PHYSICAL REVIEW X 7, 031018 (2017) 1,2,* 3 1 1 1,2 1,2 Shinji Miwa, Junji Fujimoto, Philipp Risius, Kohei Nawaoka, Minori Goto, and Yoshishige Suzuki Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan Center for Spintronics Research Network, Osaka University, Toyonaka, Osaka 560-8531, Japan Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan (Received 12 February 2017; revised manuscript received 7 June 2017; published 26 July 2017) Torque can be provided to magnetization in nanomagnets directly by electric current and/or voltage. This technique enables electric current (voltage)-to-spin conversion without electromagnetic induction, and has been intensively studied for memory device applications. Among the various kinds of torque, torque induced by spin-orbit splitting has recently been found. However, quantitative understanding of bulk- related torque and interface-related torque is still lacking because of their identical symmetry for current- in-plane devices. In this paper, we propose that a pure interface-related torque can be characterized by spin- torque ferromagnetic resonance with a current-perpendicular-to-plane tunnel junction. Epitaxial Fe- MgO-V tunnel junctions are prepared to characterize the interface-related torque at Fe-MgO. We find that the current-driven torque is negligible, and a significant enhancement of the voltage-driven torque is observed when the MgO barrier thickness decreases. The maximum torque obtained is as large as −5 2 2.8 × 10 J=ðVm Þ, which is comparable to the voltage-controlled magnetic anisotropy of 180 fJ=Vm. The voltage-driven torque shows strong dc-bias-voltage dependence that cannot be explained by conventional voltage-controlled magnetic anisotropy. Tunnel anisotropic magnetoresistance spectroscopy suggests that the torque is correlated to an interface state at the Fe-MgO. This surface-state-sensitive electric modulation of magnetic properties provides new insight into the field of interface magnetism. DOI: 10.1103/PhysRevX.7.031018 Subject Areas: Spintronics I. INTRODUCTION symmetry in CIP multilayers with some torque measure- ment such as spin-torque ferromagnetic resonance (FMR) Electric current or voltage provides torque to magneti- [20,21]. zation in nanomagnets. This enables electric current (volt- While electric current is needed to generate the afore- age)-to-spin conversion without electromagnetic induction mentioned torque, torque can also be induced by voltage and has been intensively studied. alone. For the voltage-driven torque, voltage-controlled Current-driven spin-transfer torque [1,2] has been stud- magnetic anisotropy (VCMA) at a ferromagnet-dielectric ied for memory device applications [3,4]. The spin-transfer interface [22,23] can have a significant influence on the torque can arise in a current-perpendicular-to-plane (CPP) experimentally observed torque vector in CPP magnetic magnetic tunnel junction following spin accumulation tunnel junctions [24,25]. However, in such experiments, a induced by spin injection from a ferromagnetic counter ferromagnetic counter electrode inducing tunnel magneto- electrode [5–8]. The spin-transfer torque can also arise in resistance (TMR) is indispensable for the torque measure- current-in-plane (CIP) multilayers. In the CIP multilayers, ment. Therefore, it is difficult to attain a pure voltage-driven spin accumulation can be induced by spin-dependent torque vector free from spin-transfer torque induced by the scattering in bulk nonmagnetic metals [9–16] or surface counter electrode. conductive states of topological insulators [17–19], which To characterize a pure torque vector originating from a is termed the spin-Hall or Rashba-Edelstein effect. Spin- ferromagnet-nonmagnet interface while avoiding the afore- orbit splitting at a ferromagnet-nonmagnet interface can mentioned issues, we employed a CPP tunnel junction with a also induce current-driven torque , but the existence of single