Introduction

Profound implications for the electric field control of spin states have been revealed through magneto-transport properties arising from the spin-orbit coupling (SOC)1. Such properties have been attracting great interest as foundations for high-density and low-power-consumption spintronic devices because the properties coupled to the spin states enable spin manipulation without magnetic field variation or large current injection. Among the magneto-transport processes, of interest here is the intrinsic anomalous Hall effect2 (AHE), which is related to magnetization (M) in Hall resistivity (ρAHE = RSM). In some itinerant ferromagnets such as SrRuO33, 4, the proportionality factor (RS) is governed by k-space monopoles, i.e., singularities originating from band-crossings gapped by SOC; not M but RS is potentially tuneable by electric field there. Another intriguing example is the topological Hall effect (THE) originating from scalar spin chirality concomitant with non-coplanar spin structures such as in a frustrated pyrochlore magnet5 and in metallic magnets characterized by a non-zero skyrmion number (Nsk)6,7,8,9. In the case of Nsk = 1, the topologically protected spin swirling texture is called magnetic skyrmion6, 10, 11. Despite mounting interest in electrical control of these Hall effects, however, their control in itinerant magnets has been elusive in conventional field-effect structures, that is, magnetic materials adjacent to gate dielectrics. Recent discovery of the THE in an oxide heterostructure composed of SrRuO3 and SrIrO312 brings an opportunity to develop electrical control because the strong SOC in SrIrO313 induces a SOC-related phenomenon in neighboring ferromagnetic SrRuO3. In addition to the intrinsic AHE inherent to SrRuO33, the combination of the strong SOC and the broken inversion symmetry gives rise to substantial Dzyaloshinskii–Moriya interaction (DMI)6, 14 and the concomitant THE; the underlying spin texture has been deduced to be the interface-driven skyrmion12. In view of the fact that ultrathin films of itinerant magnets have been a playground for electrical manipulation of spin states1, 15,16,17,18,19, an electric field applied to the ultrathin heterostructure may provoke effective manipulation of the spin state contending with screening effects by itinerant electrons of SrRuO3. Furthermore, we can expect that the strong SOC in SrIrO3 plays a positive role at the interface as well because both AHE and THE are magneto-transport phenomena driven by SOC.

Here, we show the clear modulation of both AHE and THE by an electric field in the heterostructure of SrRuO3/SrIrO3/SrTiO3 from magneto-transport and magneto-optic Kerr effect (MOKE) measurements. The electrical modulation is effective only when SrIrO3 is inserted between SrRuO3 and a gate dielectric, i.e., SrTiO3. This indicates the essential role of the strong SOC in nonmagnetic materials for the electrical tuning of these Hall effects and possibly other SOC-related phenomena.

Results

Stacking-order dependent electric field control

Five-unit-cell SrRuO3 thin films were epitaxially grown on SrTiO3(001) substrates by pulsed laser deposition in three stacking orders with SrIrO3 (see Methods): a single layer of SrRuO3 (SRO5/Sub), a bilayer of SrRuO3 and 2-unit-cell SrIrO3 (SIO2/SRO5/Sub), and that with the inverted deposition order (SRO5/SIO2/Sub, Fig. 1a). We first take a look at basic transport and magnetic properties before we go into the Hall effects under an applied electric field (Fig. 1b). In Fig. 1c, d, we show the temperature dependence of longitudinal resistivity (ρ xx ) and magnetization perpendicular to the film plane in the three samples. All of them show metallic conduction and ferromagnetic magnetization whose Curie temperatures (TC) are lower than the bulk value (160 K)3. These transport and magnetic properties are consistent with previously reported ultrathin SrRuO3 films20. Figure 1e shows anomalous Hall conductivity (σΑΗΕ) as a function of magnetization with temperature as a control parameter. The σAHE of the three samples behave the same way; when the magnetization gets larger, the sign of σAHE is inverted from positive to negative. This sign inversion is consistent with the previous experiments4, 12, manifesting the above-mentioned band anti-crossing singularities of SrRuO3. Conversely, such temperature dependence in AHE implies the potential for electrical control of AHE through the modification of the SOC-induced band.

