Ferromagnetic resonance excited by interfacial microwave electric field: the role of current-induced torques

Excitation of magnetization dynamics in magnetic materials, especially in ultrathin ferromagnetic films, is of utmost importance for developing various ultrafast spintronics devices. Recently, the excitation of magnetization dynamics, i.e. ferromagnetic resonance (FMR) via electric field-induced modulation of interfacial magnetic anisotropies, has received particular attention due to several advantages, including lower power consumption. However, several additional torques generated by unavoidable microwave current induced because of the capacitive nature of the junctions may also contribute to the excitation of FMR apart from electric field-induced torques. Here, we study the FMR signals excited by applying microwave signal across the metal-oxide junction in CoFeB/MgO heterostructures with Pt and Ta buffer layers. Analysis of the resonance line shape and angular dependent behavior of resonance amplitude revealed that apart from voltage-controlled in-plane magnetic anisotropy (VC-IMA) torque a significant contribution can also arises from spin-torques and Oersted field torques originating from the flow of microwave current through metal-oxide junction. Surprisingly, the overall contribution from spin-torques and Oersted field torques are comparable to the VC-IMA torque contribution, even for a device with negligible defects. This study will be beneficial for designing future electric field-controlled spintronics devices.

These authors contributed equally. * Author to whom any correspondence should be addressed.
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When an electric field is applied at ferromagnet/oxide interfaces, the relative change in the electron population of out-ofplane 3d orbitals of ferromagnets with respect to the in-plane orbitals at the interface modulates both perpendicular magnetic anisotropy (PMA) [47,48] and induced in-plane magnetic anisotropy (IMA) [49], if any. This phenomena enables us to generate FMR in an in-plane magnetized ultrathin FM film through the electric field induced modulation of IMA [6], even though the torque originated from the electric field induced modulation of PMA becomes zero for this magnetization orientation. Typically, VCMA-induced FMR is excited by applying a microwave signal across a magnetic tunnel junction comprising two thin magnetic layers separated by an ultrathin oxide layer [42,43,50,51]; or across the ultrathin FM layer and a top metal gate electrode fabricated on oxide layer [4]. However, in either case, an unavoidable microwave current often passes through the oxide layer due to the capacitive nature of the junction. Depending on the corresponding current density, it may lead to other torques on magnetization originated from Oersted field and spin-current in addition to existing VCMA torque. This becomes especially true for higher microwave power, higher operational frequency, and thinner oxide layer [6]. Although for smaller junctions with a submicrometer square area, the VCMA torque generally dominates over other torques because of higher junction resistance [50][51][52], for larger junctions over hundreds of micrometer square areas, other torques may surpass the VCMA torque due to reduced device impedance, which allows large enough induced microwave current through the junction. Another source of microwave current could be the presence of unavoidable defects in the oxide layers, and this is distinct in origin from the previously mentioned induced microwave current through the capacitive metal-oxide junction. In the purview of practical electric-field controlled device applications, it is essential to identify those additional charge current-induced torques and quantify their values relative to existing VCMA torque. This can help to optimize the device performance in terms of power consumption and heat dissipation. For this purpose, one of the suitable method would be to study the evolution of rectified FMR signal with varying in-plane angle of bias magnetic field, i.e. the in-plane orientation of magnetization.
The presence of other current-induced torques apart from VCMA torque was confirmed in some earlier studies, where spin-transfer torque (STT), field-like torque, and Oersted field torques were observed [42,51,53,54]. It is pretty challenging to separate the contributions of individual torques only from line shape analysis of the FMR signal. However, there are some previous studies, which show the extraction of different spin-torques contribution accurately from FMR lineshape analysis [55][56][57]. The measurement of in-plane magnetic field orientation-dependent FMR signals could be another suitable method to identify and separate different torque contributions [58]. However, a systematic experimental study on this issue has not been reported yet.
The present study investigates the evolution of voltagecontrolled in-plane magnetic anisotropy (VC-IMA) induced FMR signals (line shape and magnitude) in presence of current induced torques in [heavy-metal (HM) (Ta or Pt)]/ CoFeB/MgO/Al 2 O 3 heterostructures with varying in-plane magnetic field orientations. We adapted several experimental strategies for this study. A single magnetic layer eliminates STT contribution originating from the generation of spinpolarized current while passing microwave current through the fixed/reference magnetic layer and the contribution from the dynamic magnetostatic field generated as a result of the oscillating magnetization in the fixed/reference magnetic layer. Due to the absence of a fixed/reference magnetic layer, we change our strategy for detecting FMR signals and adapt spin pumping (SP) and inverse spin Hall effect (ISHE) technique (SP-ISHE) as described in [5,59,60]. While exciting FMR of the localized spins in the FM layer, a pure spin current is pumped into the adjacent HM layer owing to the angular momentum transfer to the conduction electrons. This spin current is converted into the charge current by virtue of the ISHE in the HM buffer layer and can be detected as a voltage signal. This method provides a quantitative comparison among various torque contributions, including VC-IMA torque. We chose a CoFeB film with an in-plane easy axis of magnetization. A relatively higher microwave power (yet within a linear regime) was used for the excitation of FMR to enhance the detected signal. This also helps us to identify and quantify various charge current-induced torques, which are especially unavoidable at higher microwave power. We found a significant contribution from spin current-induced torques and Oersted field torques apart from expected VC-IMA torque.