ferromagnetic electrode in the present study. First, the such a torque is still under debate . This is because both system enables us to characterize the interface-related torque the bulk-related and interface-related torques have the same free from the bulk-related one. An electric current flows in a rotational symmetry axis in the CPP tunnel junction; hence, there is no spin accumulation induced by the bulk-spin- email@example.com‑u.ac.jp dependent scattering. On the other hand, torque from Published by the American Physical Society under the terms of ferromagnet-dielectric interface can be observed, which is the Creative Commons Attribution 4.0 International license. understood as the inverse effect of tunnel anisotropic Further distribution of this work must maintain attribution to magnetoresistance (TAMR) . Second, any influence of the author(s) and the published article’s title, journal citation, and DOI. the spin-injection-induced spin-transfer effect could be 2160-3308=17=7(3)=031018(9) 031018-1 Published by the American Physical Society SHINJI MIWA et al. PHYS. REV. X 7, 031018 (2017) excluded because of the nonmagnetic counter electrode. Therefore, the system enables us to discuss the interface- related torque over a wide current density range. Instead of TMR, spin-torque FMR could be performed using TAMR . Moreover, while spin-torque FMR in a CIP multilayer only provides the torquevector direction [12,28], it is feasible to conduct quantitative characterization of the vector com- ponents by employing a CPP tunnel junction [29,30]. We prepared epitaxial Fe-MgO-V tunnel junctions with various MgO thicknesses, giving a wide range of current density. As a result, we found that the interface-related current-driven torque was negligible, but the voltage- driven torque increased as the MgO thickness decreased. The maximum voltage-driven torque was as large as −5 2 2.8 × 10 J=ðVm Þ. This is comparable to the VCMA at a Fe-MgO interface of 180 fJ=Vm, which is larger than any reported VCMA-induced voltage-driven torque [24,25,31–35]. The voltage-driven torque shows nonlinear dc bias voltage dependence, with a maximum around zero dc bias; thus, an electronic state in the vicinity of the Fermi level at a Fe-MgO interface is likely to be of importance to generate the large voltage-driven torque. An interface state at Fe-MgO was also found in the vicinity of the Fermi level from the TAMR spectroscopy. II. EXPERIMENTAL FIG. 1. (a) Schematic illustration of the device structure. Figure 1(a) shows a schematic of the device structure. (b) In-situ reflection high-energy electron-diffraction images of surfaces of the MgO barrier, Fe, and V buffer. An epitaxial single crystalline multilayer of MgOð001Þsubstrate-MgO bufferð5 nmÞ-V bufferð30 nmÞ- Feð0.74 nmÞ -MgOðt ¼ 0.8 – 1.8 nmÞ -Vð3 nmÞ- MgO of the device. The results measured from a tunnel junction Auð30 nmÞ was fabricated by molecular beam epitaxy with t ¼ 0.94 nm are shown. When the magnetic-field under ultrahigh vacuum. The V layer was employed MgO angle is perpendicular to the film plane (θ ¼ 90°), the because of its good lattice match with MgO and because device shows positive magnetoresistance. In an ultrathin it can induce perpendicular magnetic anisotropy in the Fe Fe layer, shape anisotropy and interface anisotropy at a [36,37]. Because the counter electrode is nonmagnetic, it is Fe-MgO interface can be comparable , and an external possible to characterize the torque vector independently magnetic field easily changes its magnetizations from in- from the spin-injection-induced spin-transfer torque. plane to perpendicular. The MR has the same symmetry as During deposition of the MgO buffer and the V buffer, the anisotropic magnetoresistance in ferromagnetic metals substrate temperature was maintained at 150 °C. The V . Figure 2(c) shows the variation of the MR ratio, buffer was post-annealed at 500 °C for 30 minutes. Other defined as the difference in