where Ca doping leads to a reduction in the Ru-O-Ru bond angle and to a dilution of the ferromagnetic interactions, which results in a χ -1 (T) dependence typical of the Griffiths' phase 97 . The arguments proposed by these researchers 97 are also supported by a recent study 100 based on density functional theory + dynamical mean-field theory (DFT+DMFT). These DFT+DMFT calculations suggest that the ferromagnetic transition in ARuO3 ruthenates depends on three parameters: the density of states (DOS) at the Fermi level EF (in accordance with Stoner's model), the DOS peak position with respect to the ruthenate band edge and its bandwidth.
Based on these theoretical models, CaRuO3 has no ferromagnetism due to its large lattice distortion (octahedra tilt and rotation in CaRuO3 is larger than in SrRuO3), which leads to a split of the DOS peak and in turn to a decrease in the DOS at the EF. BaRuO3, which has a large DOS peak, it is also characterized by larger bandwidth and by a DOS peak position further away from the upper band edge than SrRuO3these are all factors that result in a suppression of TCurie for BaRuO3 compared to SrRuO3.
In addition to epitaxial strain, which can be used to change the structure and in turn the magnetic and electronic transport properties of SrRO3, reversible control over the same physical properties has also been achieved using an electric field (E) applied, for example, via More recently, magneto-ionic effects have been reported by Li and co-workers 103 , where an E applied via ILG has been used to move ions (e.g., H + or O 2-) in or out of SrRuO3 and induce large changes in the SrRuO3 magnetic state and THEs. In this study 103 , the authors have shown that a large H + gradient induced in SrRuO3 via ILG leads to a protonated compound HxSrRuO3 with a paramagnetic metallic ground state. The reason for the ferromagnetic-to-paramagnetic phase transition is a change in the electronic band properties induced by a structural change in SrRuO3. As the proton H + concentration increases under the VG applied via the ionic liquid, the cpc-axis constant in SrRuO3 undergoes an expansion. Theoretical calculations 103 show that, in this distorted structural configuration, the DOS gets strongly modified due to a splitting of the Ru t2g bands which leads to a shift in the spectral weight towards lowers energies. As a result, the DOS changes in such a way that the Stoner criterion for ferromagnetism is not fulfilled, and the paramagnetic ground state becomes energetically favored over the ferromagnetic state.
Also, in ref. 103 , at the boundaries of the ferromagnetic-to-paramagnetic phase transition, a hump-like feature is observed in the transverse Hall resistivity ρxy, which Li and co-workers ascribe to a THE. The emergence of a THE is related to an increase in the Dzyaloshinskii-Moriya interaction (DMI) due to inversion symmetry breaking at the ionic liquid/SrRuO3 interface. From this point of view, these results suggests that magneto-ionic effects induced by ILG can be used as an effective tool to reversibly control THEs and the magnetic ground state in SrRuO3 thin films. As for the case of SrRuO3, H + migration induced by ILG has also been successfully used in the parent compound CaRuO3, where it induces a reversible E-driven magnetic transition from the paramagnetic ground state into an exotic ferromagnetic ground state 104 .
In addition to reversible E-driven variations in H + concentration under ILG, reversible Edriven changes in oxygen vacancies (VO) have also been shown to be an effective tool to vary the DMI strength and to reversibly switch on/off THEs in SrRuO3 heterostructures. To achieve a E-tunable modulation in VO, in a recent study 105 a SrRuO3 thin film was grown onto a SrTiO3 substrate, which had been pre-annealed in vacuum to generate a high VO amount. Since the VO formation energy in SrRuO3 is lower than in SrTiO3, VO tend to diffuse from SrTiO3 into SrRuO3 and to accumulate at the SrRuO3/SrTiO3 interface. Under the application of an E ~ 3 kV/cm, in this study 105 J. Lu and co-workers were able to manipulate the VO concentration at the SrRuO3/SrTiO3 interface and to reversibly enhance or suppress hump-like and bumplike features related to the THE in SrRuO3.
To summarize, in Fig. 3 we show the main physical properties of SrRuO3 and list the structural parameters and experimental tools which can be used to control such properties, as discussed in this section.

SrRuO3 down to the 0D limit
The physical properties described above together with the mechanisms that can be used to control have been deducted based on extensive studies on 3D SrRuO3 thin films and bulk SrRuO3 single crystals. There are nonetheless other physical properties and effects that emerge in SrRuO3 structures once their dimensionality is reduced. These properties and effects can become particularly relevant when making devices for quantum electronics, which are often based on SrRuO3 systems with dimensionality lower than 3D. In this section, we review the main properties of SrRuO3 that change when reducing its dimensionality from 3D to 0D.
The easiest way to realize two-dimensional (2D) SrRuO3 is by sandwiching a single SrRuO3 layer between two insulating SrTiO3 layers. For this system, it has been theoretically calculated that SrRuO3 should behave as a minority-spin half-metal ferromagnet, with a magnetic moment of μ = 2.0 μB/Ru atom 106 . In general, and magnetic reconstruction tend to destroy the metallicity and an insulating behavior is experimentally observed for such 2D SrRuO3 system, albeit with finite low-T conductivity values of ~ 10 μS (ref. 90 ).
Like for other perovskite thin films with general ABO3 structure, the dimensionality of the network formed by the BO6 octahedra (B = Ru for SrRuO3) can also be tuned by growing ABO3/A'B'O3 superlattices and properly varying the orientation of the growth substrate and the periodicity of the superlattice 107 . In the superlattice, the BO6 octahedra normally form a 2D network on a lattice matched (001)-oriented substrate (Fig. 4a), where each octahedra is connected with four others in the ab-plane and it is isolated by a B'O6 octahedron along the caxis (i.e., along the growth direction). The 2D network can be reduced to a one-dimensional (1D) network when a (110)-oriented substrate is used, since in this case each BO6 octahedron is only connected to two octahedra along one of the in-plane axes (Fig. 4a). An additional reduction to the 0D regime can be obtained if the superlattice [ABO3]1/[A'B'O3]n is grown on a (111)-oriented substrate 107 (Fig. 4a). If there are two or more consecutive ABO3 layers with one period, meaning a [ABO3]m/[A'B'O3]n superlattice (with m > 1), then the BO6 octahedra can even be connected in a zig-zag way forming a zig-zag 0D pattern 107 (Fig. 4a).
The reduction in dimensionality of the RuO6 octahedra network leads to a variation in the magnetic properties of SrRuO3 which changes from being a ferromagnetic metal in the 2D limit to an Ising paramagnet in the 1D regime to a ferromagnetic insulator in the 0D case. In the 0D regime, a very significant change in the magnetization has been observed upon strain application 107 , which can be exploited in the future for the realization of strain-actuated nanoscale memories 108 based on 0D SrRuO3. Ab-initio calculations also show that half-metallicity and orbital selective quantum confinement can be realized when the dimensionality of RuO6 octahedra network in SrRuO3 is reduced from the 3D to the 0D 107 case.
The 1D growth of SrRuO3 can be also tuned by varying the growth rate and the SrTiO3 (001) substrate miscut angle 109 , which in turn determines the height of the 1D steps (Fig. 4b).
By further increasing the substrate miscut angle, a bunching of the 1D steps can be obtained 109 .