Fig. 1
figure 1

Structure and basic physical properties of samples. a Schematics of the SrRuO3-SrIrO3 bilayer film, where SrIrO3 is inserted between SrRuO3 and SrTiO3 substrate (SROm/SIO2/Sub, m = 3–5 unit cells). Green, orange, purple, beige, and gray atoms represent Sr, Ru, Ir, Ti, and O, respectively, in the crystal structure, which is drawn using VESTA38. b Schematics of the magneto-transport properties observed in SROm/SIO2/Sub under the application of a gate electric field (E): Anomalous Hall effect (AHE) generated by magnetization (M) and topological Hall effect (THE) driven by fictitious magnetic field (beff) in the case of skyrmion formation. White box corresponds to the schematics in a. Temperature (T) dependence of longitudinal resistivity (ρ xx , c) and out-of-plane magnetization measured at 0.1 T (M, d) for SRO5/Sub, SIO2/SRO5/Sub, and SRO5/SIO2/Sub. e Anomalous Hall conductivity (σAHE) as a function of magnetization (M). f–h The sum of anomalous and topological Hall resistivity (ρAHE + ρTHE) at 2 K as a function of external magnetic field (B) under application of gate bias VG = − 180 V (blue lines) and 200 V (red lines). At the lowest temperature (T = 2 K), the largest modulation of carrier density can be realized due to the quantum paraelectric nature of SrTiO3 substrates. On top, respective sample structure is shown. ρAHE + ρTHE is deduced by subtracting a B-linear ordinary Hall component (RHB) from the Hall resistivity (ρ yx ). Black arrows indicate the sweep direction of B

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In contrast to the similarities of the basic transport and magnetic properties among the three samples, a clear difference emerges in electric field effect (see Methods). The sums of anomalous and topological Hall resistivities (ρAHE + ρTHE) under applied electric fields are shown in Figs. 1f–h as a function of external magnetic field (B). The B dependence of ρAHE corresponds to that of magnetization normal to the film plane, whereas ρTHE shows up with the formation of the topological spin texture as exemplified by the peak at around 3 T in Fig. 1h. The sum of these Hall components is obtained by subtracting the B-linear ordinary Hall term (RHB) from the Hall resistivity (ρ yx ). Both in SRO5/Sub (Fig. 1f) and in SIO2/SRO5/Sub (Fig. 1g), ρAHE + ρTHE is almost unchanged by the applied electric field. However, ρAHE + ρTHE is obviously changed in SRO5/SIO2/Sub (Fig. 1h). This striking stacking-order dependence suggests that the electric field to the SrRuO3-SrIrO3 interface causes the noticeable modulation. The thinness of the SrIrO3 layer compared with the SrRuO3 layer contributes to the preferable modulation in SRO5/SIO2/Sub because the interface in SRO5/SIO2/Sub is closer to the gate dielectric than that in SIO2/SRO5/Sub (see Supplementary Figure 1 and Supplementary Note 1). Hereafter, we focus on the control in the SRO5/SIO2/Sub sample.

Electric-field modulation of AHE

In the structure of SRO5/SIO2/Sub, the large electric field modulation gives rise to the sign inversion of AHE without changing temperature. Magnetic-field dependences of ρAHE + ρTHE under different electric fields at 30 K are shown in Fig. 2a–c. Except for the topological Hall term that shows a peak at around 0.8 T, the data are dominated by the anomalous Hall contribution. In particular, we can consider the value at high magnetic field such as 2 T to be totally derived from ρAHE since all the spins are ferromagnetically aligned without forming any topological spin textures. The sign of ρAHE above the saturation field is inverted from negative to positive when the gate voltage is varied from negative (−180 V) to positive (200 V), while ρAHE is close to vanish under zero bias. This sign inversion indicates the sign reversal of the proportionality factor RS because MOKE measurements reveal that only a minor fraction of M, <10% of the magnetization, is electrically modulated (see Supplementary Figure 2 and Supplementary Note 2). Such electrical sign inversion has never been observed in plain films of itinerant magnets including SrRuO3.

Fig. 2
figure 2

Electric-field control of anomalous Hall effect. Magnetic-field (B) dependence of anomalous and topological Hall resistivities (ρAHE + ρTHE, solid lines) at 30 K under gate voltage VG = −180 V (a), 0 V (b), and 200 V (c) for SRO5/SIO2/Sub. Magneto-optic Kerr rotation as a function of B under the same gate bias is also shown by broken lines in each panel. Yellow colored regions correspond to ρTHE. Black arrows indicate the sweep direction of B. d Temperature (T) dependence of ρAHE under VG = −180 V (blue), 0 V (gray) and 200 V (red). The black box corresponds to the data in a–c. e B dependence of ρAHE + ρTHE at 30 K under VG = −180 V (blue), 0 V (gray), and 200 V (red) for SRO5/SIO5/Sub. f T dependence of variation in anomalous Hall resistivity (ΔρAHE) between VG = 200 V and VG = −180 V for SRO5/SIO5/Sub (yellow) and SRO5/SIO2/Sub (green). Error bars include the uncertainty of the sample thickness and of electrical measurement