the saturation resistances layers were deposited at room temperature. The multilayer between perpendicular and in-plane magnetic fields, as a was then patterned into 390-nm-diameter tunnel junctions. function of the MgO barrier thickness. The MR ratio is Figure 1(b) shows reflection high-energy electron diffrac- almost identical when the MgO barrier thickness increases. tion images for the surfaces of the V (001) buffer, Fe (001), Hence, the observed MR in a Fe-MgO-V tunnel junction is and MgO (001) barrier, where the incident electron beam not anisotropic magnetoresistance in the metallic Fe layer was parallel to the  and  azimuths of the MgO but TAMR at the Fe-MgO interface. Figure 2(c) shows that substrate. Sharp streak patterns were observed in all layers, the MR ratio decreases for MgO-barrier thicknesses below indicating the formation of epitaxial and flat interfaces. 0.9 nm. It shows that for t < 0.9 nm, the resistance of Figure 2(a) shows the device resistance as a function of MgO the MgO barrier thickness (t ). The device resistance the MgO barrier does not govern the device resistance, and MgO increased exponentially as the MgO barrier thickness the resistance of the metal electrode, which has no MR, increased, indicating tunneling conduction. The right axis significantly contributes to the total device resistance. of Fig. 2(a) shows the resistance-area product (RA), defined Figure 3(a) shows a schematic of the experimental as the device resistance multiplied by the junction area. setup for torque characterization, in which the spin- Figure 2(b) shows a typical magnetoresistance (MR) curve torque FMR combined with TAMR was employed . 031018-2 STRONG BIAS EFFECT ON VOLTAGE-DRIVEN TORQUE … PHYS. REV. X 7, 031018 (2017) FIG. 2. (a) Device resistance as a function of the MgO barrier thickness (t ). (b) Typical TAMR, where t and resistance are MgO MgO 0.94 nm and 189 Ω, respectively. The magnetic-field angle definition (θ ) is depicted in Fig. 3(a). (c) Magnetoresistance ratio as a function of t . MgO Microwave-frequency voltage was applied through a bias magnetic field tilted 45° from the film plane was applied tee to the tunnel junction, and the dc voltage generated in to maximize the dc voltage signals. To characterize the the tunnel junction was measured with a lock-in amplifier. torque vector, the obtained spectra were fit by the following Figure 3(b) shows the definition of the torque vector. The equation [20,21]: blue arrow represents a unit spin vector of the Fe. The ðΔHÞ torque vector components (β , β ) can be expressed as the == ⊥ 2 2 following modified Landau-Lifshitz-Gilbert equation: ðH − H Þ þðΔHÞ FMR ðΔHÞ H − H FMR ds ds A þ V þ aH þ b: AL ¼ γ s × H − αs × − (β s × ðz × sÞ 2 2 0 eff == ΔH ðH − H Þ þðΔHÞ FMR dt dt S pﬃﬃﬃ ð2Þ þ β ðz × sÞ) ηV ; ð1Þ ⊥ rf where s and z are the unit vectors of Fe and the out-of-plane Equation 2 consists of the linear combination of the direction, respectively. H is the effective magnetic field eff Lorentzian function, the first term with the fitting parameter applied to the Fe; γ (<0); and α,S, and A are the V and the anti-Lorentzian function, and the second term gyromagnetic ratio, Gilbert damping constant, and total with the fitting parameter V . Here, H is an external spin-angular momentum in the Fe layer and area of the AL magnetic field, and V , V , resonant field (H ), line- tunnel junction, respectively. Here, η is the transmission L AL FMR width (ΔH), and linear background (a, b) are taken as efficiency of voltage due to the impedance mismatch fitting parameters. From the fitting parameters of V and between the tunnel junction and the transmission line, V , torque vector components of β and β can be and V is the amplitude of the voltage in the transmission AL == ⊥ rf line from the microwave generator. Hence, the amplitude of obtained using the following equation: pﬃﬃﬃ ηV is the applied microwave-frequency voltage in the rf 1 RðθÞðR − R Þ tunnel