Sample fabrication
At first, [Pt (10) or Ta (10)]/Co 20 Fe 60 B 20 (2)/MgO(2)/Al 2 O 3 (10) films were deposited on Si/SiO 2 (700) substrates by radio frequency (rf) sputtering at room temperature at a base pressure of 10 −8 Torr. The numbers in the parentheses indicate the nominal thicknesses of the layers in nanometers. Here thicker Al 2 O 3 layer acts as a protecting layer for CoFeB/MgO interface and ensures a higher dielectric breakdown voltage of the junction. The deposited films were then annealed in a vacuum for 30 min at 280 • C temperature in a 600 mT magnetic field applied perpendicular to the film plane. In the second step, the continuous films were patterned into 200 µm × 12 µm rectangular stripe like structures with the help of maskless UV lithography and Ar + ion milling down to the substrate. In the next step, gate electrodes were prepared by depositing Ti(5)/Au(100) layer by electron beam evaporation on top of those rectangular structures selected by maskless UV lithography. The contacts at the edges of the rectangular structures were also made in the same step for measuring resonance signals and also for performing spin-torque-induced ferromagnetic resonance (ST-FMR) measurement. Next, UV lithography and RF magnetron sputtering were used to deposit a 180-nm-thick Al 2 O 3 layer everywhere except on top of the gate electrodes and on the Ti/Au contacts for measuring FMR signals. In the final step, the contacts for applying microwave signal across the gate electrodes and larger contacts for measuring FMR signals and performing ST-FMR measurements were made by UV lithography followed by the deposition of Ti(5)/Au(220) layer by electron beam evaporation.

Experimental measurement
The FMR in CoFeB layers was excited by applying microwave signal (i.e. V rf (ω) from a signal generator) across the top electrode (Ti/Au) and CoFeB layer (see figure 1(a)). The V rf produces an rf electric field E rf at the CoFeB/MgO interface and periodically modulates interfacial anisotropies: PMA and IMA. The bias magnetic field H is applied in-plane of the sample at a variable angle ϕ made with the long axis of the rectangular film (see figure 1(b)). As the value of H is well above the IMA field, the magnetization of the CoFeB film is aligned along the H direction in the sample plane, which helps to maximize the detected signal. For the in-plane magnetization orientation, the torques originating from voltage-controlled perpendicular magnetic anisotropy (VC-PMA) become zero. In contrast, the torques originating from VC-IMA have a nonzero value because of the presence of IMA in our films. The time-varying VC-IMA excites FMR in CoFeB films at the resonance condition given by equation (2).
It is well known that rf current can also pass through an oxide barrier which acts like a capacitor. At lower microwave power and frequency, its amplitude becomes too small to produce a detectable signal as compared to VC-IMA-induced excitation. However, the situation could be different at high enough microwave power and frequency. In that condition the unavoidable microwave current through the oxide layer can produce a strong enough Oersted field. This current ultimately flows through the HM buffer layer (i.e. Pt and Ta in our case) and produces spin current through the spin Hall effect (SHE) of HMs. The spin current then enters into the CoFeB layer and exerts torques to the magnetic moments. The Oersted field and spin-torques can simultaneously excite FMR in CoFeB layer. In both cases the time-varying anisotropic magnetoresistance (AMR) because of the Oersted field and spin-torque-induced FMR is mixed with the rf current, and a rectified dc voltage appears across the rectangular CoFeB structure. It means the detected dc voltage (V dc ) has primarily three origins in our devices: (1) VC-IMA induced FMR, (2) Oersted field induced FMR, and (3) spin-torque induced FMR. For each measurement the power and frequency of V rf (ω) are kept fixed, and the bias magnetic field value is swept in between −180 mT and +180 mT. The FMR signals V dc are detected by a nanovoltmeter. For angular-dependent measurement the bias magnetic field is rotated at a step of 7.5 • or 15 • .