Step bunching in semiconductors and metals has received great attention because bunched surfaces can serve as template for the growth of low-dimensional structures 110,111 . 1D steps of SrRuO3 can therefore be used as template for the epitaxial growth of oxide nanowires including nanowires made of oxide superconductors, which can be investigated for the emergence of topological superconducting phases (see also section 2.4). It has also been shown 112 that an array of 0D SrRuO3 nanodots fabricated from a SrRuO3 thin film can exhibit higher TCurie compared to that of the original film (Fig. 4c). The reason for the increase in TCurie is a relaxation of the strain occurring as result of the removal of lateral material around each nanodot 112 compared to the original thin film matrix.
Epitaxial heterostructures of SrRuO3/CoFeO4/BiFeO3 have also been used to fabricate nanodots 113 by the nanoporous anodic alumina template method. The array of nanodots shows strong magnetoelectric coupling with clear magnetization switching induced by an applied Ewhich suggests the possibility of using these 0D SrRuO3 nanodots array for high-density memory storage (> 100 Gbit/in 2 ) or logic devices.
More recently, it has been shown 114 that a single SrRuO3 grain boundary (GB) formed in SrRuO3 grown onto a SrTiO3 bicrystal has transport properties equivalent to that of a spin valve. Apart from highlighting that GBs play a key role towards determining the performance of SrRuO3-based devices, this study 114 suggests that low-dimensionality GBs in SrRuO3 can be used for the realization of novel spintronic devices.

SrRuO 3 in conventional and quantum electronics
After reviewing the physical properties of SrRuO3 and the experimental tools that can be used to control them in section 1, in this section 2 we discuss how SrRuO3 can be combined with other material systems to exploit its physical properties for electronics applications. We do not only illustrate relevant devices that have already been realised, but we also propose devices that have never been made to date. For these new devices, we provide proof-of-concept layouts and explain how they can offer competitive advantages over their equivalents and/or how they can be used in future studies to better understand effects recently discovered in SrRuO3.
Fabrication of devices based on SrRuO3 is nowadays possible thanks to the variety of techniques suitable to make SrRuO3 thin films with excellent properties as well as thanks to the extensive number of studies reported on the optimization of these thin film properties. In addition, the fabrication of SrRuO3 in ultrathin film form and, even more recently, in the form of freestanding oxide nanomembranes have paved the way towards the investigation of material systems, where the reduced dimensionality of SrRuO3 and its interfacing to other oxides have resulted in the discovery of exciting and novel physical effects. The interplay and coexistence within the same material of different types of interactions like spin-orbit interaction, electron-electron correlations, and charge-to-lattice coupling makes SrRuO3 a rich playground for the investigation of a variety of physical phenomena and quantum effects. This wide range of physical phenomena and quantum effects includes orbital magnetic moment and polarization, magnetocrystalline anisotropy, ultranarrow magnetic domains, MIT (as thickness is reduced to the 2D limit), and Berry effects (Fig. 5).
It appears clear to us that achieving control over this rich set of phenomena and effects can lead to the development of devices for conventional electronics (e.g., spin-orbit torque and domain wall spintronics, straintronics) with better performance than existing ones as well as to novel devices for the emerging field of quantum electronics (e.g., topological electronics and superconducting electronics).
In addition to proposing new proof-of-concept electronic devices based on SrRuO3 and to illustrating their layouts, in the following we also describe the materials challenges that have to be addressed to realize such devices. We show that addressing these challenges is crucial to achieve control over the quantum effects and physical phenomena underlying the devices' functioning and ultimately affecting their performance.

Memory and spintronic devices
The application of SrRuO3 for the realization of room-T memory devices is prevented by the low TCurie ~ 160 K of SrRuO3 compared to other 3d-transition metals and ferromagnetic alloys which are currently in use for the same applications firstly because they have TCurie higher than room T. As a result of this limitation, SrRuO3 has been used mostly as epitaxial metallic electrode for the fabrication of room-T oxide memory devices based on other oxides.
The ever-growing interest in cryogenic electronics, however, is boosting the investigation of energy-efficient and high-density memory technologies that can operate efficiently also at low Ts. From this point of view and given its high compatibility with other functional oxides like piezoelectrics or ferroelectrics, SrRuO3 can play a major role for the future integration of oxide memory devices in cryogenic CMOS circuits.
We start this section 2.1 by reviewing two applications, one for room-T electronics (i.e., ferroelectric tunnel junctions) and the other for cryogenic electronics (i.e., spin valve devices) where SrRuO3 has been used with good results as metallic electrode and ferromagnetic layer, where we think that SrRuO3-based devices are unlikely to become de facto technological standards, at least until protocols for large-scale production of SrRuO3 devices with optimal properties and integrable with CMOS technology are developed (as discussed in section 1).
At the end of section 2.1, we outline two other technological applications that may stem from the exploitation of specific SrRuO3 properties. We suggest that two specific properties of SrRuO3, namely its narrow magnetic domains and high spin-orbit coupling, can be used to realise electronic devices that would offer a competitive advantage over existing devices used for the same technological applications.

SrRuO3-based devices for conventional electronics with good performance
For memory devices operating at room T, one of the applications of SrRuO3 that has already showed good results stems from its use as an epitaxial metallic electrode in ferroelectric tunnel junctions (FTJs). FTJs exploit the change in resistance observed upon polarization reversal of a ferroelectric material to encode digital information. If the ferroelectric is sufficiently thin, by flipping its polarization, it is possible to change its transmission probability for electrons which gives rise to a tunnelling electroresistance effect 115 (Fig. 6a). A variety of FTJs with SrRuO3 used as bottom metallic layer have been already realized, and the list of ferroelectrics used include BaTiO3 (refs. [116][117][118][119][120] ), BaxSr1 -xTiO3 (ref. 19 ), PbZrxTi1-xO3 (refs. [121][122][123], and BiFeO3 (ref. 124 ). The changes in resistance observed in these FTJs upon polarization reversal are typically of two orders of magnitude at room T 119 , and can increase further at cryogenic Ts due to a suppression of phonon-assisted indirect tunnelling as T is decreased 120 . Although FTJs appear promising for the development of non-volatile resistance-switching random-access memories (RRAMs), both at room T and cryogenic Ts, the direct current reading of their state is based on the measurement of tunnelling current 124 . This implies that the ferroelectric layer has to be thin to maximise the tunnelling current and facilitate the device readout. Nevertheless, ultrathin ferroelectric barriers exhibit other undesirable effect like a high leakage current which can degrade the device performance 125 . As for other oxide FTJs, also in SrRuO3-based FTJs, ferroelectricity disappears below a critical thickness of the ferroelectric barrier. This critical thickness strongly depends on the uniformity and sharpness of the terminations of the SrRuO3 interface with the ferroelectricfor which oxygen pressure during growth also plays a major role 118 . Achieving fine control over these parameters will play a crucial role towards the development of FTJ RRAMs (at either room T or cryogenic Ts) based on SrRuO3.
Similar to the case of FTJs, due to its good lattice matching with other oxides, SrRuO3 has also been used below its TCurie to exchange-bias other magnetic oxide thin films (ferromagnets and antiferromagnets) grown epitaxially onto SrRuO3. Exchange bias is typically used in spintronics devices like spin valves to pin the magnetization of a hard ferromagnetic layer, whilst the magnetization of the soft ferromagnetic layer can be switched via an applied magnetic field H.