junction. The definition and experimental method to θ¼0° θ¼90° V ¼ − sin θ sin 2θ LðALÞ obtain η are provided in our previous paper .Ina 2 R R θ¼0° θ¼90° precise sense, γ should be a tensor. However, during FMR ==ð⊥Þ × ηðV Þ : ð3Þ measurements, the magnetization angle did not change RF 2πγ ΔH significantly. Hence, we treated it as a constant. Note that z is the rotational symmetry axis if we do not take into To derive Eq. (3), we employed the analysis provided in account the fourfold crystal structure in the system. −1 Ref.  and angle dependence of the TAMR, R ðθÞ¼ Therefore, z should be the reference vector in the system, −1 −1 −1 −1 ðR þR Þ=2þðR −R Þ=2 × cos2θ. θ¼90° θ¼0° θ¼90° θ¼0° and the coordinates of s × ðz × sÞ and z × s are employed Here, RðθÞ is the device resistance when the spin-vector to express the torque vector (β , β ). Although there can == ⊥ direction defined in Fig. 3(b) is θ. From the angle be an in-plane symmetry breaking axis due to the crystal dependence of the TAMR, we can deduce the values of structure of Fe, the z reference axis is a standard and most θ in the torque analysis. suitable choice because we apply the current or voltage in the z direction. In all of the experiments in this study, the III. RESULTS AND DISCUSSION direction of in-plane projection of s is set to x, which corresponds to  azimuth of the Fe. Figure 3(c) shows Figure 4(a) shows torque vector components in typical spin-torque FMR spectra of a tunnel junction with Fe-MgO-V tunnel junctions, which were obtained by t ¼ 0.94 nm and microwave power of 0.1 μW. A spin-torque FMR spectra and Eqs. (2) and (3). Black MgO 031018-3 SHINJI MIWA et al. PHYS. REV. X 7, 031018 (2017) rf (a) Microwave oscillator dc voltage Ref (5.5 kHz) Bias-tee Lock-in amp. dc bias (c) t = 0.94 nm MgO 2 GHz (b) 4 GHz 0.1 µV 6 GHz 8 GHz 10 GHz 0 0.1 0.2 0.3 0.4 Magnetic field (T) FIG. 3. (a) Schematic illustration of the measurement setup. (b) Definition of perpendicular (β ) and in-plane (β ) torque. (c) Typical ⊥ == spectra for spin-torque FMR. The magnetic-field direction is θ ¼ 45°, and the input power (P )is 0.1 μW. H rf and red circles represent perpendicular and in-plane com- Fig. 4(a) shows that the maximum torque was about −5 2 ponents, respectively. The measurements were conducted 2.8 × 10 J=ðVm Þ, which is the same as the voltage- under a magnetic-field angle of θ ¼ 45°, and input driven torque induced by the large VCMA of 180 fJ=Vm at microwave power and frequency were set to P ¼ the Fe-MgO interface. To the best of our knowledge, this rf 0.1 μW and 5 GHz, respectively. First, a significant in- is larger than any previously reported VCMA-induced plane component was not observed in every device, and the voltage-driven torque [24,25,31–35]. perpendicular component was dominant. The theory pre- Figure 4(b) shows the input power dependence of dicted that the current-driven in-plane torque could be peak-to-peak dc voltage in the spin-torque FMR spectra dominant because of interfacial spin-orbit splitting ,but of devices with t ¼ 0.94 nm. The microwave frequency MgO this is inconsistent with our observation. This does not was 5 GHz. A linear relation between the peak-to-peak mean that there are some problems with the theoretical voltage and the input power is only confirmed in the small −4 estimation of the in-plane torque in Ref. . The incon- input power region, namely, less than 10 mW. This sistency might be because the simple model employed in indicates that large spin precession is excited by only a Ref.  did not include the physics that can induce the small input power, which is consistent with the large torque large perpendicular torque in our experiment. Second, the vector components obtained in Fig. 4(a). More quantita- perpendicular torque is voltage driven. The variation of tively, the magnetization precession angle (1.5° at −4 the perpendicular torque in Fig. 4(a) is at most twice as P ¼ 10 mW) is of the same order