Observation of Nonlinear Spin-Charge Conversion in the Thin Film of Nominally Centrosymmetric Dirac Semimetal SrIrO3 at Room Temperature

Spin-charge conversion via spin-orbit interaction is one of the core concepts in the current spintronics research. The efficiency of the interconversion between charge and spin current is estimated based on Berry curvature of Bloch wavefunction in the linear-response regime. Beyond the linear regime, nonlinear spin-charge conversion in the higher-order electric field terms has recently been demonstrated in noncentrosymmetric materials with nontrivial spin texture in the momentum space. Here we report the observation of the nonlinear charge-spin conversion in a nominally centrosymmetric oxide material, SrIrO3, by breaking inversion symmetry at the interface. A large second-order magnetoelectric coefficient is observed at room temperature because of the antisymmetric spin-orbit interaction at the interface of Dirac semimetallic bands, which is subject to the symmetry constraint of the substrates. Our study suggests that nonlinear spin-charge conversion can be induced in many materials with strong spin-orbit interaction at the interface by breaking the local inversion symmetry to give rise to spin splitting in otherwise spin degenerate systems.

2 temperature because of the antisymmetric spin-orbit interaction at the interface of Dirac semimetallic bands, which is subject to the symmetry constraint of the substrates. Our study suggests that nonlinear spin-charge conversion can be induced in many materials with strong spin-orbit interaction at the interface by breaking the local inversion symmetry to give rise to spin splitting in otherwise spin degenerate systems. * corresponding author e-mail: KOZUKA.Yusuke@nims.go.jp Interconversion of electron spins and charges is one of the central techniques in the current spintronic research. Electrons accelerated by the electric field in a nonmagnetic metal are deflected through spin-orbit interaction, generating spin current transverse to the charge current [1,2]. The spin current can be utilized to flip the magnetic moment in the adjacent ferromagnets and applied for electrical magnetization switching with low energy consumption in spintronic devices [3][4][5]. The efficiency of charge-to-spin conversion has been estimated by calculating spin Hall conductivity based on the Berry phase approach [1,6] or equivalently Kubo formula in the linear-response regime [7]. In this approach, a band degeneracy point acts as a source of Berry curvature, analogous to the magnetic field in the momentum space, and gives a large contribution to spin or anomalous Hall effects [2,8].
Recently, higher-order spin-charge conversion beyond the linear-response theory has been recognized in noncentrosymmetric materials both theoretically and experimentally, where the electric field is coupled with Berry curvature dipole, leading to the observation of secondorder nonreciprocal Hall effect [9][10][11][12][13][14][15]. Nonlinear spin-charge conversion is also found to emerge under the in-plane magnetic field for the topological surface states of a topological insulator [16]. This nonlinear planar Hall effect originates from the transverse shift of spinmomentum locked topological surface states under the in-plane magnetic field in the presence of a nontrivial k-cubic warping effect. Conversely, it is suggested that nonlinear planar Hall (and nonlinear magnetoresistance as well) can be utilized to probe the nontrivial spin texture 4 in the momentum space in several materials without relying on spin-and angle-resolved photoemission spectroscopy [16,17].
Here we report a large nonlinear spin-charge conversion detected by a harmonic measurement of the planar Hall effect in nominally centrosymmetric SrIrO3 thin films at room temperature. The orthorhombic phase of SrIrO3 is known to be a Dirac semimetal with comparable spin-orbit interaction and electron correlation (~0.5 eV) with a Dirac nodal ring about 50 meV below the Fermi energy formed from two Dirac bands [18][19][20][21]. Owing to the characteristic band structure, this material is known to show a large spin Hall effect and to generate strong spin-orbit torque to the adjacent ferromagnetic layer [22][23][24][25][26]. The crystal structure of SrIrO3 is distorted perovskite (GdFeO3-type) in the centrosymmetric Pbnm space group with lattice constants of a = 5.60 Å, b = 5.58 Å, c = 7.75 Å (corresponding to a pseudocubic lattice constant of pseudo = √(2 2 + 2 2 + 2 ) 12 ⁄ = 3.93 Å [ Fig. 1(a)] [27]. In the presence of inversion symmetry, the band structure of SrIrO3 maintains spin degeneracy, and nonlinear spin-charge conversion is not expected. However, the spatial inversion symmetry of thin films is inherently broken at the surface and the interface, which causes spin textures in the momentum space due to antisymmetric spin-orbit interaction. Comparing the nonlinear planar Hall effect of SrIrO3 thin films grown on different substrates, we conclude that the observations are interface/surface-driven phenomena irrespective of the degree of the strain with minor modification of spin texture by the symmetry constraint of the substrate. 