Topological Hall effect in single thick SrRuO3 layers induced by defect engineering

The topological Hall effect (THE) has been discovered in ultrathin SrRuO3 (SRO) films, where the interface between the SRO layer and another oxide layer breaks the inversion symmetry resulting in the appearance of THE. Thus, THE only occurs in ultra-thin SRO films of several unit cells. In addition to employing a heterostructure, the inversion symmetry can be broken intrinsically in bulk SRO by introducing defects. In this study THE is observed in 60 nm thick SRO films, in which defects and lattice distortions are introduced by helium ion irradiation. The irradiated SRO films exhibit a pronounced THE in a wide temperature range from 5 K to 80 K. These observations can be attributed to the emergence of Dzyaloshinskii-Moriya interaction as a result of artificial inversion symmetry breaking associated to the lattice defect engineering. The creation and control of the THE in oxide single layers can be realized by ex situ film processing. Therefore, this work provides new insights into the THE and illustrates a promising strategy to design novel spintronics devices.

Electron transport coupled with magnetism has attracted a great deal of attention due to its exotic physical properties and potential applications for developing high density memory devices. [1][2][3][4] Among different magneto-transport phenomena, the ordinary Hall effect is the result of the Lorentz force and thus is proportional to the magnetic field. The anomalous Hall effect (AHE) is related to magnetization in ferromagnets, which generally stems from a Berry phase in momentum space. [3] A new type of Hall effect, however, is found to depend on neither magnetic field nor magnetization. It originates from the scalar spin chirality = · ( × ) generated by non-coplanar or non-collinear spin configurations such as helices, domain walls or skyrmions. [3,5,6] When conduction electrons pass through a non-coplanar spin texture, a quantum-mechanical Berry phase is produced in the real space, associated with a fictitious magnetic field. This field is the origin of this particular kind of Hall effect termed as topological Hall effect (THE). [3] The formation of THE are, in most cases, driven by a non-zero Dzyaloshinskii-Moriya interaction (DMI), which requires the presence of strong spin-orbit coupling (SOC) and the breaking of inversion symmetry. Hence, THE induced by skyrmions has been first observed in non-centrosymmetric B20 compounds such as MnSi, MnGe, and FeGe. [7][8][9][10] THE due to the existence of topological spin arrangement can also be generated in oxides such as double-exchange ferromagnets and frustrated magnets with pyrochlore structure. [11,12] Recently, an interface-driven THE was discovered in SrRuO3-SrIrO3 bilayers. [3,13,14] The SrRuO 3 (SRO) layer is ferromagnetic (FM), whereas the top "heavy metal" SrIrO3 layer is paramagnetic and provides strong SOC. Because of the broken inversion symmetry, the interfacial DMI appears to drive the formation of magnetic skyrmions and thus the occurrence of the THE in such ultrathin bilayers. Besides, THE was measured in ultrathin (3-6 nm) SRO layers where the sizeable DMI is induced by the ionic displacement in the SRO oxygen-octahedra near the SrTiO3 substrate. [15] Lattice distortions can also be realized through the ferroelectric proximity effect at the SRO/BaTiO3 interface. [4] In the above-mentioned scenarios, however, a heterostructure system is necessary and the SRO layer thickness is limited to only a few nanometres to show a measurable THE. Is it possible to artificially break the inversion-symmetry and therefore induce THE in a not only single but also thick SRO layer?