as that of the highly rf large, whereas the current density of the tunnel junction sensitive spin-torque diode device with low resistance-area 2 −4 with t ¼ 0.8 nm is 140 times larger than that with t ¼ MgO MgO product (2.5 Ω μm , 3.6° at P ¼ 10 mW) . rf 1.4 nm. Therefore, the perpendicular component is not current To characterize the VCMA at the Fe-MgO interface in driven but voltage driven. Note that the current-induced the device, the dc-bias-voltage dependence of the resonant magnetic field cannot be the origin of the voltage-driven field was characterized as shown in Fig. 4(c). Microwave perpendicular torque. Any influence of the spin-Hall effect frequency and power were 5 GHz and 0.1 μW, respec- from the V underlayer is also excluded in the same manner. tively. Figure 4(c) shows that the resonant field changes We have also characterized the in-plane magnetization almost linearly as a function of the dc bias voltage. The direction (φ) dependence of the torque, but significant resonant field change corresponds to a VCMA of about change was not observed, which also supports our premise 20 fJ=Vm. Note that the VCMA of 20 fJ=Vm is too small that the current-induced magnetic field and the spin-Hall to reproduce the observed large perpendicular torque effect are not the origin of the torque. The analysis above component in Fig. 4(a). shows that the voltage-driven perpendicular torque origi- Figure 4(d) shows a dc-bias-voltage dependence of the nates from the Fe-MgO interface. The dashed curve in perpendicular torque component. The torque was 031018-4 dc voltage (µV) STRONG BIAS EFFECT ON VOLTAGE-DRIVEN TORQUE … PHYS. REV. X 7, 031018 (2017) (a) (c) 1.44 1.43 1.42 sin 1.41 1 sin 1.40 0 t = 0.94 nm MgO 1.39 0.8 1.0 1.2 1.4 -0.2 -0.1 0.0 0.1 0.2 t (nm) dc bias (V) MgO (b) (d) sin 1.7 V/W -1 t = 0.94 nm t = 0.94 nm MgO MgO -2 -5 -4 -3 -2 -0.2 -0.1 0.0 0.1 0.2 10 10 10 10 dc bias (V) P (mW) RF FIG. 4. (a) Torque vector components. Black and red circles represent perpendicular (β ) and in-plane (β ) torque, respectively. The ⊥ == dashed curve shows the theoretical line of the torque induced by the voltage-controlled magnetic anisotropy of 180 fJ=Vm. (b) Input power dependence of peak-to-peak dc voltage in the spin-torque FMR spectra. (c) The dc-bias-voltage dependence of the resonant field. (d) The dc-bias-voltage dependence of the perpendicular torque. All data were obtained with a magnetic-field angle of θ ¼ 45° and an input microwave frequency of 5 GHz. characterized by Eq. (3), where dc-bias-voltage depend- measured using the dc two-terminal method, and it is ence of the MR ratio is included. The torque shows displayed in Fig. 5(a) as black circles. The data in Fig. 5(a) nonlinear dc-bias-voltage dependence and takes its maxi- can be fitted using the following equations [40,41]: mum around zero dc bias. The dependence is unique because the reported VCMA at a Fe-MgO interface is −1 RðθÞ ¼ G cos 2nθ; ð4Þ linear [24,25,31–33]; hence, VCMA-induced voltage- 2nθ n¼0 driven torque should be independent of the dc bias. From the discussion above, the Fe-MgO-V tunnel cos θ H cos θ − H cos θ H d junction shows large voltage-driven perpendicular torque. ¼ : ð5Þ sin θ H sin θ The torque originates from the Fe-MgO interface; however, it cannot be explained by conventional VCMA at the Fe- MgO interface. Namely, the spin torque is equivalent to a Here, H, θ, and θ are, respectively, the magnetic field dynamic VCMA of 180 fJ=Vm; however, the Fe-MgO H strength, magnetization angle, and magnetic field angle interface shows a static VCMA of only 20 fJ=Vm. In the defined in Fig. 3(a). Note that H is the saturation magnetic previous studies of Fe(Co)-MgO interfaces, a static VCMA field in the perpendicular direction (θ ¼ 90°), and G of 20–30 fJ=Vm was reported [24,37,39], which is con- H 2nθ are fitting coefficients. The red curves in Fig. 5(a) are the fit sistent with the present study. In addition, dynamic VCMA