Origin of Topological Hall‐Like Feature in Epitaxial SrRuO3 Thin Films

The discovery of topological Hall effect (THE) has important implications for next‐generation high‐density nonvolatile memories, energy‐efficient nanoelectronics, and spintronic devices. Both real‐space topological spin configurations and two anomalous Hall effects (AHE) with opposite polarity due to two magnetic phases have been proposed for THE‐like feature in SrRuO3 (SRO) films. In this work, SRO thin films with and without THE‐like features are systematically Investigated to decipher the origin of the THE feature. Magnetic measurement reveals the coexistence of two magnetic phases of different coercivity (Hc) in both the films, but the hump feature cannot be explained by the two channel AHE model based on these two magnetic phases. In fact, the AHE is mainly governed by the magnetic phase with higher Hc. A diffusive Berry phase transition model is proposed to explain the THE feature. The coexistence of two Berry phases with opposite signs over a narrow temperature range in the high Hc magnetic phase can explain the THE like feature. Such a coexistence of two Berry phases is due to the strong local structural tilt and microstructure variation in the thinner films. This work provides an insight between structure/micro structure and THE like features in SRO epitaxial thin films.


Introduction
Noncolinear and noncoplanar spin textures such as domain walls, vortex, bubble, meron, and skyrmion have drawn great attention due to their promising applications in next-generation highdensity nonvolatile memories, energyefficient nanoelectronics, and spintronic devices. Furthermore, such features can also offer opportunities to investigate nontrivial topological physics. [1] One of the major reasons behind non-trivial spin configuration is often attributed to the Dzyaloshinskii-Moriya interaction (DMI), observed in the presence of strong spinorbit coupling and broken inversion symmetry. [2][3][4] Such DMI-driven nontrivial spin textures with nonzero scalar spin chirality χ ijk = S i · (S j × S k ) gain a quantum mechanical Berry phase and give rise to a fictitious magnetic field in real space. When electrons in motion interact with chiral spin texture (e.g., skyrmion), they The discovery of topological Hall effect (THE) has important implications for next-generation high-density nonvolatile memories, energy-efficient nanoelectronics, and spintronic devices. Both real-space topological spin configurations and two anomalous Hall effects (AHE) with opposite polarity due to two magnetic phases have been proposed for THE-like feature in SrRuO 3 (SRO) films. In this work, SRO thin films with and without THE-like features are systematically Investigated to decipher the origin of the THE feature. Magnetic measurement reveals the coexistence of two magnetic phases of different coercivity (H c ) in both the films, but the hump feature cannot be explained by the two channel AHE model based on these two magnetic phases. In fact, the AHE is mainly governed by the magnetic phase with higher H c . A diffusive Berry phase transition model is proposed to explain the THE feature. The coexistence of two Berry phases with opposite signs over a narrow temperature range in the high Hc magnetic phase can explain the THE like feature. Such a coexistence of two Berry phases is due to the strong local structural tilt and microstructure variation in the thinner films. This work provides an insight between structure/micro structure and THE like features in SRO epitaxial thin films.
