Modulation of spin-torque ferromagnetic resonance with a nanometer-thick platinum by ionic gating

The spin Hall effect (SHE) and inverse spin Hall effect (ISHE) have played central roles in modern condensed matter physics especially in spintronics and spin-orbitronics, and much effort has been paid to fundamental and application-oriented research towards the discovery of novel spin–orbit physics and the creation of novel spintronic devices. However, studies on gate-tunability of such spintronics devices have been limited, because most of them are made of metallic materials, where the high bulk carrier densities hinder the tuning of physical properties by gating. Here, we show an experimental demonstration of the gate-tunable spin–orbit torque in Pt/Ni80Fe20 (Py) devices by controlling the SHE using nanometer-thick Pt with low carrier densities and ionic gating. The Gilbert damping parameter of Py and the spin-memory loss at the Pt/Py interface were modulated by ionic gating to Pt, which are compelling results for the successful tuning of spin–orbit interaction in Pt.

layer. The physics behind the gate-tunable ISHE is the formation of nanometer-thick Pt (ultrathin Pt, with a thickness of ca. 2 nm) and Fermi level shifting due to the sufficient accumulation of electrons at the ultrathin Pt by ionic gating. Ultrathin Pt is considerably resistive, and its spin Hall mechanism is governed by the intrinsic mechanism, where the spin Hall conductivity σ SH is dependent on the conductivity σ (σ SH ~ σ 2 ) 18 . The intrinsic spin Hall regime is governed by inter-d-band excitation, and the density of states of the d-orbital in Pt rapidly diminishes above the Fermi level 19 . Indeed, first-principle calculations revealed that the spin Hall conductivity of Pt decreased above the Fermi level 20 . A positive gate voltage application enabling electron accumulation gives rise to an upshift of the Fermi level from the intrinsic one in Pt, which allows suppression of the spin Hall conductivity, i.e., suppression of the ISHE.
Given that the SHE and the ISHE are interconnected by Onsager reciprocity, detection of the reciprocal effect of the abovementioned gate-tunable ISHE in ultrathin Pt, i.e., a gate-tunable SHE, can be expected. In a previous work 12 , spin current was injected from YIG to Pt by spin pumping, and the spin current was converted to charge current by the ISHE, which was gate-tunable, resulting in the detection of gate-tunable electromotive forces. Thus, one of the simplest reciprocal experiments to detect the gate-tunable SHE is planned as follows: an AC electric current flowing in ultrathin Pt allows generation of AC spin current due to the SHE. The generated AC spin current propagates into the adjacent ferromagnet and provides spin-torque to the ferromagnet, yielding spintorque FMR (ST-FMR). The magnitude of the SHE can be suppressed by positive ionic gating and the ST-FMR is tunable, i.e., gate-tunable SOT. Consequently, the Gilbert damping parameter α of the ferromagnet can be tuned by ionic gating because the σ SH of the ultrathin Pt is suppressed. Within this scheme, YIG is not appropriate as an adjacent material for the ST-FMR because YIG is a ferrimagnetic insulator and no electron conduction can flow in YIG, resulting in the no ST-FMR signal which is originated from the anisotropic magnetoresistance of a ferromagnet adjacent to Pt. Here, in this study, we demonstrate gate-tunable SOT as manifestation of Onsager reciprocity in spin-charge interconversion by using a Pt/Ni 80 Fe 20 (Py) bilayer film. The magnitude of the SOT is measured as the change in α of Py in ST-FMR measurements. The modulation of the ST-FMR signal in our ST-FMR device by gating indicates the representation of the reciprocal effect of gate-tunable ISHE in Pt as studied in the previous work 12 . Figure 1a and b show an optical microscopic image and a measurement circuit of a gate-tunable SOT (ST-FMR) device consisting of Pt/Py. To clarify how ionic gating modulates the resistivities of the Pt/Py devices, the gate voltage dependence of the resistivity of Pt (1.2, 1.4, and 1.8 nm) grown on Py (3 nm) was measured (see Fig. 2a). Gate voltages from 0 V to + 1.25 V were applied since the suppression of the ISHE in ultrathin Pt manifests itself only under a positive gate voltage 12 . Here, note that the gate voltage was limited at + 1.25 V because of a rapid increase in the gate leakage current above + 1.25 V, which hinders precise experiments (see Supplementary  Information No. 1). The resistivity decreases as a function of gate voltage in all devices, and more importantly, modulation of Pt resistivity is the most prominent in the Pt (1.2 nm)/Py (3 nm) device. The decrease in Pt resistivity under a positive gate voltage is attributed to efficient charge accumulation, which also induces an upshift in the Fermi level. The modulation of Pt resistivity in the device is, in principle, consistent with that in the previous study 12 , i.e., thinner Pt revealed a stronger modulation of resistivity for the same gate voltage. Meanwhile, the gate voltage dependence of Pt resistivity is not substantially larger in Pt/Py than in Pt/YIG, www.nature.com/scientificreports/ which can be rationalized by the intrinsic carrier densities in the devices. In contrast to the previous study 12 , a metallic ferromagnet, not an insulator, is used in this study. To maintain equilibrium in the charge distribution in Py/Pt, carriers in Py flow into Pt in the formation of the bilayer because the carrier concentration of ultrathin Pt is considerably low (ca. 6 × 10 21 cm −3 ) 12 . Thus, the carrier density of Pt on Py increases, which gives rise to a weak response in resistivity to the gate voltage resulting from the extrinsically modulated Fermi level in Pt. In a simple calculation using the Drude model, the modulation of the resistivity of 1.2 nm-thick Pt on Py (3 nm) was calculated to be 18% by the application of V G = + 1.25 V, which is equivalent to that measured here (12%, see also Supplementary  The ST-FMR signals are nicely seen at ca. 90 mT, which is ascribed to the fact that the AC electric current flowing in the 1.2 nm-thick Pt generates AC spin current and the AC spin current provides sufficient spin torque to Py to excite FMR. As seen in Fig. 2c and d, modulation of the symmetric component S and the antisymmetric component A as a function of the gate voltage are indiscernible. Here, S is related to the spin current density Js generated by the spin Hall effect of Pt, whereas A is due to the sum of the Oersted field around the Pt and the field-like torque and is related to the charge current density Jc 21 . Thus, the spin-conversion efficiency η, the ratio of spin current to charge current densities, also slightly changes with the gate voltage (see Fig. 2e). Without taking the spin-memory loss (SML) into account, η is described as, where t Py and t Pt are the Py thickness and the Pt thickness, ℏ is the Dirac constant, μ 0 is the vacuum permeability, M S is the saturation magnetization of Py, M eff is the effective saturation magnetization of Py and H res is the resonance field.