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As shown in Fig. 2d, the tendency of AHE change is nearly temperature independent; the positive (negative) bias voltage increases (decreases) ρAHE regardless of the sign of AHE. Since singularities in the band structure of SrRuO3 originate from band anti-crossings gapped by SOC, we speculate that the electric field control of AHE is ascribed to the redistribution of the singularities caused by the variation of SOC. The pronounced controllability in SRO5/SIO2/Sub compared with its absence in SIO2/SRO5/Sub suggests that the electric field from SrIrO3 side induces certain modification of SOC in the bilayer even if it has itinerant carrier density as high as 1022 cm−3 in the magnetic SrRuO3 layer. This is in sharp contrast to the case of chemically doped EuTiO321, where carrier-density variation inverts the sign of AHE accompanied by the shift of Fermi energy (EF). The insertion of the SrIrO3 layer makes a more important contribution to the AHE modulation than the EF shift in SrRuO3 does. The controllability may partly rely on the lower carrier density of inserted semimetallic SrIrO3, the order of 1019 cm−3 22.

In order to clarify the effectiveness of the heterointerface close to the gate dielectric, we also fabricate the heterostructure with thicker (5 unit cells) SrIrO3 (SRO5/SIO5/Sub, see Supplementary Figures 3–5 and Supplementary Notes 3 and 4). Figure 2e shows magnetic field dependences of ρAHE + ρTHE under different electric fields at 30 K in SRO5/SIO5/Sub, where the change of ρAHE is apparently suppressed. In Fig. 2f, we compare the variation of ρAHE (ΔρAHE = ρAHE (VG = 200 V)−ρAHE (VG = −180 V)) in SRO5/SIO5/Sub with that in SRO5/SIO2/Sub, where we can clearly see the suppression of the modulation in the thicker SrIrO3 sample within all the measured temperatures. We attribute this suppression to the significant screening of the electric field within the thicker SrIrO3 layer.

Electric-field modulation of THE

THE is also modulated by electric field in the structure of SRO5/SIO2/Sub. In order to evaluate ρTHE from magneto-transport measurement, ρAHE has to be subtracted from ρAHE + ρTHE. Since MOKE is proportional to magnetization as anticipated from its perturbative nature and also as experimentally verified in the previous report12, MOKE under applied electric field can be utilized as the reference of ρAHE, which is also proportional to magnetization at a constant temperature. The magnetic field dependences of Kerr rotation are shown by the broken lines in Fig. 2a–c. Each Kerr rotation is normalized by ρAHE at high magnetic field under each applied electric field; the normalized curves represent the B dependence of ρAHE. By subtracting them from ρAHE + ρTHE, we deduced ρTHE (yellow colored regions in Fig. 2a–c). Figure 3a shows the electric field-controlled peak of ρTHE around B = 0.8 T. The electric field also tunes the range of magnetic field where finite ρTHE appears; when the positive (negative) gate voltage is applied, ρTHE gets smaller (larger) and the magnetic field region gets shrunk (enlarged). The variation in peak of ρTHE (ΔρTHE = ρTHE (VG = 200 V)−ρTHE (VG = −180 V)) normalized by zero-bias value (ΔρTHE/ρTHE (0 V)) is as large as 55%. The sign of THE remains the same during the sign inversion of AHE by electric field, supporting that the origins of AHE and THE are clearly distinct from each other as previously indicated12.

Fig. 3
figure 3

Electric-field control of topological Hall effect. a Topological Hall resistivity (ρTHE) at 30 K as a function of external magnetic field (B) under VG = −180 V (blue line), 0 V (gray line) and 200 V (red line) for SRO5/SIO2/Sub. Black arrows indicate the sweep direction of B. b Temperature (T) dependence of ρTHE under gate bias. Color map of ρTHE in the T-B plane under VG = −180 V (c), 0 V (d) and 200 V (e)