In this work, we report that ion irradiation can generate THE in thick SRO layers, hence demonstrating that an interface is not necessary for the appearance of THE. The magnitude of THE closely depends on the irradiation fluence. We attribute the origin of THE to defect engineering by ion irradiation, which breaks the bulk inversion symmetry through altering oxygen octahedral rotation and thus produces DMI in thick SRO films. [16][17][18][19] The crystallographic structures of the SRO films before and after the He ion irradiation were checked by XRD, as shown in Figure 1A. The pristine SRO film is epitaxially grown on the STO (asub = 3.905 Å) substrate. The scan around the (002) reflection for pristine SRO shows a single peak that can be attributed to the orthorhombic (O) bulk-like phase of SRO. The relative intensity of O-like peak decreases after irradiation and its position slightly moves to lower angles with increasing fluence, while a second peak appears and continuously shifts to a lower angle. This second peak can be associated with tetragonal (T) SRO. For both O-and T-peaks, the shift to lower angles can be ascribed to the strain induced by defects that expands the outof-plane lattice parameter. In the region where the strain is large enough, a phase transition from O-to T-phase occurs. [16] The appearance of XRD fringes at lower angles for the highly irradiated sample is due to the gradient distribution of defects shown in Figure 1C, D. This is phenomenon has been observed and explained before, for example, in the study by Boulle and Debelle. [20] The O-T phase transition is also clearly observed in reciprocal space mappings  [16,21] Note that T-SRO and O-SRO all show the same H value as STO, indicating that both phases are still epitaxially locked to the substrate. [22] We can draw the following picture about the structural evolution of the SRO film with He irradiation. The pristine film is of pure orthorhombic structure, as has been reported for films grown on STO substrates. The orthorhombic phase has an aac + oxygen octahedral rotation pattern. [23] Ion irradiation creates an inhomogeneous defect concentration throughout the film as shown in Figure 1C by the stopping and range of ions in matter (SRIM) simulations. [24] The defects induce lattice distortions, most notably a lattice expansion along the perpendicular direction and changes in the oxygen octahedral rotation pattern, as shown in Figure 1D, that lead to a transition to a tetragonal structure with a 0 a 0 c + octahedral rotations above a certain defect concentration threshold. [16] Consequently, the T-SRO part of the film is getting more intense at the expense of the O-SRO phase as a bigger part of the film is transformed with increasing ion fluence. For example, for the 1×10 15 sample the curve for increasing magnetic field at 5 K shows a bump of negative sign between the field strength 0.9 T and 2.4 T. When we sweep along the opposite direction, the dark curve is monotonic in the same field range. Generally, the Hall resistivity is described by where the first, second, and third terms represent the ordinary Hall effect, AHE and THE, respectively. To estimate the contribution of the THE to the Hall resistivity, the first term is already subtracted from the data in Figure 2. We can clearly see that the bump behavior is not attributed to the magnetization (M-H) curve (All the films show typical out-of-plane magnetic hysteresis loops, see Figure S1 in Supporting Information). It should be assigned to the third term THE. In order to understand this behavior more clearly, we present a magnified view of the detailed temperature-dependent Hall resistivity of the 1×10 15 sample in Figure 3A. When the temperature is less than 80 K, the Hall resistivity consists of AHE and an additional THE.
AHE changes its sign at around 90 K, at which THE also vanishes in the Hall resistivity. Similar phenomenon can also be observed for the 2.5×10 15 He/cm 2 sample (see Figure 2). Even for the highest fluence of 5×10 15  Note that the AHE varies non-monotonically with temperature and the irradiation fluence, and even changes its sign. Similar observation was reported for SrRuO3 and Sr1-xCaxRuO3. [25][26][27] A scaling behavior between the transverse conductivity σxy and the magnetization was obtained, which can be well explained by considering the intrinsic origin of the anomalous Hall effect in SrRuO3. [25][26][27] In the Supplementary Materials, we followed the procedure in Refs. 25-27 to calculate σxy. We obtained a qualitative similar scaling behavior as shown in Figure S2.
This also provides strong evidence for the persistence of intrinsic AHE in ion irradiated SRO films.
To precisely investigate the THE, we have extracted it from the Hall resistivity by further subtracting the AHE on basis of field-dependent magnetization data . [28] The procedure is shown in Figure 3B using representative data of the 1×10 15 sample at 60 K. At high fields, the saturation of the Hall resistivity is purely determined by the AHE and the saturation of the magnetization. The residual THE in Figure 3B displays sharp extrema at μ0H = ±0.16 T. This indicates that a topological spin structure with scalar spin chirality is introduced in the ferromagnetic SRO matrix near this magnetic field. Similar THE behavior has been reported in bulk and interfacial magnetic skyrmion systems. [3,[7][8][9][10] In the following, to see the global feature of , we present a contour map of the derived as function of both T and H, as shown in Figure 3C for the 1×10 15 sample. Obviously, the THE is stabilized over a broad region in the T-H plane, persisting from 5 K to 80 K. Moreover, the sharp maximum in THE shows a change of sign from negative to positive with increasing temperature, which is in agreement with previous studies. [8,10] The sign of THE is considered to have close relation with the spin polarization of charge carriers that is very sensitive to the position of Fermi level. [10] Therefore, a small change in the band structure due to the strain or temperature variation may influence the spin polarization, and then invert the sign of THE.