5 The experimental details are explained in the supplemental material. Briefly, the 1(a) [28]. The second-order term of the planar Hall effect is characterized by an out-of-phase second-harmonic component using lock-in amplifiers with an alternating current frequency of 33 Hz [17]. The first-principles density-functional calculations including the spin-orbit interaction are carried out with the aid of the Vienna ab initio simulation program (VASP) [29][30][31]. Figure 1(b) shows a θ-2θ scan of X-ray diffraction for SrIrO3 thin films grown on LSAT (001), GdScO3 (110), and NdGaO3 (110) substrates, indicating epitaxial growth with out-of-plane lattice constants of 3.99 Å for LSAT, 3.89 Å for GdScO3, and 3.97 Å for NdGaO3, which deviate from the bulk value to compensate in-plane compressive (for LSAT and NdGaO3) and tensile (for GdScO3) strains (reciprocal space mapping shown in Fig. S1). The crystal structure is additionally characterized by high-angle annular dark-field transmission electron microscope (HAADF-STEM) images as shown in Fig. S2. While all films show clear 6 epitaxial growth on the substrates, dislocations are partly observed for LSAT and NdGaO3 substrates probably due to large lattice mismatch and presence of twins. The resistivity shown in Fig. 1(c) is only weakly temperature dependent as typical semimetallic behavior of SrIrO3, consistent with other PLD-grown films in previous reports [32][33][34]. The triangles in (b) show peaks of SrIrO3 thin films.
To characterize the nonlinear planar Hall effect, we measure angular dependence (φ) of second-harmonic Hall voltage on in-plane magnetic field direction with respect to the current direction using a Hall bar structure as shown in Fig. 2(a). Figure 2(b) shows a typical secondharmonic planar Hall measurement as a function of φ for a film grown on an LSAT substrate at 300 K under a constant magnetic field (H) of 10 T. The second-harmonic resistance is defined as 2 = 2 / , where 2 is the out-of-phase second-harmonic voltage and I is the externally applied alternating current. The data in Fig. 2(b) clearly shows cos dependence. So far, a similar cosine dependence of the second-harmonic planar Hall effect has been ascribed to nontrivially spin-momentum locked band structures in noncentrosymmetric materials [17] although, at first sight, this mechanism is not compatible with centrosymmetric SrIrO3.
In order to obtain an insight into the origin, the magnitude of the second-harmonic planar Hall signal (Δ 2 ) is extracted by fitting with 2 = Δ 2 cos (after subtracting a constant background) [17]. First, as shown in Fig, S3 magnetic field (H) as previously observed in Bi2Se3 [16,17]. We have also confirmed the second-harmonic component of anisotropic magnetoresistance ( [19,20]. In the case of thin film, however, antisymmetric spin-orbit interaction induces momentum-dependent spin splitting at the interface, leading to complex spin texture in the two Dirac bands. Indeed, the nonlinear planar Hall effect was also observed at the LaAlO3/SrTiO3 interface [17] which is known to possess complex spin texture originating from the anti-crossing of three t2g bands [35,36].
To test this consideration, we compare the second-harmonic planar Hall signal for substrates, we find a significantly large anisotropy between two current directions along [001] and [11 ̅ 0]. For fair comparison for films with different resistivity, we use a coefficient of the bilinear magnetoelectric effect = Δ 2 / , where Δ 2 = Δ 2 , which is shown in Table I [17]. We find that the room temperature value for the sample grown on LSAT is almost comparable to the previously reported value for a Bi2Se3 thin film at 5 K ( ≈ 0.02 mΩ μm 2 /VT ), which rapidly decreases with increasing temperature toward room temperature. Remarkably, is significantly large for orthorhombic GdScO3 and NdGaO3 with the current along [001] but negligibly small along [11 ̅ 0]. Furthermore, the sign of differs between two current directions in the case of the GdScO3 (110) Fig. 1(a)]. On the contrary, such anisotropy is not present in the case of the cubic LSAT substrate but an orthorhombic twin structure is known to appear based on the detailed structural analysis of SrIrO3 thin films reported in [37]. This twin structure may average out the anisotropic nonlinear planar Hall signal in the case of the LSAT substrate. 13 To confirm this hypothesis, we have performed first-principles calculations of electronic band structure using an unstrained SrIrO3 slab model [ Fig. 4 it difficult to differentiate these contributions [39,40]. As the nonlinear planar Hall effect [17] has to do with the nonlinear Hall effect observed at zero magnetic field [14,15] in terms of Berry phase dipole in the intrinsic case, we expect that both phenomena may also be similarly influenced by the disorder. As suggested in Ref. [40], precise disorder tuning would be necessary to separate these contributions.
In conclusion, we have observed the nonlinear planar Hall effect in nominally centrosymmetric SrIrO3 thin films at room temperature, which is expected only in  [13,41]. We expect future theoretical studies will clarify how to effectively design symmetry breaking to induce a large nonlinear spin-charge conversion.
We acknowledge A. Kurita for the technical assistance of thin film growth, Y.
Toyooka for the synthesis of the target, and J. Uzuhashi for transmission electron microscopy. For electrical transport measurement, a Hall bar structure is defined by photolithography and ion milling followed by the deposition of Ti/Au electrodes, which results in a typical channel width of 10 μm. The second-order term of the planar Hall effect is characterized by an out-of-phase second-harmonic component using lock-in amplifiers with an alternating current frequency of 33 Hz. The signal is found to be almost independent of the excitation frequency up to around 1 kHz, indicating that parasitic capacitance is not significant.