Device characterization
The devices for this study were fabricated from the multilayer stacks: Pt(10)/Co 20 Fe 60 B 20 (2)/MgO(2)/Al 2 O 3 (10) and Ta(10)/Co 20 Fe 60 B 20 (2)/MgO(2)/Al 2 O 3 (10). Two devices with a Pt buffer layer and one with a Ta buffer layer, as schematically shown in figure 1(a), were used for all the measurements presented in this article. A real image of the device with measurement geometry is also shown in supplementary figure S1. For simplicity, the devices will be indicated as: Pt/-CoFeB/MgO #1, Pt/CoFeB/MgO #2, Ta/CoFeB/MgO #3 or simply #1, #2, #3 in the rest of the article. As described in the earlier section, a microwave signal V rf from a signal generator is applied across the top electrode (Ti/Au) and CoFeB layer of the devices for the excitation of FMR in CoFeB films (figure 1(a)). In this configuration, the FMR in the CoFeB layer is excited by: (1) VC-IMA torque, (2) torque induced by Oersted field generated by induced microwave current through the CoFeB/MgO junction, and (3) torque induced by the spin current generated due to flow of microwave current through HM (Pt or Ta) buffer layer. It means the detected resonance voltage V dc across the devices also has above-mentioned three origins. To determine the contributions from the individual torques quantitatively, we measure the FMR signals for different orientations (ϕ) of in-plane bias magnetic field H, tilted from the long axis of rectangular-shaped devices, as shown in figure 1(b). Figure 1(c) represents a measured FMR signal (solid points) as a function of H from Pt/CoFeB/MgO #1 device. To extract the values of signal amplitude, resonance field H 0 , and resonance line-width, the FMR signals are fitted to the following expression [5,61,62]: Here, V 0 is the background of V dc , V s and V a are the weights of the symmetric Lorentzian and dispersive functions, respectively, and σ is the half width at half maximum (HWHM) of the FMR spectrum. The solid curves in figure 1(c) represent the fit to equation (1), showing that the symmetric Lorentzian part dominates over the dispersive part (dispersive part V a is about 28% of the symmetric part V s ). The other two devices, Pt/ CoFeB/MgO #2 and Ta/CoFeB/MgO #3, also show the dominance of the symmetric Lorentzian part over the dispersive part (See supplementary figures S2(a) and (b)). We found that the dispersive parts are about 47% and 26% of the symmetric parts for devices #2 and #3, respectively. One interesting difference among the resonance spectra of the devices is that the baseline of resonance spectra of devices #2 and #3 are shifted towards the positive V dc value as opposed to the resonance spectra of device #1. This indicates the presence of small dc current in devices #2 and #3, which probably arises from some defects in the oxide layer.