One of the peculiarities of the exchanged-biased heterostructures based on SrRuO3 is that both negative and positive exchange bias can be realised at the interface between SrRuO3 and another magnetic oxide (Fig. 6b). Negative (positive) exchange bias occurs as result of a ferromagnetic (antiferromagnetic) alignment of interfacial spins of the two coupled magnetic materials, and it manifests as a shift of the magnetization hysteresis loop along the same (opposite) direction of the applied cooling H. Negative exchange bias has been reported for SrRuO3 epitaxially grown onto the antiferromagnet Sr2YRuO6 (ref. 126 ), whilst positive exchange bias has been reported for SrRuO3 grown onto the half-metal ferromagnetic oxide La2/3Sr1/3MnO3 (refs. [127][128][129][130] or onto Pr0.7Ca0.3MnO3 (ref. 131 ).
In general, positive exchange bias is more difficult to realize experimentally compared to negative exchange bias, and it has been reported only for a few other materials combinations including FeF2/Fe (ref. 132 ), Cu1-xMnx/Co (ref. 133 ) and Ni81Fe19/Ir20Mn80 (ref. 134  Within the same heterostructure, however, the sign of the exchange bias can be changed upon varying Hcool or T. In general, for a bilayer system consisting of two coupled magnetic materials, a large enough Hcool can induce either a negative exchange bias for a ferromagneticlike interface coupling, or positive exchange bias for antiferromagnetic-like interface coupling.
In a few systems, a sign change in the exchange bias has been observed upon increasing Hcool which is typically due to the formation of domain walls parallel or antiparallel to the bilayer interface 135 . For SrRuO3-based systems, a change in the sign of the exchange bias induced by a variation in Hcool has been reported, for example, in SrRuO3/PrMnO3 superlattices 136  can be developed and gain a competitive advantage over devices like those in ref. 137 .

SrRuO3-based devices for conventional electronics with competitive advantage
The two applications discussed in section 2.1.1 and shown in Fig. 6 are less likely to be carried out with SrRuO3-based devices other than with already existing devices based on other materials. Nonetheless, we identify two other applications for conventional electronics, where SrRuO3 devices can offer better performance than existing devices and become the better alternative, once high reproducibility and scalability in their fabrication is also achieved.
The first application which we illustrate stems from a characteristic magnetic property of SrRuO3, consisting in its domain walls being much narrower than in other oxide ferromagnets.
The narrow domain walls of SrRuO3 can be used for low-dissipation racetrack cryogenic memories. In racetrack memories based on domain wall motion, data bits are stored in the form of magnetic domains that are then moved along a nanowire strip, typically through the application of a current 138 . The main issue of the racetrack memories proposed to date, however, is the significant Joule heating induced by the large currents which are typically required to move the magnetic domains through small nanowires 139 . Thanks to its small domain wall width (DWW), SrRuO3 can be potentially used to overcome this issue and realise racetrack memories with lower energy dissipation than those proposed to date. It has been already reported, for example, that domain wall motion in SrRuO3 can be induced with a current density that is at least one order of magnitude lower than that needed for ferromagnetic metals with similar depinning fields 140,141 . Although an exact measurement of the DWW in SrRuO3 has still not been done, it has been estimated 140 that the DWW in SrRuO3 can be as low as 3 nm at T < 100 K. An upper limit of 10 nm has also been estimated for DWW in SrRuO3 based on scanning tunnelling spectroscopy (STS) measurements 142 at 4.2 K on SrRuO3/YBa2Cu3O7 bilayers. The upper limit for DWW in this STS study 142  In addition to the large σSH, other studies also show there exists a direct correlation in SrRuO3 between the spin orbit interaction and the rotation and tilting of the RuO6 octahedra 144 .
To achieve precise tunability over the SOT strength, further investigation is required, since it is currently difficult to disentangle all the mechanisms affecting the SOT strength (e.g., strain,

RuO6 octahedra rotations).
Independently on the physical mechanisms (or combinations thereof) affecting SOT, it seems that the SOT strength can be tuned electrically. Some mechanisms like the RuO6 octahedra rotation and strain, which seem to affect the SOT strength, can be indeed controlled electrically. One possible way to achieve the electrical control is by applying a voltage to a piezoelectric exerting strain onto SrRuO3, as sketched in Figs. 7d and 7e. We think that achieving electrical tunability of the SOT strength in SrRuO3 will pave the way for new SOT spintronic devices with electrical control of their state.
By carefully engineering the SrRuO3 strain in Ni81Fe19/SrRuO3 bilayers and using a combination of ST-FMR and in-plane harmonic Hall voltage measurements 146,147 , it has already been shown that the SOT efficiency and σSH can increase by almost two orders of magnitudes. The authors of these studies 146,147 correlate the increase in SOT strength and σSH with a change in the crystal structure of SrRuO3 from orthorhombic (under compressive strain) to tetragonal (under tensile strain). We note that these large σSH (up to ~ 441 × ℏ/e S cm -1 ) and SOT efficiency (up to ~ 0.89) values 146,147 have been measured for SrRuO3 at room T.

FIG. 7. Application of SrRuO3 for spin-orbit torque memories. Illustration of a typical spin-transfer torque magnetoresistive random access memory (STT-MRAM) device in (a) and of a spin-orbit torque-(SOT-) MRAM device in (b). [Panels (a) and (b) are adapted from ref. 148 ]. In a STT-MRAM device the switching of the magnetization of the free magnetic layer is obtained via a tunnelling current injected through a magnetic tunnel junction, whereas in a SOT-MRAM device the current is injected through a layer with high spin orbit coupling that exerts SOT on the free layer. (c) Main advantages and challenges for the realization of SOT-MRAM devices based on SrRuO3 with the layout shown in (d) and (e), where a gate voltage VG applied to the piezoelectric is used to reversible switch the RuO6 octahedra and tilt them between two configurations. Each configuration leads to a different SOT on the free magnetic layer, allowing to electrically switch the device between two states.
Based on the above results and considerations, we envision that the SrRuO3-based devices that we propose with high SOT efficiency can be used also at room T. As a result, these devices can find application in the next generation of SOT-magnetoresistive random-access memories (SOT-MRAMs). SOT-MRAM been recently proposed to overcome the major limitations of spin-transfer torque memories (STT-MRAMs) 148 , which represents the current state-of-the-art MRAM technology 149 (Fig. 7a). STT-MRAM has already entered volume production in all major foundries, also thanks to its compatibility with CMOS technology 149 .
The main limitations of STT-MRAM are related to large switching currents needed for STT-MRAM operation. These large switching current prevent the application of STT-MRAM for ultra-fast operations at the sub-nanosecond regime, also due to the stochastic nature of STT. In addition, large switching currents also generate reliability issues because they have to flow through the thin oxide of the magnetic tunnel junction (MTJ) as shown in Fig. 7a, which reduces the MRAM endurance over time. By contrast, the switching current in SOT-MRAM does not flow across the MTJ, but through a heavy metal or another material coupled to the magnetic free layer (Fig. 7b).