experience an additional transverse scattering due to the fictitious field. As a result, a new kind of Hall effect is observed, termed as topological Hall effect. [5][6][7] The Hall resistivity in the presence of skyrmion in a magnetic material exhibits a hump/ dip feature in addition to the ordinary Hall effect (OHE) and anomalous Hall effect. SrRuO 3 (SRO) is a 4d ferromagnet (FM) with multiple Weyl nodes at the Fermi level. [8] Such Weyl nodes, due to the entanglement of conduction and valence band, act as monopoles in the momentum space with a fixed chirality and can be a source (+ chirality) or sink (-chirality) of Berry curvature. [9] Therefore, SRO is one of the rare materials in which intrinsic AHE originates from the Berry curvature. [10] The temperature dependence of anomalous Hall resistivity does not precisely follow the magnetization behavior and can become zero at certain temperatures, even at nonzero magnetization. [11,12] Nonvanishing momentum space and real space Berry curvature can coexist in a correlated topological system. [13] In recent years, such intriguing phenomena have made THE in SrRuO 3 the subject of intensive study. The formation of skyrmions was inferred as the reason behind the observed Hall anomaly. [3,7,[14][15][16] Although, the existence of skyrmions or other nontrivial spin textures in SRO has been observed before, [17] the explanation of Hall anomaly based on two AHEs with opposite signs resulted from two magnetic phases makes the subject matter debatable. [18] It has been proposed that two distinct magnetic phases having different saturation magnetization and coercivity are the reason behind the two AHEs. [10,19,20] For the two channel AHE model, it is believed that two distinct magnetic phases arise from a range of variables such as thickness variation, [13,19] intrinsic and extrinsic mechanisms, [21] strain relaxation-induced defects, [22] and stoichiometric deviation. [23] These factors are often encountered by experimentalists due to changes in processing conditions. For example, surface roughness within one to two nanometers is possible. Strain relaxation beyond a certain film thickness is also a common phenomenon. Interestingly, the temperature ranges for the hump/dip feature seems connected with film thickness. Qin et al. observed the hump feature between 40 to 60 K in SRO thin films having a thickness between 3 to 10 nm. [14] Gu et al. reported the existence of hump features in films with thickness less than 10 unit cells. [24] Although the temperature range for THE feature is widely scattered as reported in the literature, [3,15,19,23,[25][26][27] thinner films in general exhibit hump features in a wider temperature range. It seems that thicker films are often free of hump feature. It is likely that the higher density structural defects in thinner films is tied to the hump feature.
To investigate the origin of the hump-like feature in SRO films, we have explored relatively thick (>25-unit cells) SRO films with different degrees of structural defects. The thinner 14 nm SRO film with larger lattice tilt shows clear hump features, while the 24 nm SRO film with less lattice tilt shows no sign of hump features. Comparing samples with and without hump features should give critical information regarding the origin of the hump feature. By systematically investigating their Hall transport, magnetoresistance (MR), and magnetism, two distinct magnetic phases are identified. However, the hump feature cannot be explained by the two channel AHE model based on these two magnetic phases. In fact, AHE is dominated by one particular phase, i.e., the magnetic phase with higher H c . AHE sign change was observed in both samples, near 110 K. The hump feature emerges near the AHE sign change temperature region, only in the 14 nm sample. Therefore, we propose two channels arise from the coexistence of two Berry phases with opposite polarity in a heavily modified magnetic phase due to structural defects induced competing magnetic interactions in the system. Figure 1a shows the X-ray θ-2θ local scan of two SRO/STO heterostructures. The appearance of only (00l) reflections indicates the formation of preferentially oriented single-phase SRO films (shown in Figure S1, Supporting Information). Laue fringes shown in both films indicate a sharp interface between the substrate and the film. The film thickness was calculated from diffraction fringes and found to be ≈14 and ≈24 nm, respectively. These two samples have been labelled as S14 and S24, respectively. The calculated out-of-plane lattice parameters were 3.944 Å (S14) and 3.935 Å (S24), respectively. Reciprocal space maps (RSM) near STO (103) reflection, as shown in Figure 1b, suggest a pure pseudo-cubic SRO grew epitaxially on STO (001) substrate for both samples. The similar q x for the films and the substrate indicates SRO films are strained to the STO substrate. Figure 1c,d show the cross sectional TEM images for these two SRO films on STO substrates, which confirms a sharp SRO/STO interface. In addition, the thickness variation is confirmed by TEM. For example, S14 shows island growth with periodic mesa-like morphology of a higher thickness (region A) and plateaus with a lower thickness (region B), as shown in the low magnification TEM image (Figure 1d). The thinner region is ≈2 nm, and the thicker region is ≈14 nm. However, the S24 showed much less thickness variation. The thicker region is ≈31 nm and the thinner region is ≈23 nm (Figure 1c). It was reported that the growth rate of SRO film strongly depends on the surface termination of STO substrate. [28] On the SrOterminated surface, SRO grows much more slowly than on the TiO 2 -terminated surface. On STO substrates with mixed SrO and TiO 2 terminations, a thinner layer is expected to exhibit a large thickness variation, while a relatively thicker film is expected to reveal a much smaller thickness variation. The stoichiometry of both films was obtained by fitting the RBS data ( Figure S4, Supporting Information). The Sr:Ru ratios for S14 and S24 are 1:0.75 and 1:0.85, respectively. It has been reported that Ru vacancy is necessary for the observation of hump-like  [23] We can see, our RBS data indicates certain amount of Ru vacancy is present in both the samples.