Result
Nevertheless, the Gilbert damping parameter α, which is calculated from the frequency dependence of the half-width at half-maximum of the ST-FMR spectrum by using the relation, Δ = Δ 0 + 2παf / γ (Δ and Δ 0 are the half-width at half-maximum for non-zero f and f = 0 Hz, respectively, and γ is the gyromagnetic ratio), exhibits salient modulation under a positive gate voltage (see Fig. 3 and Supplementary Information No. 5). The Gilbert damping parameter α of a ferromagnet depends on the SOI of the adjacent nonmagnet, and α is smaller when the SOI of the adjacent nonmagnet is weaker. Hence, the smaller α under the greater positive gate voltage is ascribed to the weaker SOI of the gated Pt, i.e., the SHE (i.e., σ SH ) in the 1.2 nm Pt is suppressed by positive gate voltages. Thus, this result demonstrates the reciprocal effect of the gate-tunable ISHE in ultrathin Pt 12 .
The spin Hall conductivity σ SH is related to the spin Hall angle, which is described as the ratio of the spin current and charge current densities. Furthermore, the ratio of S and A in an ST-FMR spectrum is related to the The spin-conversion efficiency, η, can be expressed in terms of the damping-like-torque and field-like-torque efficiencies, ξ DL and ξ FL , described as 22 : Then, ξ DL and ξ FL can be estimated via the t Py dependence of η by postulating that both torques are independent of t Py . Here, M S is inversely proportional to t Py , and μ 0 M S ~ μ 0 M eff = a / t Py + b, where a and b are fitting parameters used to estimate the thickness-dependent M S 23,24 (see the inset of Fig. 4a). Figure 4a shows the relationship between the inverse of t Py and the inverse of η at f = 8 GHz with applied gate voltages V G = 0 and 1 V. The results are nicely fitted by Eq. (2), and ξ DL and ξ FL are estimated to be 6.2 × 10 −2 and 1.4 × 10 −2 at V G = 0 V and 5.1 × 10 −2 and 1.0 × 10 −2 at V G = 1 V, respectively. Figure 4b and c show the frequency dependence of ξ DL and ξ FL , respectively. The changes in ξ DL and ξ FL with the application of a gate voltage are indiscernible within the error bars, and the application of a gate voltage does not influence either the damping-like torque or field-like torque in this measurement.