results. Fit coefficients of twofold (G =G ) and fourfold was observed, as the voltage-driven torque was basically 2θ 0 (G =G ) components are depicted in Figs. 5(b) and 5(c). identical to the static VCMA [24,25,32,33]. Contrary to 4θ 0 The error bars in Figs. 5(b) and 5(c) are the results when H this, the dynamic VCMA is several times larger than that of varies from 0.4 to 0.7 T. the static VCMA in the present study. The TAMR is correlated with electronic states at the Figure 4(d) shows that electronic states at the Fe-MgO interface around the Fermi level are likely to have a strong Fe-MgO interface [40–42]. The origin of the twofold influence on the unique torque property. Hence, to char- component in the TAMR is similar to the AMR. The acterize the electronic state of the Fe-MgO interface, the twofold component can appear if one symmetry axis exists: dc-bias-voltage dependence of the TAMR was character- that is, electric current direction and spin-dependent scat- ized. For this purpose, a device with t ¼ 1.77 nm, with tering due to the spin-orbit interaction at the Fe-MgO MgO interface. The fourfold component cannot be explained in 10-μm -sized junctions, was fabricated. The magnetoresist- ance under 1.5 T at various magnetic field angles was the same manner. It should be correlated with the crystal 031018-5 Peak-to-peak voltage (μV) -5 2 Spin-torque (10 J/(Vm )) -5 2 Spin-torque (10 J/(Vm )) SHINJI MIWA et al. PHYS. REV. X 7, 031018 (2017) (a) (b) dc bias t = 1.77 nm 0.2% MgO +0.80 V +0.60 V +0.40 V +0.20 V +0.05 V -0.8 -0.4 0.0 0.4 0.8 −0.05 V dc bias (V) (c) 0.6 −0.20 V 0.4 Fe V 0.2 −0.40 V −0.60 V 0.0 −0.80 V -0.2 Fe -0.4 -90 -60 -30 0 30 60 90 -0.8 -0.4 0.0 0.4 0.8 θ (deg.) dc bias (V) FIG. 5. (a) The dc-bias-voltage dependence of TAMR. Black circles and red curves are experimental data and fitting curves using Eq. 4, respectively. (b) Twofold component of the TAMR. (c) Fourfold component of the TAMR. structure of Fe and/or MgO that has fourfold symmetry. As obtained with post-annealing. Contrary to this, post- shown in the previous study , the fourfold component annealing was not conducted in the Fe-MgO tunnel in the TAMR indicates the existence of an interface state at junction in the present study. In addition, we have also the Fe-MgO interface. Figure 5(c) shows that the fourfold conducted similar measurements with the same sample component is not significant under negative dc bias and that post-annealed at 250 °C for 30 minutes, and we found that it is only significant under positive bias. This indicates that the magnitude of the torque was almost identical to as- an interface state at the Fe-MgO interface exists around the deposited devices, but the perpendicular magnetic Fermi level of the Fe as schematically shown in the inset of anisotropy and ferromagnetic resonance linewidth of the Fe slightly increased. Therefore, it should be noted that Fig. 5(c). An interface resonance state with a similar energy the existence of the large torque is robust to the sample level at the Fe-MgO interface is also reported in previous fabrication process. The only unique point in our sample studies [43,44]. Interestingly, the torque component in is the small MgO barrier thickness (<1.1 nm). All of Fig. 4(d) takes its maximum when the energy level is the previous studies concerning VCMA in magnetic almost identical to the interface state characterized by the tunnel junctions employed thicker MgO barriers than the angular dependence of the TAMR as shown in Fig. 5. present study. As discussed, the Fe-MgO-V tunnel junction in the The influence of electrochemical reactions [50–53] and/ present study shows unique properties as compared with or charge traps  should be discussed as a possible origin previous studies [24,37,39]. Namely, the dynamic VCMA of the large torque. However, in such cases, dynamic that induces voltage-driven perpendicular torque is several VCMA inducing torque should be smaller than static