To make the switching of the free layer magnetization in a SOT-MRAM device more deterministic, a small H field is often applied perpendicular to the free layer. Several H-free schemes have also been proposed [150][151][152][153] , but these usually result in a more complex memory cell fabrication. Recently, a H-free switching of the perpendicular magnetization in SrRuO3 was achieved in WTe2/SrRuO3 bilayers at 40 K, where the WTe2 acts as source of out-of-plane spin polarization due to its reduced crystal symmetry 154 .
We envision new SOT devices where the SOT strength in SrRuO3 can be tuned, also at room T, via voltage-driven strain exerted by a piezoelectric coupled to SrRuO3 (Figs. 7d and e). The voltage-driven modulation in SOT strength leads to a change of the switching current for the magnetization of a free layer grown onto SrRuO3 between two values. The bistability in the switching current is used to reversibly switch the SOT device between two states.

Straintronics
The possibility of modulating the spin-orbit interaction in SrRuO3 by inducing structural distortions in the material can also be exploited for the realization of novel transducers, actuators, and sensors. Shape memory effect materials like Heusler compounds, which exhibit changes in their shape in response to the application of an external stimulus (e.g., temperature, magnetic field, strain) are nowadays already studied for these applications.
Although shape memory effects are rare in oxides with the only exception of oxide multiferroics, they have recently been observed 155 also in SrRuO3. In SrRuO3, shape memory effects emerge possibly due to a combination of the strong spin-orbit interaction with a weak pinning of the magnetic domain walls. It has been shown that, upon field cooling SrRuO3 in a H of ~ 1 Tesla applied along the [110]pc axis, a single domain state can be induced in SrRuO3, as result of the growth of domains parallel to the applied H 155 . Unlike for Heusler alloys 156,157 , SrRuO3 remains in this structurally distorted phase, which is stable at low Ts and against magnetic field sweeps. Upon warming above TCurie 155 , SrRuO3 exhibits a shape memory effect and relaxes back from a single domain into a multidomain state configuration.
It has been recently shown that epitaxial strain can also be used as an effective tool to vary the magnitude and sign of the Berry curvature and in turn modulate related effects. Several groups had already demonstrated that epitaxial strain affects the magnetic properties of SrRuO3 thin films 41,74,78,[158][159][160][161] . The magnetic properties are affected by strain due to the strong coupling existing between lattice distortion and electronic band structure in SrRuO3. In their recent study, Wakabayashi and co-workers 53 have performed a systematic investigation of the effect of epitaxial strain on the electrical and magnetic properties of ultrahigh-quality SrRuO3 thin films. These thin films were deposited using machine-learning-assisted MBE on various perovskite substrates with mismatch ranging from -1.6% to 2.3% (compared to bulk SrRuO3).
Following this approach, the authors could single out all the effects that strain induces on its own on magnetic and transport properties in SrRuO3. All the other concurrent factors typically affecting magnetic and transport properties (e.g., defects, off-stoichiometry etc.) were in fact not present in these thin films due to their ultrahigh quality.
Motivated by these previous results and by the fact that Berry effects are also very sensitive to changes in the electronic band structure, Tian and co-workers 162 have recently investigated the effect of epitaxial strain on the AHE in both tensile-and compressive-strained SrRuO3. In their study 162 , they have found that epitaxial strain can be used as a tool to manipulate the Berry curvature, and the corresponding AHE (in amplitude and sign). Consistently with previous reports 41,78 , Tian and co-workers have shown that, as the strain changes from compressive to tensile, the magnetic easy axis of the SrRuO3 thin films changes from an out-of-plane to an in- low Ts, in contrast with the typical hysteretic behavior expected for an AHE, which recovers in ρxy (H) for SrRuO3 thin films under compressive strain. Also, whilst for compressive-strained SrRuO3 thin films, ρxy changes sign with T and it goes from positive to negative at a T typically of ~ 125 K before becoming null at TCurie, for tensile-strained thin films ρxy is negative independently on T. These results reported by Tian et al. 162 pave the way for the application of epitaxial strain engineering to reversibly control AHEs in SrRuO3-based devices.
By applying strain to SrRuO3 in the form of freestanding nanomembrane, it should be possible to achieve larger variations in the SrRuO3 crystallographic structure, and in turn a larger modulation of the SrRuO3 physical properties (transport and magnetic) and of related effects (e.g., AHEs and THEs). Free-standing single-crystal oxide membranes of various materials including SrRuO3 have already been fabricated either via either chemical or mechanical lift-off [163][164][165][166][167][168][169] from the growth substrate (Fig. 8). Both processes are non-destructive, unlike other physical release methods used for silicon-on-insulator technology 170 or for lightemitting diodes based on GaN 171 . Freestanding oxide nanomembranes can be made without any thickness limitations down to the monolayer limit 167 and can sustain strain up to 8% (ref. 169 ), which is unachievable through conventional strain engineering of thin-film heteroepitaxy. In addition to the large strain that can be exerted onto them, SrRuO3 oxide nanomembranes can be stacked onto materials that are difficult to grow epitaxially onto SrRuO3 either because they have different lattice parameters or because they are stable under different growth conditions 163,164 .
The fabrication of freestanding SrRuO3 nanomembranes using the chemical lift-off approach has already been reported by several groups 168,[172][173][174][175][176] . In all these cases, the SrRuO3 thin film has been grown onto a lattice-matched sacrificial layer which is grown, without breaking vacuum, in between the substrate and SrRuO3. To date, the sacrificial layer that has been mostly used is Sr3Al2O6, which can be dissolved in water as illustrated in Fig. 8a.
Nonetheless, the water solubility of Sr3Al2O6 also represents a limiting factor for practical applications due to its instability in air. A more stable sacrificial layer is the brownmillerite SrCoO2.5, which has been successfully used by H. Peng and co-workers 176  Probing the T evolution of the mechanical response of resonators fabricated from freestanding SrRuO3 nanomembranes through laser interferometry, it has been also shown that structural phase transitions occurring in SrRuO3 can be identified 175  Freestanding of ultrathin SrRuO3 can also be stacked onto ultrathin nanomembranes of other oxide materials, as it is done to make heterostructures of 2D van-der-Waals (vdW) materials.
Heteroepitaxial oxide nanomembranes with SrRuO3 can be tested, apart from their flexoelectric figure of merit, also for their flexomagnetic properties, meaning for an increase in their magnetization under an applied strain gradient (Fig. 9). Flexomagnetism has not been yet estimated nor observed in complex oxides, but SrRuO3 may exhibit large flexomagnetic effects due to its strong coupling of lattice and spin degrees of freedom. Flexomagnetic SrRuO3-based NEMS devices can be potentially used for the realization of magnetic sensors with extremely high sensitivity 178 and resonant frequency tuneable over a very wide frequency range 179 .

Berrytronics
Engineering non-collinear magnetic textures and achieving control over topological effects correlated to them has emerged as a promising route for the development of novel quantum electronic devices. Studies triggered by these motivations have also led to the discovery of new phases in condensed matter, which is crucial for the development of quantum technologies.
In the ongoing studies on topology associated to non-collinear spin textures, SrRuO3 has gained a primary role. SrRuO3-based heterostructures with strong inversion symmetry breaking and spin-orbit coupling can be engineered [180][181][182] . Strong inversion symmetry breaking, and spin-orbit coupling are key ingredients to generate spin textures that are non-collinear in real space and have a topological character.