Out-of-plane and in-plane magnetic anisotropies of the devices
To characterize the out-of-plane and in-plane magnetic anisotropy fields of the studied devices, we measured resonance spectra as a function of in-plane bias magnetic field orientation (ϕ). The spectra from devices #1 and #2 were measured at 6 GHz frequency and 18 dBm (i.e. 63 mW) microwave power, whereas the spectra from device #3 were measured at 5 GHz frequency and 18 dBm microwave power. In general, this is a bit high microwave power. However, most of the applied power is reflected from the devices as a consequence of impedance mismatch [42]. So, the actual power consumed by the device should be much lower than the applied power. We verified that the microwave power is low enough to excite FMR in the linear regime (see supplementary figure  S3). Each spectrum's resonance field H 0 is extracted by fitting with equation (1) and then plotted as a function of ϕ as shown in figures 2(a)-(c). The µ 0 H 0 versus ϕ data points are fitted to the following equation [49]: where, f is the microwave frequency, γ is the gyromagnetic ratio, µ 0 is the permeability of free space, H k is the IMA field, β is the angle of the IMA direction. Here M eff (= M s − H p ) is known as effective magnetization, M s is saturation magnetization and H p is the PMA field. From the fitting (shown by red curves in figures 2(a)-(c)), we find that IMA fields µ 0 H k = 2.88 ± 0.15, 3.65 ± 0.15 and 0.68 ± 0.06 mT for devices #1, #2 and #3, respectively, along β = − 5 • ± 2 • . In this fitting µ 0 H k , µ 0 H p , β were set as free parameters. In our films (or devices), the IMA is introduced during the annealing even without the in-plane bias magnetic field. This uncontrolled annealing sets the in-plane anisotropy direction for all the devices nearly along their long axes. The PMA fields µ 0 H p for devices #1, #2, #3 are 859, 875, 1035 mT, respectively, considering µ 0 M s = 1.5 T for all the films. These results indicate that Ta buffer layer helps to enhance PMA, as seen in some previous reports [63][64][65], whereas Pt buffer layer helps to induce IMA. Nevertheless, all the films possess PMA and IMA. A small difference in PMA and IMA in devices #1 and #2 is observed as the devices were fabricated separately from the same deposited film.

Angular dependent behavior of resonance signal
Our previous work showed that the torque τ generated by VCMA can be expressed as [6]: where ∂H p /∂V is the voltage-control coefficient of the PMA field, ∂H k /∂V is the voltage-control coefficient of the IMA field, V rf is the applied microwave voltage, and θ is the elevation angle of magnetization. For perfectly in-plane orientation of magnetization (i.e. for θ = 0 • ), τ becomes proportional to ∂H k ∂V V rf sinϕ cosϕẑ, as the VC-PMA torques vanish. Then the overall contribution to τ comes mainly from VC-IMA torque. The FMR signal excited by VC-IMA torque and detected through SP-ISHE technique should be proportional to θ 2 c sinϕ , where θ c is the cone angle of magnetization precession. In the linear excitation regime, τ should also be proportional to θ c . Therefore, the FMR signal excited by VC-IMA torque should be proportional to cos 2 ϕsin 3 ϕ for inplane orientation of magnetization [6]. Notably, the FMR, excited by VC-IMA torque, detected through SP-ISHE should produce a perfectly symmetric Lorentzian line shape [66]. In contrast, the Oersted field torque generated due to the induced microwave current should produce a rectified FMR signal with a dispersive line shape through AMR effect [7,67]. It is well known that the spin current (⃗ s) generated from charge-to-spin conversion via SHE can induce torques on magnetization vector ⃗ m which can be damping-like (⃗ m ×⃗ s × ⃗ m) and field-like (⃗ m ×⃗ s) [61,68]. Typically, the damping-like torque produces symmetric Lorentzian line shape, whereas the field-like torque produces dispersive line shape [61,62,67] in the FMR signal. Both, symmetric Lorentzian and dispersive line shape may also be produced because of the detection of FMR by anomalous Hall effect (AHE) [69] of CoFeB layer itself. However, we exclude that effect as our longitudinal measurement geometry should have a negligible contribution from AHE, in spite of the fact that CoFeB shows relatively large AHE [70]. Hence, the symmetric Lorentzian line shape can originate from ISHE voltage for VC-IMA induced and damping-like spin-torque induced FMR. Dispersive line shape originates from AMR voltage from Oersted field induced and field-like spin-torque induced FMR. Now let us look at the angular dependent line shape of the resonance spectra for three devices (see figure 3).  3(a)). In contrast, for devices #2 and #3, the signal amplitudes at 45 • and 225 • are larger than the signal amplitudes at 135 • and 315 • (figures 3(b) and (c)). In this study, we simply analyze the symmetric Lorentzian component to understand the contribution of VC-IMA torque and damping-like spin-torque in the devices. The FMR signal induced by damping-like spin-torque should be proportional to sinϕcos 2 ϕ for x-polarized spin current and sin 2 ϕcosϕ for y-polarized spin current [71,72]. Assuming that the considered torques excite FMR in the linear regime, the magnitude of the symmetric Lorentzian component of detected FMR signals can be expressed as: Here, a, b, and c are the proportionality constants for the FMR signals excited by VC-IMA, x-polarized spin current and y-polarized spin current-induced damping-like torques, respectively.
For each device, we plot the magnitudes of the symmetric Lorentzian component from each resonance spectra as a function of ϕ in