Besides, the fact that the peak position of (HP) is close to the coercive field (HC) suggests again that the THE is driven by topologically nontrivial magnetic structures.
We note that previous studies have reported the emergence of the THE in ultra-thin SRO films, originating from the enhanced DMI and the reduced ferromagnetism at the oxide interface to another layer or the substrate. [2][3][4]13] In our system, however, it is the first time that THE is artificially created in single and thick SRO films without the need of an interface. The sample with a lower fluence (1×10 15 He/cm 2 ) shows robust THE in the wide temperature range from 5 K to 80 K, whereas for the SRO film irradiated with the highest fluence (5×10 15 He/cm 2 ), the THE becomes very weak. This phenomenon is different with a previous study that the superposition of the Hall signals from two phases can result in similar Hall resistance. [29] In the case of the superposition of the Hall signals from two phases, the abnormal feature in the Hall resistance is more pronounced in a particular intermediate temperature range, indeed not in the low temperature range. In our case, we have the effect more pronounced at lowest measured temperature and decreased with increasing temperature. Therefore, we propose that the observed THE in our system can be attributed to inversion symmetry breaking due to defect engineering by ion irradiation. On the one hand, the created defects expand the out-of-plane lattice constant, which leads to O-to T-SRO phase transition that is accompanied by a change of the oxygen octahedral rotation pattern. [16] This change of oxygen octahedral rotations at the O-T phase boundary naturally breaks the inversion symmetry, as illustrated in Figure 1D. The situation can be compared with earlier studies on ultrathin SRO films where the shift in the octahedral rotation pattern are induced at oxide interfaces. [30] On the other hand, there is a gradient in the density of defects and therefore also in the strain distribution along the depth (see Figure 1C). [23,31] Thus, the local structural distortion associated with the gradient strain profile can also lead to the inversion symmetry breaking. [4,19,32] In the study by Wang et al. [4] , the authors have calculated the DMI constant by density functional theory. A sizeable DMI emerges as the lattice is distorted due to the ferroelectric polarization from the interface between BaTiO3 and SRO thin films. The DMI constant increases with the ionic displacement between O and Ru along the [001] axis and reaches a maximum when the displacement is 0.15 Å. [4] In our case, ion irradiation induced effects result in an ionic displacement, probably with a broad range, although we cannot quantify it with the current data. One can expect also sizeable DMI in the irradiated SRO films, leading to the formation of nontrivial magnetic structures, which in turn is responsible for the observed THE in the transport. At the highest fluence, the decrease of the THE suggests the decrease in DMI probably due to the further increase of the ionic displacement or the dramatic lattice damage in the film caused by ion irradiation.
In summary, our results demonstrate the presence of THE in a single-thick SRO layer by He ion irradiation. We attribute these observations to the emergence of DMI as a result of artificial inversion symmetry breaking associated to the lattice defect engineering. The possibility to design defects and strain profiles ex situ by ion irradiation provides a new path to explore and control the THE in complex transition metal oxides. Moreover, ion irradiation has been well developed for semiconductor-chip technology. It allows for a lateral pattern down to the nanometre scale by lithography and builds a natural link between nontrivial magnetic spintronics and microelectronics.
The phase purity, crystal structure and epitaxial quality were examined by X-ray diffraction (XRD) scan and reciprocal space mapping (RSM) analysis (PANalytical X'Pert PRO diffractometer) using Cu Kα radiation. Transport properties were measured using Van der Pauw geometry with a magnetic field applied perpendicular to the film plane in a Lake Shore Hall measurement system. The magnetization data was collected by a superconducting quantum interference device (Quantum Design, SQUID-VSM) magnetometer.

Anomalous Hall effect in SrRuO3
Fang et al. [1] and Mathieu et al. [2,3] have investigated the anomalous Hall effect in SrRuO3 and Sr1-xCaxRuO3. They observed the Hall resistivity (ρH) varies non-monotonously with temperature and even changes its sign. There is a scaling behavior between the transverse conductivity σxy and the magnetization. This can be well explained by their first-principles band calculation by considering the intrinsic origin of the anomalous Hall effect in SrRuO3. By following the calculation procedure in refs. [2,3], we calculated transverse conductivity σxy.
The magnetization was measured for different samples measured at different temperature as shown in Fig. S1. The scaling between σxy and magnetization is shown in Fig. S2.    Figure S1.