Results and Discussion
We have performed Hall measurements on these two SRO films in the temperature range from 10 to 120 K. The experimental Hall resistivity data have been anti-symmetrized using ρ xy = [ρ xy (H+) − ρ xy (H-)]/2 to avoid any magnetoresistance contribution. The total Hall resistivity in the absence of THE can be described as the sum of ordinary Hall resistivity (ρ OHE ) and anomalous Hall resistivity ρ AHE , where ρ AHE of a ferromagnet typically mimics the magnetic hysteresis and can be expressed as, where R 0 is the ordinary Hall coefficient that mainly depends on the majority charge carrier density, H Z is the applied external magnetic field perpendicular to the sample plane, R A denotes the AHE coefficient, and M Z is the magnetization along the magnetic field direction. Figure 2a,b show magnetic field-dependent Hall resistivity measured for both samples at temperatures ranging from 10 to 120 K (all the temperatures are shown in Figure S2, Supporting Information). Both films exhibit hysteresis in the Hall resistivity. We extracted the anomalous Hall resistivity by subtracting the ordinary Hall contribution from the total Hall resistivity at different temperatures. The polarity of AHE is defined by the sign of R A at a certain field direction. The ρ AHE as a function  Magnetic field-dependent Hall resistivity of SRO film for a) S14 and b) S24. c) Change in anomalous Hall resistivity with temperature describing the polarity change in Hall resistivity near 110 K for both the samples d) scaling relation between σ AHE xy versus σ xx for S14 and S24 suggests intrinsic scattering is dominant.

www.advelectronicmat.de
of temperature is shown in Figure 2c, where it decreases with increasing temperature initially but beyond a certain temperature it starts increasing and changes sign from negative to positive ≈110 K for both S14 and S24, respectively. The temperature of polarity change matches well with previous reports. [10,23,29,30] Interestingly, the Hall resistivity of S14 showed hump-like features at 100 and 110 K. It is noted that the rotation direction of Hall hysteresis changed around these temperatures. However, such a hump-like feature was absent for S24 even though a similar change in the sign and rotation sequence of AHE was present. The hump-like feature was previously described as i) THE in the presence of non-collinear/noncoplanar spin texture (e.g., skyrmion) or ii) as a sum of two anomalous Hall effects with opposite polarity. In single-phase SRO films, such a hump-like feature was often reported in ultrathin SRO films in the range of a 4-10 uc thickness. In some cases, even below 10 nm film has shown THE feature over the different temperature ranges. However, the hump-like feature was observed within a narrow temperature range in our relatively thick SRO film (14 nm).
To understand the origin of THE like feature in S14, we investigated the scaling relation of σ AHE xy versus σ xx , temperature-dependent MR, and magnetic property of both samples.