, without stack) and tested for its flexoelectric (at room T or below) and flexomagnetic properties (below TCurie). (b) Main advantages and challenges of NEMS devices made from SrRuO3-based oxide nanomembrane heterostructures.
Most of the topological and spin-transport phenomena studied in SrRuO3 are intimately related to the curvature of a band structure property of materials known as Berry phase (ΦB) and to its curvature ΩB, which in SrRuO3 is non-null. ΦB is a geometric quantum phase 183 , while ΩB (Fig. 10a) [191][192] , electrical polarization [193][194] , quantum charge pumping 195 , and topological superconducting phases [196][197] .
The ΩB in momentum-(k-) space induces a cyclotron motion of electronic modes around a crossing point that gives a nonzero intercept in the Landau level phase diagram. The existence of this motion has been verified experimentally in transport experiments through measurements of Shubnikov-de Haas oscillations 181,198  In oxides like SrRuO3, due to a sizable spin-orbit coupling and a non-trivial spin texture, the Berry curvature can also be strongly enhanced and modulated in sign and amplitude. This is possible due to the coexistence of a magnetic spin texture in real space and a non-trivial Berry curvature ΩB in k-space in SrRuO3 (Fig. 10b). Such coexistence is quite unique, but it also indicates a high complexity which requires distinct strategies for exploiting and disentangling the difference sources of Berry curvature effects. In this context, for the engineering of new devices as well as for fundamental reasons, it is challenging to evaluate how modifications of the spin texture of SrRuO3 (e.g., via VG-applied strain) can tune physical effects stemming from its intrinsic non-null ΩB (see also section 2.4).
One of the current most important challenges related to ΩB effects in SrRuO3 is understanding how to differentiate and separately access real-space and k-space contributions to ΩB. Disentangling these two types of contributions is crucial to achieve control over their magnitudes in the Hall response and other quantum transport effects exploited for SrRuO3based quantum electronic devices. The ongoing debate on the actual existence of topological spin textures (skyrmions) in SrRuO3 also fits into this wider research objective. We note here that the magnetic ground-state phase diagram of SrRuO3-based systems with DMIs is hard to compute theoretically because it is difficult to quantify the DMI amplitude and to use models with localized spins and short-ranged interactions in the metallic state of SrRuO3.
Results like those of Matsuno and co-workers 180 on the H-dependence of σAH are therefore difficult to model. A similar H-dependence of σAH to that first reported in ref. 180 has also been shown in other studies 181,199 . Nevertheless, features resembling a THE have also been measured for SrRuO3 thin films deposited on SrTiO3 without any SrIrO3 or similar interface layer [200][201][202][203][204] .
These results and the subsequent observation of bump-and hump-like features also in the H variation of σAH of asymmetric SrTiO3/SrRuO3/SrIrO3 and symmetric SrIrO3/SrRuO3/SrIrO3 trilayers 205 have led to consider alternative mechanisms to skyrmions to explain the physical origin of the hump-and bump-like features in the SrRuO3 σAH. The characteristic T evolution of the σAH at H = 0 also suggests that intrinsic contributions, in addition to real-space magnetic spin textures, must play an important role in determining the AH response of SrRuO3 thin films. The sign change in σAH occurring at a T approximately equal to half TCurie, and the variation in both sign and amplitude of σAH when going from SrTiO3/SrRuO3/SrIrO3 to SrIrO3/SrRuO3/SrIrO3 trilayers 205 , cannot be explained on the basis of conventional mechanisms contributing to the AHE in ferromagnetic materials like side-jump and screw-scattering contributions (Fig. 12). Also, these variations in σAH cannot be accounted for only based on skyrmions, as they occur at the same H values where the SrRuO3 magnetization (M) reverses its direction in the M(H) loops.
The σAH variation in an applied H must be also connected to the intrinsic nature of the SrRuO3 electronic bands in the ultrathin limit. The low-energy electronic structure and band topology of SrRuO3 is in fact characterized by topologically nontrivial spin-polarized bands at the Fermi energy (Fig. 12). These bands act as sources of non-null Berry curvature ΩB and lead to competing contributions in the AH response 205 . It is hence clear that k-space contributions to ΩB, in addition to the real-space magnetic textures, are essential to fully understand and control the AH response of SrRuO3-based systems. Apart from the above heterostructures based on SrRuO3, a remarkable evolution of ΩB in k -space has been recently reported also for a system consisting of ultrathin SrRuO3 combined with LaAlO3, which is a polar wide bandgap insulator 206 . Van Thiel and co-workers have shown 206 that the synthesis of RuO2-terminated SrRuO3 ultrathin films interfaced with LaAlO3 results in levels of charge doping of SrRuO3 that go well beyond those obtainable with electrostatic gating. The high doping results in a pronounced profile with excess electron density along the growth axis of the SrRuO3 thin film. In the ultrathin limit of SrRuO3, the doping-induced electronic charge reconstruction leads in turn to a variation of the ΩB sign in k-space, which manifests experimentally as a variation in the σAH sign 206 .
The theoretical analysis carried out in ref. 206 identifies the charge pinning at the SrRuO3/LaAlO3 interface and the resulting inversion symmetry breaking as the dominant mechanisms responsible for the reconstruction of ΩB in k-space. This implies that the change in ΩB sign is a consequence of a topological-like transition in k-space other than of a change in the electronic band occupation. The results of this work 206 suggest that electronic charge reconstruction can be used in the future as an effective tool to manipulate ΩB and correlated topological transitions in SrRuO3, which in turn affect measurable quantities like σAH.
Based on the above consideration, it is evident that SrRuO3 represents a material with potential coexistence of k-and real-space Berry effects, whose origins and characteristic scales are completely distinct. A remarkable aspect of this coexistence is that topological configurations in real and k-space occur only for specific regions of the phase diagram as a function of parameters such as T, H and electron filling.
Apart from mapping the parameters' space to determine the configurations with a dominant real-or k-space character of ΩB in SrRuO3, another future challenge is to differentiate configurations based on real-space topological spin textures from those with a non-trivial topology in k-space. To address all these questions, we suggest two possible experiments.
Our first proposal is sketched in Fig. 13 and exploits the spin dependence of σAH in SrRuO3 in its ferromagnetic state. The key point here is to evaluate the spin content of the AH voltage measured across a SrRuO3 Hall bar. To do this, a spin-polarized current can be injected into SrRuO3 (e.g., through a half-metal ferromagnet coupled to SrRuO3) and the resulting AH voltage should be detected with ferromagnetic electrodes. This should be done for different configurations, where the magnetization is switched from parallel to antiparallel with respect to the SrRuO3 magnetization or from oriented along the SrRuO3 easy axis or along the SrRuO3 hard magnetic axis. The as-measured transverse Hall signal would contain information about transport processes conserving spin and can be compared (in sign and amplitude) to another transverse Hall signal measured on the same Hall bar with normal-metal electrodes (Fig. 13).
The comparison would allow to understand whether the transverse voltage is due to a ΩB dominated by spin-conserving processes (related to k-space topological contributions) or by non-conserving spin scattering processes (related to real-space topological contributions).