Sample
PMA field (mT) IMA field (mT) same as a for device #1, whereas, for devices #2 and #3, the total values of b and c surpass a. It turns out that the overall spin-torque contribution significantly surpasses the VC-IMA torque contribution for devices #2 and #3, most likely due to higher current density than device #1 (see figures 4(b) and (c)). Interestingly, torque contribution from x-polarized spin current dominates over the y-polarized current for all the devices. We also plot the amplitudes of the dispersive part and the symmetric Lorentzian part of the FMR spectra in figures 4(d)-(f). It can be extracted that the dispersive parts have maximum values up to 30%, 62% and 7% compared to the symmetric Lorentzian parts for devices #1, #2 and #3, respectively. The negligible values of the dispersive part for the Ta buffer layer compared to the Pt buffer layer may be as a consequence of the higher resistivity of Ta compared to Pt. The higher electrical resistance reduces the microwave current density through the Ta layer, limiting Oersted field-induced FMR contribution. Interestingly, although the damping-like torque contribution is much higher than the VC-IMA torque for device #3 compared to device #2, the field-like torque for device #3 is way smaller than device #2, as seen from a negligible dispersive component amplitude in device #3. Finally, it is worthy to note here that the VC-IMA torque contribution (in percentage) for device #3 is lower than device #2, which is expected because of the lower value of IMA and hence lower value of VC-IMA coefficient ∂H k /∂V for device #3 as compared to device #2. In our earlier work, we had explored the voltage controlled magnetization dynamics in the lower frequency regime where VC-IMA is dominant [6]. In contrast, the present study reports the findings in the higher frequency regime where the VCMA and spin torque effects can co-exist.

Comparison with spin-torque induced FMR measurement
Finally, we performed ST-FMR measurement concerning a standard technique to gain a comparative insight into the above results. The measurement was performed in device #1. As shown in figure 5(a), the measurement circuit is the same as generally used for ST-FMR measurement [20,62]. An rf current I rf from a signal generator is sent to the device through the capacitive port of a bias tee. The rf current flows through the Pt and CoFeB films. The rf Oersted field h rf generated by I rf and the spin current generated by Pt buffer layer through direct SHE excites FMR in CoFeB when bias magnetic field H satisfies the resonance condition. The AMR contribution of the CoFeB film originating from the oscillations of magnetization and the I rf are mixed to produce the rectified dc voltage V dc signal, which can be measured through the inductive port of the bias tee. Here, we would like to clarify that AMR in ultrathin CoFeB films is generally very low. However, in present study the thickness of the CoFeB thin films is 2 nm, and we do observe ST-FMR signal from the devices fabricated using these films. The spin Hall magnetoresistance (SMR) could be another source of oscillating magnetoresistance, which can also produce static output signal after mixing with microwave current. The SMR depends on HM/CoFeB interface, rather than CoFeB thickness [73,74]. For SMR, the angular dependence should be sinϕ, whereas for AMR the angular dependence should be sin 2 ϕ,  figure 2(a) to equation (2), whereas values of b, c are extracted by fitting the data points in figure 5(c) to equation (4).