The scaling relation between σ AHE xy and σ xx can reveal the underlying scattering mechanism behind the AHE. In general, three proposed scattering mechanisms are considered in the literature to explain the AHE: i) an intrinsic mechanism, where the band structure of the ferromagnet provides an effective magnetic flux (momentum space Berry phase); ii) extrinsic (skew scattering), which is impurity driven asymmetric electron scattering due to spin-orbit coupling; and iii) extrinsic side jump. [12] The characteristic scaling behavior of the anomalous Hall conductivity (σ AHE xy = ρ AHE xy /(ρ xx 2 + ρ AHE xy 2 )) with longitudinal conductivity (σ xx = ρ xx /(ρ xx 2 + ρ AHE xy 2 )), which depends on the relative strength of the scattering rate h/τ (h, Planck's constant and τ, transport lifetime) with respect to the Fermi energy E f, can provide in-depth information about the AHE behavior in our samples. [31][32][33][34] When the scattering rate h/τ ≥ E f (dirty region), σ AHE xy exhibits a power law dependence on σ xx (σ AHE xy ∞ σ xx n ), whereas for h/τ ≤ E f (moderately dirty region), σ AHE xy is intrinsic in nature and is independent of σ xx (n = 0). In the super clean regime (h/τ << E f ) , where σ xx is very high, σ AHE xy is linearly dependent on σ xx (skew scattering, n = 1). [35][36][37] It is important to mention that all these scaling relations are obeyed in logarithmic scale. We have investigated the σ AHE xy versus σ xx for both samples and the results are shown in Figure 2d. Both SRO films have longitudinal conductivity in the range of ≈10 4 Ω −1 cm −1 and anomalous Hall conductivity in the range of 10 3 Ω −1 cm −1 , indicating both films are moderately in the dirty region. [35][36][37] In moderately dirty region, the intrinsic scattering is said to be the governing mechanism for anomalous Hall effect and ideally anomalous Hall conductivity is not affected by longitudinal conductivity in this region. Our σ AHE xy for both S14 and S24 has marginal change with σ xx indicating that AHE in our samples is mostly intrinsic in nature. The relative intrinsic nature between S14 and S24 has been compared by calculating the ratio r = [σ AHE xy (10 K) -σ AHE xy (120 K)]/[ σ xx (10 K) -σ xx (120 K)]. The ratio r = 0.009 for S14 as compared to r = 0.017 for S24 indicates AHE for S14 has more intrinsic contribution than S24, i.e., more Berry phase driven.
It is often reported that the hump feature can be induced by the inhomogeneity of magnetic phases and/or skyrmions in single-phase SRO films. Previous studies have reported the two-phase nature of SRO with magnetic force microscopy (MFM). [3,16,19] Meng et al. [3] and Wang et al. [16] have shown the magnetic inhomogeneity as skyrmions, but Kimbell et al. [19] have found two magnetic regions spatially separated with opposite AHE polarity and different temperature dependence as the reason behind the Hall anomaly. Recent investigations on the hump feature emphasize this two-channel AHE mechanism. [10,19,21,38,39] Since two-phase nature of SRO is responsible for two AHE with opposite polarity, to have a better understanding of these two phases, we explore the magnetic property of both samples.
To investigate the correlation between AHE and magnetism, we measured the magnetic field-dependent magnetization (M-H), temperature-dependent magnetization (M-T), and temperature-dependent resistivity (ρ-T) of these two samples.  Figure S3, Supporting Information). The films exhibit two characteristic jumps in magnetization (as shown in the inset of Figure 3a for 10 K), suggesting two magnetic phases with different coercivities (H c ) are present, as previously reported. [40][41][42][43] The extracted H c of these two phases from dM/dH versus H curve for S14 and S24 are shown in Figure 3b,d, respectively. The larger and smaller coercivities have been denoted as H c1 and H c2 , respectively, in the inset of Figure 3b. Based on the M-H measurements, we define the phase with a larger H c as P1 phase, where a rapid decrease in H c was observed with increasing Figure 3. a) Out-of-plane M-H loops at 80, 100, and 120 K for S14, and b) corresponding field derivative dM/dH versus H. c) Out-of-plane M-H loops for S24 at 80, 100, and 120 K and d) corresponding dM/dH versus H. Right inset of b) shows the presence of two magnetic phases in sample S14 with coercivities H c1 and H c2 , respectively. www.advelectronicmat.de temperature. The phase with a smaller H c is defined as the P2 phase, where H c slowly decreases with increasing temperature.