Our second proposal to understand the dominant contributions to ΩB in SrRuO3 is based on the design of heterostructures where SrRuO3 is interfaced with a superconducting material. As discussed in detail in section 2.4, we expect that the interplay of magnetic states having a non-trivial ΩB in real or k-space with a superconductor would allow to distinguish between the two types of topological contributions.

Topological superconductivity and superconducting berrytronics
Due to its good lattice matching with other oxide perovskites including high-temperature superconductors (HTSs) like YBCO, SrRuO3 has been already studied in a variety of superconducting devices such as Josephson junctions [26][27][28]207,208 (JJs) and superconducting spin valves 209 . As a result of its good lattice matching with YBCO and thermal stability, it has also been shown that SrRuO3 can also be used as buffer layer to improve the performance of HTS coatings 210 and to boost their superconducting critical current (Ic) density.
Several groups have characterised the superconducting properties of JJs with SrRuO3 as weak link including YBCO/SrRuO3/YBCO JJs (refs. 26,28,207 ) and hybrid metal/metal-oxide JJs like Nb/Au/La0.7Sr0.3MnO3/SrRuO3/YBCO (ref. 208 ). Most of these experiments and independent low-T STS measurements on SrRuO3/YBCO bilayers 142 suggest that the superconducting order parameter can penetrate into SrRuO3 over a depth larger than 20 nm at 4.2 K (refs. 26,27,142,207 ), which is an order of magnitude larger than the typical superconducting coherence length ξF in a strong ferromagnetic metals like Ni or Co (~ 1-2 nm; refs. 211,212 ). This long-ranged proximity effect has been ascribed to crossed Andreev reflections taking place near domain walls at the SrRuO3/YBCO interface 142 or to resonant tunnelling of quasiparticles through an oxygen-depleted layer forming at the SrRuO3/YBCO interface 207 . It should be noted, however, than in hybrid metal/metal-oxide Nb/Au/La0.7Sr0.3MnO3/SrRuO3/YBCO JJs a long-ranged proximity effect is only observed when both ferromagnets (La0.7Sr0.3MnO3 and SrRuO3) are present 208 . The authors of ref. 208 216 which makes it difficult to study the superconducting proximity effect between the superconductor Sr2RuO4 and other materials. According to Anwar and co-workers, the PLD growth of SrRuO3 on Sr2RuO4, restores metallic behaviour at the SrRuO3/Sr2RuO4 interface and it allows to measure proximity-induced superconductivity in SrRuO3 over a ξF of ~ 9 nm (ref. 217 ). In addition to the long ξF, which is comparable to that reported in YBCO/SrRuO3 systems 26,27,142,207 , Anwar et al. also studied the proximity-induced superconducting gap in SrRuO3 by fabricating Au/SrTiO3/SrRuO3/Sr2RuO4 tunnel junctions 218 . The shape and T-evolution of gap features in the differential conductance dI/dV of these junctions show an unusual behavior which the authors reconcile with an anisotropic superconducting gap induced in SrRuO3 with p-wave or d-wave symmetry 218 . It is worth noting that the interplay between different mechanisms including orbital loop current magnetism recently discovered 219 at the Sr2RuO4 surface and inverse proximity 220 makes the Sr2RuO4/SrRuO3 interface a complex system to study and that can indeed host spin-triplet and other unconventional superconducting states.
The study of the interplay of Berry effects in SrRuO3 with conventional or unconventional superconductors represents an unexplored line of research, which can lead to the discovery of topologically protected superconducting states for quantum electronics.
We first discuss here the topological phases that may arise if SrRuO3 is coupled to another spin-singlet superconductor. The first case that we consider refers to the superconducting proximity between a conventional spin-singlet superconductor and SrRuO3 acting as a topological metal with uniform magnetization. This assumption is supported by the fact that We expect that a very good electronic matching is needed at the interface between SrRuO3 and a conventional s-wave superconductor to trigger topological superconductivity. For this reason, the epitaxial growth of a metal-oxide superconductor (e.g., LiTi2O4) with a spin-singlet s-wave order parameter onto SrRuO3 would be ideal to meet this requirement. Moreover, the charge and spin conductance will be affected by the presence of topological modes in a way that will be different from the case of tunneling into a pure nodal d-wave superconductor.
An additional path that we foresee for the realization of topological superconductivity in superconducting heterostructures based on SrRuO3 stems from the non-collinear magnetic spin textures (e.g., skyrmions) which have been suggested to nucleate in ultrathin SrRuO3 at its coercive field or in heterostructures 180 combining SrRuO3 with a high-spin orbit coupling material like SrIrO3 (see also section 2.3). The proximity effect between a conventional spinsinglet superconductor and a non-collinear magnetic spin texture (Fig. 14c) can be exploited to convert spin-singlet pairs into chiral or helical spin-triplet pairs. This physical scenario is inspired by the theoretical finding that an s-wave superconductor can be turned into a p-wave superconductor, if it is interfaced with a semiconductor with large Rashba spin-orbit interaction, under the assumption that a source of time-reversal symmetry breaking (e.g., a magnetic exchange field) is also present 225,226 . Fabricating this type of devices sketched in Fig. 14b, however, requires achieving a systematic control over the generation of skyrmions in SrRuO3-based systems and then performing systematic studies on their coupling to superconductors.
FIG. 14. SrRuO3-based system for realization of topological superconductivity. Illustration of a superconducting heterostructure consisting of a d-wave superconductor (e.g., YBCO) with nodal gapless density of states (a) and realization of a topological superconducting state in YBCO with gapped density of states due to a combination of inverse proximity with SrRuO3, spin-orbit coupling and inversion symmetry breaking (b). Schematic of another system for the realization of topological superconductivity (c) consisting of an s-wave superconductor in proximity coupling with a non-collinear magnetic spin texture (e.g., a skyrmion) in SrRuO3. The topological states forming at the boundary of the non-collinear magnetic region are chiral and give rise to a spontaneous current flowing along the edge.
Since a rotating magnetic field is equivalent, from the point of view of conversion of spinsinglets into spin-triplets, to the combination of Rashba spin-orbit coupling with an applied homogenous magnetic field, one can engineer quasi-1D topological superconductors with magnetic spin textures, or alternatively with antiferromagnetism or ferromagnetism in the presence of external currents and Zeeman fields. A magnetic helix crystal hence represents a suitable system to realize topological superconductivity when coupled to a conventional superconductor, since a magnetic helix can simultaneously generate spin-orbit coupling (due to inversion symmetry breaking) and a magnetic exchange field. While a magnetic helix is sufficient to induce a topological superconducting state, to achieve a strong topologically protected state in a number of dimensions greater than one, however, it is necessary that the magnetic spin texture winds in all direction. As a result, whilst a magnetic helix coupled to a conventional superconductor can induce spinless p-wave pairing in 1D, a spin skyrmion is necessary to get an effective spinless chiral p+ip topological superconductor in 2D. Evidence for topological superconductivity stabilized by non-trivial magnetic spin textures has been recently demonstrated in various materials platforms consisting of magnetic atoms/clusters deposited on a superconductor surface or of superlattices hosting chiral magnetic textures [227][228][229][230] . One of the challenges to address in the future to achieve topological superconductivity from the proximity effect between a superconductor and magnetic skyrmions in SrRuO3 is to control the mutual competition between the magnetic and superconducting order parameters and to determine the best magnetic spin texture for the realization of topological superconductivity 231 .