RECIPROCAL SPACE MAPPING
The in-plane relationship of SrIrO3 thin films and substrates is characterized by reciprocal space mapping around (103) diffraction of a pseudocubic representation as shown 22 in Fig. S1. The SrIrO3 thin film grown on GdScO3 substrate is fully strained, whereas the films grown on LSAT and NdGaO3 are overall strained but partially relaxed. The low intensity of the SrIrO3 film grown on NdGaO3 is due to the low crystal quality as also seen in the θ-2θ scan in Fig. 1(b).
FIG. S1: Reciprocal space mapping of the SrIrO3 thin films grown on LSAT (001), GdScO3 (110), and NdGaO3 (110) substrates. The reciprocal space point of the bulk SrIrO3 is indicated by a red circle.

SCANNING TRANSMISSION ELECTRON MICROSCOPY
In addition to X-ray diffraction, the crystal structures of SrIrO3 thin films grown on LSAT (001), GdScO3 (110), and NdGaO3 (110) substrates are observed by the high-angle annular dark-field scanning transmission electron microscope (HAADF-STEM) images as 23 shown in Fig. S2. In the case of GdScO3 (110) substrate, SrIrO3 thin film is found to show coherent lattice matching without noticeable dislocation, while dislocations and twins are partly observed for LSAT (001) and NdGaO3 (110) substrates. LSAT has a cubic structure unlike orthorhombic SrIrO3 and therefore twin is inherently expected in the film. For NdGaO3, the crystal is isostructural with SrIrO3 but a relatively large lattice mismatch may cause the dislocations at the interface as seen in Fig. S2(c).

PLANAR HALL EFFECT
Here we show the current and magnetic field dependences of the nonlinear planar Hall tends to saturate at a large current above ~ 2 mA. This indicates that another mechanism is present to restrict the nonlinear effect at a large current, but the reason is not clear at the moment.

RESISTANCE
The second-harmonic component of the anisotropic magnetoresistance ( 2 ) is shown in Fig. S4 together with the nonlinear planar Hall effect ( 2 ) for the SrIrO3 thin film grown on LSAT (001) substrate, measured at 100 K under 8 T. Figure S4 shows the sinφ dependence of 2 and cosφ dependence of 2 as in the case for Bi2Se3 in Ref. [17]. In general for the SrIrO3 films, 2 is much noisier than 2 probably due to larger background firstharmonic component, and 2 is not discernable unlike 2 at room temperature. The ratio

NONLINEAR PLANAR HALL MEASUREMENT FOR A SrRuO3 FILM
As a control experiment, we have performed the nonlinear planar Hall measurement 28 for a SrRuO3 thin film (thickness: 13 nm) grown on an LSAT (001) substrate. SrRuO3 is a typical paramagnetic metal among oxide materials at room temperature (in contrast to the lowtemperature ferromagnetic phase). As shown in Fig. S6, the cosφ dependence is not discernable for the SrRuO3 thin film compared with SrIrO3 thin film, measured under similar conditions (T = 300 K and H = 8 T). Although the signal of SrRuO3 is noisier due to higher resistance, the absence of the nonlinear planar Hall signal is clear.

FIRST-PRINCIPLES BAND STRUCTURE CALCULATION
The first-principles density-functional calculations including the spin-orbit interaction are carried out with the aid of the Vienna ab initio simulation program (VASP) [29]. Here, the 29 generalized gradient approximation (GGA) [30] is adopted for the exchange-correlation energy and the projector augmented wave (PAW) potential [31] is used to treat the effect of core electrons properly. A plane-wave cut-off energy of 500 eV is employed for the wave function and 8  8  2 k points (11  11  8 k points for bulk) are used for the Brillouin-zone integration.
In this study, on-site Coulomb interaction U is not included as U is known not to qualitatively change the result [19]. corresponding Brillouin zone is shown in Fig. S7(d).
The band structures of the bulk and the slab models are shown in Figs. S7(e)-S7(j) 30 along the red lines shown in Fig. S7(d). As a result of the redefinition of the unit cell for the slabs, we take the equivalent cut in the Brillouin zone shown in Fig. S7(d)

NONLINEAR PLANAR HALL EFFECT
The temperature dependence of the nonlinear planar Hall effect, carrier density, and mobility is measured as shown in Fig. S9. The nonlinear planar Hall signal shows nearly the same temperature dependence as the mobility. This tendency is qualitatively consistent with a theoretical prediction of τ-linear dependence of Δ 2 , where τ is the carrier scattering time. Temperature dependence of (b) carrier density, mobility, and (c) magnitude of the nonlinear planar Hall effect.