Sample
PMA field (mT) IMA field (mT) with ϕ being the angle between in-plane magnetic-field and microwave current. In our ST-FMR devices, amplitude of the symmetric component of the signals follow the sin 2 ϕcosϕ dependence. Such an angular dependence is well understood to be originated from AMR, where sin 2 ϕ comes from AMR and cosϕ comes from the angular dependence of spin-torque [67]. All these confirm the origin of our resonance signals as AMR, but not SMR. The V dc was measured as a function of H, at fixed microwave frequency of 6 GHz, microwave power of 22 dBm (i.e. 158 mW) for different bias magnetic field orientations ϕ.
The resonance spectra, as plotted in figure 5(b) for ϕ = 45 • , 135 • , 225 • , and 315 • , show the dominance of symmetric Lorentzian component over the dispersive component. We plot the amplitude of the symmetric Lorentzian part as a function of ϕ (see figure 5(c)) and fit to equation (4) by setting the coefficient a = 0, i.e. the contribution from VC-IMA torque as zero. As expected, the data points fit very well to equation (4) with zero VC-IMA torque contribution. From the fitting, the contribution from the y-polarized spin current is found to be negligible compared to the x-polarized spin current due to the flow of current along the long axis, i.e. the y-axis of the rectangular device (see table 2 and figure 5(c)). This arises from SHE in the HM layer with strong spin-orbit coupling. This is in contrast to the previous measurements when FMR is excited by applying microwave signal across the top electrode and CoFeB; the induced current also has a significant component along the short axis (i.e. x-axis) of the device, giving rise to y-polarized spin current. In figure 5(d), we plot the amplitudes of the dispersive part and the symmetric Lorentzian part of the FMR spectra. In this case, the dispersive parts also have two origins: (1) the Oersted field generated because of the microwave current passing through the buffer layer and CoFeB layer, and (2) the field-like torques exerted by the spin current generated as a consequence of the microwave current passing through the buffer layer. From figure 5(d), it can be extracted that the dispersive parts have maximum values up to 30% with respect to the maximum value of the symmetric Lorentzian part in device #1.

Conclusion
In this study, we have investigated rectified voltages of FMR in CoFeB/MgO heterostructures with Pt and Ta buffer layers excited by applying microwave signal across CoFe-B/MgO junction. The excited FMR signals are detected by SP induced ISHE and spin rectification voltages. Interestingly, the measured resonance line shapes deviate from the expected symmetric Lorentzian FMR signal excited by VC-IMA torque, which indicates the presence of other torques. To get more into the details, we performed the measurements of resonance spectra for different orientations of the in-plane magnetic field. When the amplitude of the resonance spectra are plotted as a function of the in-plane angle of bias magnetic field and fitted with an analytical expression including the other possible torques, we find that a significant contribution also comes from the torques induced by spin current and Oersted field because of the flow of microwave current through the buffer layer and CoFeB layer. Surprisingly, the spin-torques and Oersted field torques are found to significantly contribute to the FMR excitation compared to the VC-IMA torque contribution, even for a device with negligible junction current. Notably, the contribution from the spin-torques and Oersted field torques further increases in the presence of a small junction current in the device. Our study shows that utmost care should be taken while analyzing the VC-PMA, VC-IMA induced FMR excitation results. As a guideline, the line shape analysis and angular dependent behavior should always be performed to confirm the electric field-induced excitation.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

B R acknowledges RIKEN Incentive Research Project Grant
No. FY2019. B R also acknowledges the NCN SONATA-16 project with Grant Number 2020/39/D/ST3/02378. The authors sincerely thank Dr Katsuya Miura and Dr Hiromasa Takahashi from the Research and Development Group, Hitachi Ltd, Tokyo, Japan, for preparing the thin films for the study.

Author contributions
B R fabricated devices. A D, B R performed measurements, analyzed data and wrote the manuscript. All the authors discussed the results and commented on improving the quality of manuscript.