A magnetic skyrmion in SrRuO3 can also trigger formation of vortices into a superconductor coupled to SrRuO3. The spin polarization of the skyrmion combined with the spin-orbit coupling can induce a charge current at the superconductor/SrRuO3 interface. An important challenge here is to differentiate between effects genuinely induced by the exchange coupling between the skyrmions in SrRuO3 and the superconductor from those instead merely related to the magnetic stray fields. It should be noted that exotic spin-polarized quasiparticle states can also form in these topological superconducting phasesthese quasiparticle states can be exploited for low-dissipation spin transport in the superconducting state 232 .
Although the complexity of the superconducting topological phases based on SrRuO3/superconductor hybrids is very high, there are several degrees of freedom that can be exploited to control these phases including the type of magnetic spin texture in SrRuO3 triggering them, their shape, and the strength of their coupling between the spin texture and the superconducting condensate. Deviations of the magnetic spin texture from a magnetic helix, for example, can induce different types of topological superconductivity due to changes in the corresponding spatial distribution of the magnetic moments. For an inhomogeneous magnetic helix, for example, topological domains may form inside the magnetic material along with topologically protected modes nucleating at the domain walls 233 . This suggests that control over topological superconducting phases can be achieved, for example, by engineering domains with inequivalent non-collinear magnetic spin texture. Local spectroscopy techniques can be used to resolve the spatial profile of the magnetic texture. We expect that variations in the magnetic spin textures are likely to occur in SrRuO3 and SrRuO3-based heterostructures due to the itinerant ferromagnetism of SrRuO3 and to nonuniform stray fields.
In addition to the generation of topological superconductivity, we foresee another important application of SrRuO3, which relies on using its Berry curvature as mechanism for spin-triplet generation in superconducting spintronic devices. The possibility that magnetic materials with non-null Berry curvature can be used to convert spin-singlet pairs into spin-triplet pairs has been proposed in a recent study 234 , where the authors have reported long-ranged Josephson coupling (up to ~ 160 nm) between two Nb electrodes separated by the chiral antiferromagnet Mn3Ge. When the antiferromagnet Mn3Ge, which has non-null Berry curvature, is replaced by another antiferromagnet (IrMn) with trivial spin texture and null Berry curvature, no longranged currents due to spin-triplet pairs is observed 234 .

FIG. 15. Superconducting spintronics with SrRuO3 exploiting Berry effects. Illustration of a device for reversible control over spin-triplet generation induced by the non-null
Berry curvature of a SrRuO3 weak link separating two superconducting (S) electrodes (a). The application of a gate voltage VG to a piezoelectric coupled to SrRuO3 induces strain-driven modifications in its real-space spin texture, which in turn result in variations (in sign and amplitude) of the SrRuO3 Berry curvature (b). The modulation of the Berry curvature leads to changes in the amplitude of the spin-triplet critical current Ic flowing between the two S electrodes, which switches between null (small) and non-null (large) values thus realizing the equivalent of a superconducting switch.
Compared to the conventional mechanism used to date in superconducting spintronics for spin-triplet generation, which consists in coupling of a spin-singlet superconductor to a ferromagnet with an inhomogeneous magnetization [235][236] (or a to stack of ferromagnets with non-collinear magnetizations 237 ), using the Berry curvature as alternative mechanism for spintriplet generation offers several advantages for applications.
In materials like SrRuO3 due to its sizable spin-orbit coupling and a non-trivial spin-texture, the Berry curvature can be strongly enhanced and modulated (in sign and amplitude) due to the correlation existing between magnetic spin texture in real space and Berry curvature in k-space.
This also implies that, in Josephson junctions where SrRuO3 is used as weak link between two superconducting electrodes, changing the magnetic spin texture of SrRuO3 in real space (e.g., via VG-driven strain through a piezoelectric coupled to SrRuO3) can in turn affect its Berry curvature in k-space and therefore reversibly enhance or suppress the spin-triplet channel in SrRuO3 (Fig. 15). If the two superconducting electrodes are separated by a distance larger than the spin-singlet coherence length, switching on/off the long-ranged spin-triplet channel in SrRuO3, can turn the SrRuO3 weak link from resistive (triplets off) to superconducting (triplet on). This type of superconducting device would act as a switch and represent the first superconducting spintronic device with full electrical control of its state.
Voltage-driven devices would offer many advantages compared to existing superconducting spintronic devices, whose state is currently controlled by switching the ferromagnet's magnetization from homogeneous (triplets off) to inhomogeneous (triplets on) via an applied magnetic field. Superconducting devices with magnetic control of their logic state are in fact more sensitive to environmental noise, less scalable and less energy efficient than equivalent devices whose logic states is controlled electrically.
We also note that the Berry curvature per se acts for electrons as the equivalent of a magnetic field. Therefore, in addition to variations in the Berry curvature of SrRuO3 induced by voltagedriven strain, one may fabricate superconducting spintronic devices where the combination of spin-polarization (in SrRuO3 itself or in another oxide ferromagnet coupled to SrRuO3) and Berry curvature in SrRuO3 can be used for the generation of spin-triplet pairs for superconducting spintronics.

Summary and outlook
In this Research Update, we have given an overview of some of the most recent work done on SrRuO3 which holds promising potential for the development of novel electronic (conventional and quantum) applications. We have first discussed the main physical properties of SrRuO3, which have kept the interest in material always very high over the past 60 years, and the most recent advances in recent techniques for the fabrication of high-quality SrRuO3 with high reproducibility and over large scales. We have then explained the structural parameters and experimental tools which previous studies have demonstrated to be useful to control specific SrRuO3 properties. To illustrate how properties change with dimensionality and confinement, which is relevant for quantum applications based on SrRuO3, we have also reviewed progress recently made on SrRuO3 structures with dimensionality lower than 3D.
In the second part of this manuscript, we have discussed how, thanks to its rich physics, SrRuO3 represents a material platform with great potential for the realization of electronic devices not only useful for conventional electronics, but also for emerging quantum electronics.
In this section of our Research Update, we have not only limited ourselves to review recent progress made on SrRuO3 devices, but also taken some personal perspectives on future research directions which can bring new insights into effects recently discovered in SrRuO3. We have also proposed devices never realized to date both for conventional and quantum electronics and sketched possible layouts useful for their realization. From this point of view, we hope that this manuscript will inspire the research community to perform new investigations on some of the SrRuO3 heterostructures and devices that we propose.
For the specific application of SrRuO3 for conventional electronics, we have discussed two of most promising applications where SrRuO3 devices can offer a competitive advantage over existing ones. These two applications concern the realization of racetrack memories based on domain wall motion and spin-orbit-torque memories. In addition to large-scale production and reproducibility in their properties, which are essential requirements to meet for applications, other materials challenges must be faced for the realization of such SrRuO3 devices. These challenges include obtaining reversible control over the strength of the spin-orbit coupling in SrRuO3 (e.g., via modulation in the tilting of the RuO6 octahedra), quantifying the width of SrRuO3 domain walls and achieving their manipulation under current injection.