Discussion
Since there is no sizable change in either the damping-like or field-like torque by gating, we propose that gating modulates the spin-memory loss (SML) 25,26 , explaining the unchanged S/A. SML manifests in heterostructures consisting of a heavy metal and is attributed to the SOI of the heavy metal and interfacial disorder. SML gives rise to depolarization of the spin current propagating through the interface and is salient in Pt-based heterostructures. Indeed, the spin flip parameters, δ, in Co/Pt and Pt/Py are 0.9 and 0.63 27,28 , respectively, and are substantially larger than those of other d-electron-material-based heterostructures. Since the SOI is related to the SML as described above, modulation of the SOI by gating enables modulation of the SML. The right-hand side of Eq. (1), including the ratio S/A, is unchanged by gating in our experiments. However, in reality, the spin current generated by the SHE in Pt, J S0 , does not fully flow into Py, and part of it dissipates at the interface due to the sizable SML. In fact, by considering SML, merely 53% of the spin current generated in Pt by the SHE flows into Py at V G = 0 V (note that the spin flip parameter δ of Pt/Py is 0.63 and the spin depolarization at an interface in SML is described as [1 − exp(− δ)]). Hence, the transmitted spin current from Pt to Py at V G = 0 V is equal to J S0 exp(− 0.63). Meanwhile, under the application of V G = + 1.25 V, the charge current density flowing in Pt slightly increased (+ 14%; see the modulation of ρ Pt shown in Fig. 2a), whereas the spin current density originally generated in Pt by the SHE at V G = + 1.25 V, J S0 ' , decreased to approximately 70% of that at V G = 0 V, J S0 (see Fig. 4 of our previous report 12 ). Since the ratio S/A is unchanged at V G = + 1.25 V, the spin flip parameter in www.nature.com/scientificreports/ Pt/Py at V G = + 1.25 V is estimated to be 0.14. The sizable suppression of δ by gating is due to suppression of the SOI in Pt by gating, given that SML originates from the SOI and the δ of a bilayer consisting of weak SOI metal is, for example, 0.017 for Pd/Py 28 and 0.25 for Co/Cu 25 . Thus, the suppression of δ by gating also corroborates the gate-tunable SOI of Pt.

Conclusion
In summary, we experimentally demonstrated the gate-tunable SHE of 1.2 nm-thick Pt grown on 3 nm-thick Py as manifestation of the gate-tunable SOI by employing ST-FMR and ionic gating techniques. The Gilbert damping parameter α was decreased by positive gating, which is due to the suppression of the SOI of ultrathin Pt by gating. Although the ratio of spin and charge currents in Pt was not substantially changed by gating, these changes are ascribed to the modulation of SML in Pt/Py. The suppression of the spin flip parameter δ in SML by gating was the other compelling result for the gate-tunable SOI in Pt. The results obtained in this study are a manifestation of the Onsager reciprocity between the SHE and the ISHE, and this study opens up a novel pathway to gate-tunable SOT devices and other gate-switchable spintronic devices.

Measurement and analysis of the ST-FMR spectrum.
An RF current with an input power of 10 mW (10 dBm) was applied in the longitudinal direction of the sample with an in-plane external magnetic field H ext at an angle of θ = 45° with respect to the longitudinal direction. The frequency of the RF current was set to 4, 6 and 8 GHz. All measurements were carried out at room temperature. FMR is caused by the Oersted field due to a charge current in the Pt layer and a spin current generated by the spin Hall effect in Pt. The field-induced FMR spectrum has an anti-symmetric component in an output voltage at the resonance field. Meanwhile, the spin current due to the spin Hall effect in the Pt layer is injected into the adjacent Py layer and excites a spin-current-induced FMR, which has a symmetric component in the output www.nature.com/scientificreports/ voltage. The mixed FMR of these two components can be detected as a DC voltage via the rectification effect, which can be expressed as 21 , V = C[AF A (H ext ) − SF S (H ext )], which is the fitting function used in this study. Here, C is a coefficient related to the anisotropic magnetoresistance, F S (H ext ) = Γ 2 /[(H ext − H res ) 2 + Γ 2 ] is a symmetric Lorentzian with a resonance field H res with Γ being the half width at half maximum of the ST-FMR spectrum, and F A (H ext ) = F S (H ext ) × [(H ext − H res )/Γ] is an anti-symmetric Lorentzian. The symmetric component S is related to the spin current density J S generated by the spin Hall effect of Pt, whereas the asymmetric component A is due to the sum of the Oersted field around the Pt and the field-like torque and is related to the charge current density J C .