The P1 phase in S14 shows a much higher H c (6.1 kOe) than that of the S24 sample (2.2 kOe), indicating the P1 phase in S14 is more difficult to magnetize and demagnetize as compared to the S24. It is important to point out the key difference observed in the magnetic measurement of these two samples is following. The magnetic state at 100, 110, and 120 K of S14 is not detectable from the high coercivity phase (P1) whereas 24 nm film still has it. Interestingly, the hump feature in S14 appeared at 100 and 110 K (Figure 2a), where magnetic measurement suggests the film has one coercivity. The field-cooled M versus T and residual resistivity ratio (RRR) obtained from ρ versus T plot are shown in Figure S5a,b (Supporting Information), respectively. The M-T plot exhibits conventional paramagnetic to ferromagnetic transition upon cooling for both films. The T C obtained from dM/dT versus T and dρ/dT versus T curves for S14 and S24 are ≈130 and ≈145 K, respectively. The RRR was found to be higher for S24 than the S14, indicating lower density of structural defects in the sample S24.
Our X-ray diffraction and TEM results suggest that there are obvious structural differences between the 14 and 24 nm films. This implies that the magnetization and AHE might closely relate to interfacial effect, thickness variation, and/or lattice distortion. In this scenario, it is not surprising that the hump feature in the ultrathin film is greatly enhanced and exists in a much wider temperature range since the interfacial effect and structural defects are greatly enhanced in thinner films. [14,25,44] Therefore, to figure out the effect of structural defects on magnetic and magnetotransport properties, we further investigated the microstructure and local strain/tilt of SRO films by atomic force microscopy (AFM) and X-ray nanodiffraction, respectively. AFM images shown in Figure S6 (Supporting Information) clearly illustrate a marked difference in morphology between the two films. The thinner film has nanoscale pits ( Figure S6a, Supporting Information). [28,45] This is consistent with the TEM results shown in Figure 1d, and such a microstructure is due to mixed terminations on STO substrates. The dark contrast in the AFM image indicates a thickness of ≈2 nm, while the light contrast represents a thickness of ≈14 nm (the majority of the film).
Whereas the 24 nm film is quite uniform with negligible pits in the scanned region ( Figure S6b, Supporting Information). Figure 4a,b show respectively the calculated lattice tilt and integrated intensity for the S14 and S24 obtained from X-ray nanodiffraction. [46] The lattice tilt was marked by arrows, where the feature size is linearly proportional to the magnitude of the tilt. A downward pointing arrow indicates the lattice tilting in the YZ plane toward the negative Y direction, while a rightpointing arrow indicates the lattice tilting in the XZ plane toward the positive X direction. The actual lattice tilt is often a combination of both. For information on the extraction of the lattice tilt, the reader is referred to the supplementary Figure S7 (Supporting Information). The integrated diffraction intensity on logarithmic scale is also shown. A darker contrast indicates a lower integrated intensity which is caused by voids in the SRO film as verified by AFM measurements. At areas where film thickness varies significantly, the lattice is tilted as a means to relax the epitaxial strain. For the S14 sample, the surface is rough with a high density of tilted lattice at the edge of the small domains. Whereas, for the S24, the surface is relatively flat. Its domain size is larger with a lower density of lattice tilt. The higher concentration of lattice tilt in the S14 degrades the local crystallinity, which explains why the thinner sample in this case has a broadened reciprocal lattice point, as observed in benchtop XRD measurements.
The microstructural difference between S14 and S24 hints that a higher defect density in S14 might be a reason for magnetic domain pinning, as reported in references. [47][48][49][50][51][52][53] Therefore, the coercivity of P1 phase in S14 is ≈3 times higher than that in S24, whereas, the coercivity of P2 phase is similar in magnitude for both samples.