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Assuming the skyrmion formation in this heterostructure, we discuss the relation of this THE modulation with skyrmion length scale. ρTHE is an outgrowth of ordinary Hall effect under fictitious magnetic field (beff) caused by the non-coplanar spin texture of skyrmion6. Since one skyrmion generates one flux quantum (Φ0 = h/e), ρTHE is described as a function of skyrmion density (nsk):

$$\rho _{{\mathrm{THE}}} = PR_{\mathrm{H}}b_{{\mathrm{eff}}} = PR_{\mathrm{H}}n_{{\mathrm{sk}}}\Phi _0$$
(1)

where P is spin polarization of conduction electrons in SrRuO3. Ordinary Hall coefficient RH is inversely proportional to carrier density. The change of P or RH is negligible because EF in SrRuO3 remains almost unchanged judging from the variation of ρ xx as small as the order of 1% as discussed later. Therefore, the modulation of ρTHE indicates the change of nsk. The skyrmion size, estimated by \(r_{{\mathrm{sk}}} \cong 1/\sqrt {n_{{\mathrm{sk}}}}\), is varied from 15 nm (VG = 200 V) to 12 nm (VG = −180 V) adopting P = −9.5% as a typical value of SrRuO323 and RH evaluated from the B-linear component of Hall resistivity under VG = 0 V at 30 K. Since rsk is proportional to the ratio of ferromagnetic interaction J to DMI D, or J/D6, the positive (negative) gate voltage should increase (decrease) J/D. The controlling knob of ρTHE is thought to be D rather than J; the variation of J is negligible because the applied electric field hardly varies TC, which can be evaluated by a kink structure in ρ xx 3 (see Supplementary Figure 6 and Supplementary Note 5). The real-space observation of such electrical control of skyrmion size would be one of the future challenges.

We examine the other possibilities of the underlying spin texture. One of the candidates is the conical spin structure, which is topologically trivial and is reported to give rise to THE-like signal24. In our case, this can be excluded since the spin structure is dominated by conventional ferromagnetic phase with finite anisotropy as exemplified by open hysteresis loops in magnetization (see Supplementary Figure 2). The possibility of non-coplanar spin structures stabilized only under geometrical frustration5, 25 can also be excluded because such frustration is apparently absent in our heterostructure. We then focus on a topological spin texture other than skyrmion e.g., biskyrmion or meron, of which topological number (Nsk) is not unity9, 26, 27. The emergent fictitious magnetic field can thus be generalized as ntopoNskΦ0, where ntopo is the density of the topological spin texture. Since Nsk is constant inherent in the topological spin structures and hence independent of the gate bias, the electric field modulation of ρTHE is attributed to the modulation of ntopo. In order to realize topologically nontrivial spin structures in SrRuO3, the interface-driven DMI is required as discussed in the above-mentioned skyrmion case. The ratio of J/D is inversely correlated with ntopo for any type of topological spin textures. The consequence therefore remains the same; positive (negative) gate voltage should increase (decrease) J/D.

Considering that the variation of DMI is attributed to the modification of SOC at the interface, both modulations of AHE and THE are brought about by the same origin; this appears in the temperature dependence. The tendency of ρTHE change is independent of temperature as shown in Fig. 3b. The expansion of the observable magnetic field region under negative electric field is discerned at every temperature below 40 K (Fig. 3c–e). These indicate that the obtained modulation of THE is independent of the sign of AHE, which is inverted at 30 K. The temperature independent trend of the electric field effect on THE is in accord with that on AHE (Fig. 2d), implying the common origin of SOC variation. In fact, the MOKE measurements indicate that the coercive force (HC) is shifted from 0.73 T (VG = 200 V) to 0.76 T (VG = −180 V) at 30 K (see Supplementary Figure 2 and Supplementary Note 2). This shift of HC also supports the modification of SOC because the magnetic anisotropy originates from SOC.

Discussion

The observed modulations of the AHE and THE are not simply explained by the variation of carrier density. In order to show this clearly, the variations of AHE (ΔρAHE) and THE (ΔρTHE/ρTHE (0 V)) with different thickness of SrRuO3 films are shown in Fig. 4a, b, respectively, as a function of ρ xx variation normalized by zero-bias value (Δρ xx /ρ xx (0 V)) at various temperatures (see Supplementary Figures 7–9 and Supplementary Notes 6–8 for detailed transport and magnetic properties). Δρ xx /ρ xx (0 V) ranges from 1.2% in SRO5/SIO2/Sub to 6.6% in SRO3/SIO2/Sub at 10 K. Since ρ xx is inversely proportional to carrier density (n), the order of magnitude is consistent with the expected electron accumulation by a SrTiO3-back-gate transistor (Supplementary Note 8). ΔρAHE in bilayers indicates that the gate-bias control of AHE has the specific tendency regardless of the film thickness. The same plots of SrRuO3 single layers (SROm/Sub) are also depicted for comparison. They have negligible change in AHE, while their ρ xx variation is in the same range with that in bilayers with the same SrRuO3 thickness. As already pointed out, these results demonstrate the importance of inserting the SrIrO3 layer rather than the EF shift in SrRuO3. According to the equation (1), ρTHE is proportional not only to nsk (or ntopoNsk) but also to RH. We show the calculated variation of ρTHE contributed from RH, i.e., n variation (ΔRH i.e. Δn = n(VG = 200 V) − n(VG = −180 V)) with the red dash-dotted line in Fig. 4b, assuming small Δn (ΔRH ∝ Δn/n2, i.e., ΔρTHE ∝ Δn) and VG-independent electron mobility. All the modulations in heterostructures are located far above the red dash-dotted line. Therefore, most of the observed ΔρTHE is attributed to the change in size of the topological spin texture, i.e., DMI. These pronounced modulations of the AHE and THE are both achieved not by carrier-density variation in SrRuO3 but by modification of SOC at the interface of SrRuO3 and SrIrO3.