times larger than the static VCMA. Finally, we would like VCMA. This is because electrochemical reactions and/or to discuss unique points in the device structure and possible charge trap inducing static VCMA have limited operation origins of the large voltage-driven torque. speed owing to thermal activation processes. Moreover, it is The V buffer layer is worth discussing because it is a reported that there is no voltage-driven electrochemical unique feature of the device structure, and V can form an reaction that substantially changes a valence state of d alloy with Fe. In addition, because the lattice constants of orbitals [54–56]. Fe, V, and MgO are 0.286, 0.303, and 0.298 nm, respec- To explain the observed phenomena in a different way, tively, the in-plane lattice constant of the Fe can be they occur only when very high frequency (>GHz) or small expanded. It is reported that the underlayer material can pﬃﬃﬃ −4 (for instance, ηV under P ¼ 10 mW is 3.2 mV) change the VCMA coefficient and its dc-bias-voltage rf rf dependence at the Fe(CoB)-MgO interface [36,45–49], external voltage is applied; thus, a large voltage-driven which can be induced by alloying with the underlayer perpendicular torque was induced. Hence, if the MgO materials  and/or lattice distortion [48,49].However,in barrier in the tunnel junctions has some localized state  all the studies mentioned above, large modified VCMAwas and its capacitance shows dc-bias-voltage dependence, then 031018-6 MR -3 -3 −G / G (10 ) G / G (10 ) 4 0 2 0 STRONG BIAS EFFECT ON VOLTAGE-DRIVEN TORQUE … PHYS. REV. X 7, 031018 (2017)  J. Z. Sun, T. S. Kuan, J. A. Katine, and R. H. Koch, Spin the nonlinearity in the bias dependence of the torque can be Angular Momentum Transfer in a Current-Perpendicular explained. In either case, nonlinear dc-bias dependence of Spin-Valve Nanomagnet, Proc. SPIE Int. Soc. Opt. Eng. the voltage-driven torque in Fig. 4(d) demonstrates the 5359, 445 (2004). importance of the surface state at the Fe-MgO interface.  H. Tomita, S. Miwa, T. Nozaki, S. Yamashita, T. Nagase, K. Interestingly, the voltage-driven torque takes its maximum Nishiyama, E. Kitagawa, M. Yoshikawa, T. Daibou, M. around the interface state at the Fe-MgO interface as shown Nagamine, T. Kishi, S. Ikegawa, N. Shimomura, H. Yoda, in Fig. 5. For further discussion, a theoretical approach and Y. Suzuki, Unified Understanding of Both Thermally including a first-principles study would be indispensable. Assisted and Precessional Spin-Transfer Switching in Perpendicularly Magnetized Giant Magnetoresistive Nano- IV. CONCLUSION pillars, Appl. Phys. Lett. 102, 042409 (2013).  S. Miwa, S. Ishibashi, H. Tomita, T. Nozaki, E. Tamura, K. To conclude, the torque vector at an epitaxial Fe-MgO Ando, N. Mizuochi, T. Saruya, H. Kubota, K. 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V. voltage-driven torque component shows nonlinear dc- Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, bias-voltage dependence, and it takes its maximum when and P. Gambardella, Perpendicular Switching of a Single the energy level is in the vicinity of the Fermi level, where Ferromagnetic Layer Induced by In-Plane Current Injec- the interface state at the Fe-MgO interface is also located. tion, Nature (London) 476, 189 (2011). This surface-state-sensitive electric modulation of magnetic  L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, properties provides new insight in the field of interface Spin-Torque Ferromagnetic Resonance Induced by the Spin magnetism. Hall Effect, Phys. Rev. Lett. 106, 036601 (2011).  L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. ACKNOWLEDGMENTS Buhrman, Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum, Science 336, 555 (2012). We thank E. Tamura and Y. Niimi of Osaka University,  Y. Niimi, Y. Kawanishi, D. H. 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Published: Jul 1, 2017
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