It is well accepted that the peak in longitudinal MR appears at the magnetic coercivity due to its relation with magnetization reversal. The anomalous Hall effect is also related to the magnetization of the material. To decipher the underlying mechanism behind the hump feature, we compared these three properties and their characteristic fields in the whole measurement temperature range. It will be interesting to notice that the hump feature is not observed in the Hall resistivity when M-H measurements reveal two magnetic phases (i.e., P1 and P2). Therefore, the presence of two magnetic phases (i.e., P1 www.advelectronicmat.de and P2) in our SRO films might not have a direct correlation to THE like feature. In fact, only S14 shows THE like feature in a narrow temperature range. We further fitted the Hall data by treating coercivity as a variable to see which phase is responsible for the transport. We found that one hysteresis can describe the AHE in the whole temperature range except at 100 and 110 K (see Figure 5) for S14. For example, Figure 5a shows AHE at 80 K can be fitted by one hysteresis (not shown for the lower temperature results). We used the two AHE model to fit the data at 100 and 110 K to inquire about the magnetic counterparts of these two AHEs. [19] Indeed, the two AHE model with opposite polarity can fit the Hall resistivity to give rise to the hump feature, as shown in Figure 5b,c. The AHE at 120 K is also fitted by using one hysteresis, as shown in Figure 5d. For S24, the AHE in the whole temperature range can be fitted by one hysteresis. A close relationship between the magnetic phase, MR and Hall resistivity exists in S14, except 100 and 110 K (Figure 5a,d). The fitting results for S14 and S24 are summarized in Figure 6. The H c from Hall resistivity is shown in solid red circles. The H c from M-H loops for P1 (the magnetic phase with relatively larger coercivity) and P2 (the magnetic phase with relatively smaller coercivity) are shown in solid and open squares, respectively. Figure 6 shows that the H c of Hall resistivity in general follows the H c of P1, which is consistent with SRO/SrIrO 3 superlattices. [20] This result indicates that the Hall resistivity is primarily dominated by the magnetic phase with higher coercivity (P1 phase) at low temperatures for S14 and at the whole temperature range for S24. It is likely that the low coercivity phase (P2) is relatively insulating in nature and therefore its contribution is limited in the Hall resistivity. Otherwise, the AHE from low coercivity phase would have given rise to step feature (when the polarity is same) or hump feature (when the polarity is opposite) in the experimental AHE. Figure 6a shows the fitted Hall resistivity (at temperatures of 100 to 110 K) by two hysteresises with opposite signs and the obtained coercivities of +ve and -ve AHEs are shown by halfred solid circles with blue and green lines (fittings are shown in Figure 5b,c). However, M-H measurements failed to reveal the fitted two coercivities obtained by the two channel AHE model. Also, the fitted two coercivities at these two temperatures do not match exactly with either P1 or P2. This concludes that the hump feature cannot be explained by the two channel AHE model based on these two observed magnetic phases. We hypothesize that the hump feature might not be induced by two distinct magnetic phases, rather by two Berry phases. These two Berry phases are present in the high coercivity phase and local structural tilt, microstructural variation and temperature dependent spin interaction between two magnetic phases have a significant role in Berry phase transition.
We therefore propose a diffusive Berry phase transition model to explain the hump feature. Both S14 and S24 samples show AHE sign change with changing temperatures and therefore, there are two Berry phases (B1 and B2) with opposite signs. Around 110 K, Berry phase B1 changes from negative to B2 (positive). This kind of sign change in AHE due to change in Berry phase is well accepted. We assume only the B1 is responsible for -ve AHE at low temperatures, whereas B2 phase is responsible for +ve AHE beyond 110 K for both S14 and S24. The difference in S14 and S24 lies in the nature of transition from B1 phase to B2 phase. A schematic view of berry phase transition is shown in Figure 7, where the transition is sharp in case of S24 and the transition is diffusive for the S14. When these B1 and B2 Berry phases coexist, THE like feature will arise in the system between T 1 and T 2 temperature  www.advelectronicmat.de (as observed in case of S14 between 100 and 110 K). We argue that such a diffusive Berry phase transition should be related to the higher density of structural defects such as lattice tilts, thickness variation, and magnetic interaction in S14. If such a coexistence never takes place, AHE will only change the sign at temperature T s without any hump feature (as observed in S24).