Within the field of conventional electronics, we have also outlined that the very recent realization of ultrathin freestanding SrRuO3 membranes can pave the way for the fabrication of NEMS devices and sensors with unprecedently high figures out merit. The fabrication of SrRuO3 membranes with optimal properties and the testing of their reliability over several operation cycles remain key materials challenges for the future development of these devices.
In the field of the quantum electronics, future applications will certainly stem from the interplay between different mechanisms and quantum effects in SrRuO3. It is currently wellestablished that SrRuO3 becomes a very rich quantum system close to the 2D limit and when interfaced to other materials. We have explained that the possibility to couple different quantum orderings and phases at SrRuO3 interfaces and to tailor the confinement potential in the ultrathin limit provides novel paths for the generation, control, and manipulation of electronic states with nontrivial Berry curvature and topological properties.
As we have discussed in the manuscript section on quantum applications, the interplay of Berry curvature and non-trivial topological states with superconductivity paves the way for the testing and fabrication of a new quantum electronic devices. The devices which we propose exploit quantum effects provided by the Berry phase of SrRuO3 in both real and momentum space. Being able to differentiate between momentum-space (spin-conserving) and real-space (non-spin-conserving) contributions to the SrRuO3 Berry curvature remains one of the most important challenges to realize berrytronic devices on SrRuO3. Also, the realization of superconducting systems where the SrRuO3 Berry curvature acts as a mechanism for spintriplet generation and it can be reversibly manipulated (in sign and amplitude), can lead to the realization of the first class of superconducting spintronic devices with full electrical control of their state. A hallmark feature of the quantum devices that we envision is their tuneability achieved through control of magneto-orbital effects, strain, and interfacing of SrRuO3. This area is not yet fully explored and calls for significant research efforts, particularly in materials science, to master quantum transport properties and coherent effects arising from the SrRuO3 electronic and magnetic states.
In addition to the promising applications described above in the manuscript, there are other research directions with great potential for the discovery of novel effects in SrRuO3 and the consequent development of devices relying on the same effects.
One of these new research directions concerns the study of quantum effects related to the geometric properties of the electronic structure of SrRuO3. We have already outlined that SrRuO3 is characterized by a Berry curvature that has sources both in real and momentum space and that can be tuned through various parameters including dimensionality, strength of the magnetization, inversion symmetry breaking, interfacing with other materials. We expect that exciting discoveries can be made in future studies on Berry effects in ultrathin SrRuO3 films. This is because, for ultrathin SrRuO3 films close to the one-unit-cell-thick limit, sources of Berry curvature in real space can be nucleated at the SrRuO3 film surface or at the interface with another material inducing inversion symmetry breaking. These systems can trigger the formation of distinct magnetic patterns, which may act as source of nonvanishing Berry curvature whilst retaining a topological character. Also, ultrathin SrRuO3 films can be coupled to oxides with properties that can also affect the Berry curvature like strong spin-orbit coupling, large structural mismatch, polar interface, and superconductivity. Experimental evidence for magnetic patterns at the surface or interface of ultrathin SrRuO3 films is still missing. The hurdles in the identification of these magnetic patterns also suggest that SrRuO3 is a unique platform to develop and test new experimental probes and setups suitable to detect such nontrivial magnetic patterns. It is worth noting that the connection between magnetic patterns and Berry curvatures is per se very complex and it will require dedicated studies to gain further insights into it. Even a simple uniform magnetic domain has topological electronic bands in momentum space, with electronic charges that can be controlled via an applied E or strain and that depend on the strength of magnetism and Rashba spin-orbit coupling.
SrRuO3 also represents an ideal platform to investigate emergent phenomena in correlated topological metals. From this point of view, we believe that future studies on topological magnetic effects in high-electron density conditions can be carried out using SrRuO3 other than semimetallic materials or materials with low-carrier density. This proposed line of research can lead to the discovery of new magnetotransport effects deriving from the combination of the high sensitivity of strongly correlated electron systems (as they undergo phase reconstructions) with phase transitions induced by small changes in an external perturbation. In addition, the interplay between Coulomb interaction, spin-orbit coupling and crystal field potentials in SrRuO3 can also trigger magnetotransport effects that are scalable in space and controllable in the time domain. This is another exciting research direction that remains to date unexplored.
The orbital quantum degrees of freedom are another important feature of SrRuO3, whose potential has not been fully explored to date. It is well-established that SrRuO3 is a multi-orbital ferromagnet and that the orbital character of its electronic states at the Fermi level can be modified via an applied E, strain, or geometric design. Studies aiming at controlling orbital effects in SrRuO3 under external stimuli, however, remain still at their infancy. This suggests that SrRuO3 offers an enormous potential for the discovery of orbital effects and the development of orbitronic devices. We believe that future studies targeting specifically the control over the orbital quantum degree of freedom in SrRuO3 may lead to the detection of large orbital Hall effects or orbital selective anomalous Hall effects. The discovery of orbital Hall effects can set the basis for low-consumption quantum spin orbitronic 238 . This perspective is particularly relevant in SrRuO3 structures with reduced dimensionality, where confinement and inversion symmetry breaking can be used to control the orbital population and the orbital angular momentum at the Fermi level.
Another major research route that can lead to important fundamental discoveries is the study of SrRuO3-based heterostructures combining the magnetic properties of SrRuO3 with superconductivity. In section 2.4 we have proposed several SrRuO3-based superconducting devices which can be tested and that can lead to a paradigm shift in the field of superconducting spintronics. Once again, the realization of topological superconducting phases with Cooper pairs having non vanishing spin and orbital angular momenta (i.e., spin-and orbital-triplet pairs) may be easier for ultrathin SrRuO3 films with topological electronic bands. As discussed in section 2.4, one of the major material challenges to achieve topological superconductivity, however, is to obtain a high interface quality between SrRuO3 and another superconductor.
The successful integration of Berry curvature effects with superconducting spintronic elements can also facilitate the developments of electronic devices where spin Hall effects or anomalous Hall effects can be employed to control the superconducting supercurrent and vice versa. If these novel superconducting berrytronic devices were realized, they would represent a huge boost for low-consumption quantum electronics.
More research studies should also be carried out to clarify the physical mechanisms behind phenomena recently discovered in SrRuO3 like the Hall crystal effect 239 , phonon-driven magnetic exchange 240 , and magnetic domain manipulation 241 .
An obvious drawback for device applications of SrRuO3 in the field of conventional spintronics is the fact that the TCurie of SrRuO3 is below room T. A critical challenge is therefore to find ways to increase the TCurie of SrRuO3. A route that could be tested for this would consist in developing a suitable geometric design to modify the bandwidth of the electronic bands and in turn enhance the density of states of SrRuO3 at the Fermi level. An alternative to such approach would consist in employing substitutional transition metal elements to increase the magnetic moment strength in SrRuO3. This could be carried out, for example, using Fe or Mn as substitutional dopants for Ru in SrRuO3.
Future work on SrRuO3 heterostructures can also lead to great technological advancements, especially after freestanding SrRuO3 nanomembranes are fully integrated into them 174 . The study of the effects of geometric parameters related to the large curvature of nanomembranes on SrRuO3 properties is still at its infancy. It is very likely, however, that studies on the topic may lead to the discovery of magnetic and topological Hall effects that are fully geometrically driven and that can have an impact on novel quantum electronic devices.