Fig. 4
figure 4

Qualitative analyses of modulations in AHE and THE. a Difference in anomalous Hall resistivity (ΔρAHE) between VG = 200 V and VG = −180 V as a function of longitudinal resistivity variation ratio (Δρ xx /ρ xx (0 V)) at temperatures ranging from 2 K to 80 K. b Modulation ratio of topological Hall resistivity (ΔρTHE/ρTHE (0 V)) as a function of Δρ xx /ρ xx (0 V). Red dash-dotted line is the calculated variation where gate bias only changes carrier density (Δn). Pink dotted line is the guide to the eyes. Broken arrows indicate temperature variation

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Recent theoretical calculations28, 29 have revealed that the DMI is enormously affected by the singularities in band structures as well as the AHE, although the precise dependencies differ between them. This has been confirmed in itinerant chiral magnets30 and a semiconducting Dirac electron system31. We speculate that our bilayers have some band deformation when applying an electric field to the interface. In both plots in Fig. 4, thinner SrRuO3 films exhibit smaller variation in spite of the larger Δρ xx /ρ xx (0 V). This thickness dependence is probably attributed to band structure deformation as observed in the thin limit of SrRuO332; the density of states near EF shrinks as SrRuO3 gets thinner.

One of the plausible pathways in the electric field-induced change of SOC is through the interface potential gradient, which is observed as the electrical control of Rashba-type band splitting in a semiconductor quantum well33. In contrast to the conventional Rashba systems, however, we have to take into account of the strong SOC of SrIrO3, the magnetic properties of SrRuO3, and their strong hybridization. Furthermore, since the itinerant-electron systems including SrRuO3 and SrIrO3 have complicated distribution of band-anti-crossings in their band structures22, 34, 35, the quantitative evaluation of the electric field-induced modulation in the heterostructures requires elaborate theoretical investigation. Nevertheless, the present observations clearly indicate that the electric field applied to the thin SrIrO3 plays the crucial role in SOC at the interface and even brings about the significant modification of magnetic properties in the neighboring itinerant ferromagnet. The method of inserting a thin nonmagnetic material with strong SOC between a ferromagnet and a gate dielectric may be applicable to tuning many intriguing spin-orbit coupled phenomena such as magnetic anisotropy15, domain wall motion36 and the DMI iteself37.

Methods

Sample preparation

The epitaxial bilayers composed of SrIrO3 and SrRuO3, and single layer films of SrRuO3 were deposited on SrTiO3(001) substrates by pulsed laser deposition using a KrF excimer laser (λ = 248 nm). The substrate temperatures during the growth of SrRuO3 and SrIrO3 were 730 °C and 600 °C, respectively, where oxygen partial pressure was 120 mTorr. The laser fluence was 1.2 J/cm2 for SrRuO3 and 2.6 J/cm2 for SrIrO3.

Measurement of magnetic and transport properties

The magnetization data were recorded by a SQUID magnetometer with a magnetic field applied perpendicularly to the film plane and along the magnetic easy axis grown on SrTiO3(001). Magneto-optic Kerr effect was measured with a laser at 690 nm wavelength in polar geometry by using a photoelastic modulator.

Transport properties were measured in Hall bars cut by a diamond wheel saw (1 mm × 2.5 mm) and ultrasonically bonded with Al wires. The applied current was 10 μA, which corresponds to 3.6 × 106 A/m2 for SRO5/SIO2/Sub. Back-gate transistors were fabricated using 0.5-mm-thick SrTiO3 substrates as a gate dielectric and silver paste as a gate electrode at the opposite side of the deposited films. Antisymmetrizations were performed for both the Hall resistivity and the Kerr rotation angle. Ordinary Hall term was subtracted from the Hall resistivity by linear fitting in a higher magnetic field region.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.