It is also reported that oxygen vacancy and irradiation induced defects in SRO gives rise to DMI as a results of inversion symmetry breaking. [15,24,54] The resultant DMI can stabilize skyrmion like nontrivial spin texture that give rise to real space Berry phase and THE like feature in SRO. Therefore, we identify our result in 14 nm sample as a possible combination of two Berry phases and these two Berry phases, both can be in momentum space or in momentum space and real space respectively. The spin interaction between present two magnetic phases is the possible reason behind the emergence of real space Berry phase.

Conclusion
In conclusion, we have compared the Hall resistivity, MR and magnetic property of epitaxial SRO thin films deposited under similar growth conditions with two different thicknesses (≈14 and 24 nm). The thinner sample with a larger local thickness variation and structural tilt/strain shows a THE feature in Hall resistivity in a narrow temperature range. The thicker sample with a much smoother surface and less structural tilt does not show THE feature in the Hall resistivity. Both samples show two magnetic phases and clear AHE sign change ≈110 K. The comparison of coercivities obtained from the anomalous Hall resistivity and magnetic measurement suggests that the high coercivity phase primarily dominates the AHE in SRO films. The THE feature cannot be explained by the conventional two channel AHE model based on these two magnetic phases. We proposed a diffusive Berry phase transition model to explain the hump feature. Such a diffusive Berry phase transition is linked to higher density of structural defects. Our work provides a possible relationship between structure/microstructure and THE like feature in SrRuO 3 epitaxial thin films.

Experimental Section
Epitaxial SRO thin films with a thickness of 14 nm and 24 nm were grown on (001) SrTiO 3 (STO) substrates by pulsed laser deposition (PLD) with a KrF excimer laser (λ = 248 nm). The as-received STO substrates were annealed at 1000 °C for 2 h in the air before the growth of SRO by PLD. The base pressure of the chamber was ≈1 × 10 −7 Torr. The processing parameters to achieve bulk-like ferromagnetic SRO properties were initially optimized and maintained at a growth temperature of 700 °C, an oxygen pressure of 100 mTorr, a frequency of 2 Hz, and a 1-2 J cm −2 laser fluence. The substrate-target distance was 8 cm. To get uniform laser fluence, an imaged rectangle laser beam was focused onto the target. [55] The samples were cooled at the rate of 10 °C min −1 after the deposition, where the chamber was filled with 200 Torr oxygen at 450 °C during the cooling process. The structural properties of all the films were characterized using a Panalytical X'pert PRO X-ray diffractometer with Cu Kα radiation. The microstructure was also characterized by TEM (FEI Tecnai F30 analytical TEM operating at 300 kV), where the cross-sectional TEM samples were prepared by a standard manual grinding and thinning procedure followed by a final ion-polishing step (Gatan PIPS II precision ion polishing system). The surface morphology of the films was investigated by Bruker Dimension Icon AFM, where a ScanAsyst-Air tip with a tip height of 2.5 to 8.0 µm and a tip nominal radius of 20 nm was used. The stoichiometry of samples was investigated by Rutherford Backscattering Spectroscopy (RBS). Further surface and structure characterization was performed by atomic force microscopy (AFM) and X-ray nanodiffraction microscopy at the 26-ID-C endstation of the Advanced Photon Source, Argonne National Laboratory. Magnetic and magneto-transport properties were investigated using the vibrating sample magnetometer (VSM) and DC resistance setup in Physical Property Measurement System (Quantum Design). Before the Hall measurement, the samples were wired in five-probe geometry using indium metal, where the longitudinal direction measures the normal resistance and the transverse direction measures the Hall resistance. The Hall measurement has been carried out between −4 to 4 T magnetic field. The sample had been warmed up to 200 K (above the T c of SRO) after each measurement to avoid any remnant magnetization in the film. The out-of-plane M-H measurements were carried out at different temperatures within a field range from −3 to 3 T. The M -T data were collected at 100 Oe while warming the samples from 10 to 200 K under field-cooled conditions.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.