SUPPLEMENTARY INFORMATION

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Christine Harrell
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1 Induction of coherent magnetization switching in a few atomic layers of FeCo using voltage pulses Yoichi Shiota 1, Takayuki Nozaki 1, 2,, Frédéric Bonell 1, Shinichi Murakami 1,2, Teruya Shinjo 1, and Yoshishige Suzuki 1,2,* 1 Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan 2 CREST, Japan Science Technology Agency, Kawaguchi, Saitama, Japan Present address: Spintronics Research Center, AIST, Tsukuba, Ibaraki, Japan 1. Quantitative evaluation of magnetic anisotropy change by voltage application There are several approaches to evaluating the voltage-induced PMA change in MTJs spin-transfer-induced ferromagnetic resonance (FMR) measurements using a rectifying effect 21 and magnetoresistance (MR) measurement 22 under different bias voltage applications. Here, we used an electrical FMR measurement from the magnetic noise spectrum; this method is relatively simple while still being adequate for quantitative evaluation. Since the thermal energy excites the dynamics of the magnetization and is resonantly enhanced at the FMR frequency, a Lorentzian-type peak noise appears in the noise spectrum 27. If we assume that crystalline anisotropy and saturation magnetization are not affected by the voltage application, the voltage-induced surface anisotropy change can be estimated from the observed peak frequency shift under a constant external magnetic field. For the magnetic noise measurement, we used a lock-in modulation technique. A schematic illustration of the measurement setup is shown in Fig. S1a. A dc bias voltage with a small ac modulation current (180 μa at 20 khz) was applied to the MTJ through the dc port of the bias tee. The rf voltage was detected by a spectrum analyzer after amplification (+40 db). The frequency-selected noise, which appeared at the intermediate frequency output of the spectrum analyzer, was rectified by a quadratic diode detector. The detected voltage, which is proportional to the noise spectrum intensity, is finally detected by the lock-in amplifier. Owing to this lock-in NATURE MATERIALS 1

2 modulation technique, we can suppress the influence of other electrical noise such as the Johnson noise. Figure S1b shows the resonant frequency f 0 as a function of the applied electric field under a perpendicular magnetic field of 3000 Oe; this value is higher than H s,perp (~1500 Oe). Subsequently, H s,perp was obtained using the modified Kittel s formula 28 for the perpendicular external magnetic field, as follows: ( H ext H s,perp )( H ext H s,perp + H c ) H ext H s, perp γ f 0 = ; > 2 π (S1), where H c and H s,perp denote the in-plane coercive field and saturation magnetic field in the perpendicular direction, respectively. The term γ (= Hz/Oe) represents the gyromagnetic ratio of FeCo 29. The calculated value of H s,perp, from eq. (S1), is shown on the right vertical axis of Fig. S1b. In the negative (positive) voltage region, the PMA is induced (suppressed) by increasing the applied voltage; this observation is consistent with our previous results 6,16,21,22. PMA changes linearly in the investigated electric field range, and no hysteretic behaviour was observed. The estimated slope of the anisotropy change was 38.5 fj/vm. This value is almost consistent with that obtained in our previous works 21,22. a Bias Tee b Fe (10) MgO (1.5) FeCo (0.7) Au H ext 1kΩ 2kΩ Lock-in amplifier RF pre-amp 40 db Frequency : 20 khz Amplitude : 0.4 V Spectrum analizer IF out Detector (Quadratic detection) Fig. S1 a, Schematic diagram of experimental setup for magnetic noise measurement using a lock-in modulation technique. b, Ferromagnetic resonance (FMR) frequency of ultrathin FeCo layer as a function of applied electric field measured under a perpendicular magnetic field of 3000 Oe. The right vertical axis indicates the perpendicular saturation field calculated from eq. (S1). f 0 (GHz) E lectric field (mv/nm) ΔK s (V) = 38.5fJ /Vm H s,perp (Oe) 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION 2. Influence of pulse-current-induced magnetic field and spin-transfer torque The possible effects of magnetic field pulses 30 and/or the spin-transfer torque 1,2 in our experiments are explained in this section. The maximum current in our experiment was -3.8 ma, which corresponds to a current density of A/m 2. By considering the design of the co-planar waveguide type electrode (thickness = 0.1 μm, signal line width = 4 μm), the applied current pulse can produce a magnetic field as high as 12 Oe from a rough estimation upon using Ampere s law. The field strength value is approximately 1/67 of the anisotropy field change induced by the voltage pulse, and it may have only a negligibly small effect. In addition, since this value is smaller than the in-plane coercive field, the Oersted field cannot excite coherent magnetization switching. As pointed out in main text, the spin-transfer torque is an anti-damping (damping) torque for the negative (positive) applied pulse in the AP state. Therefore, it may cause a switching from the AP to the P state; however, a switching from P to AP cannot occur without change in the polarity of the pulses. Therefore, we can exclude spin-transfer switching in our experiment with certainty, in which two-way toggle switching was realized by employing electric pulses with unique polarity (Fig. 3 b). In order to quantitatively discuss the magnitude and effect of the spin-transfer torque, we investigated pulse-current-induced magnetization switching (CIMS) by employing an identical MTJ structure but with a thinner MgO tunnelling barrier (1.20 nm), since too large a resistance of the sample employed in the voltage switching experiments prevents the CIMS measurements. Figure S2a shows the magnetoresistance curve of the minor loop under a magnetic field in the in-plane easy-axis direction. From this measurement, the resistance-area product in the parallel state and the magnetoresistance ratio are 10 Ωμm 2 and 14.5%, respectively. Subsequently, CIMS was measured under an external magnetic field of 76 Oe; this field compensated for the offset field originating from the dipole coupling (Fig. S2a). Figure S2b shows the critical switching current I c measured at NATURE MATERIALS 3

4 different current-pulse durations (τ pulse ) from 10-6 s to 10-1 s. All the measurements in each pulse duration were repeated five times. All the pulse duration results are summarized in Fig. S2b with the fitting in the thermal activation region described as following equation 31 : I 1 τ 1 ln Δ τ ( 10 s τ 10 s) pulse c = I c 0 pulse (S2) Here, I c0 and Δ denote the intrinsic switching current and thermal stability, respectively, as the fitting parameters. According to the fitting, the averaged value of I c0 was estimated to be 5.8 ma, and from this value, Slonczewski s spin-transfer efficiency was estimated to be g = 0.07 for the AP state. This small value of efficiency can be attributed to the small MR effect and the small free-layer thickness in our sample. a Resistance (Ω) Magnetic field (Oe) I c (ma) b τ pulse (ms) P AP AP P Fig. S2 Results of current-induced magnetization switching experiments done using a similar MTJ with a thinner MgO barrier (1.2 nm). a, MR curve of minor loop under magnetic field in the in-plane easy-axis direction. b, Critical switching current I c as a function of pulse duration τ pulse. Using the spin-transfer efficiency obtained in the abovementioned experiment, we simulated the switching probability as a function of pulse duration in the same magnetic state for pulse-voltage-induced magnetization switching (VIMS) and CIMS.; this is shown in Figs. S3a, b. Both simulations were performed under the assumptions that the temperature was 300 K and the external magnetic field of 700 Oe was tilted 6 from the film normal. We used the macro-spin model 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION simulation, using the identical parameters as in the main experiment (in the main text) for α, H c, H dipole, and H s,perp. For VIMS (blue circles in Figs. S3a, b), the switching probability shows clear oscillations and acquires a constant value of 0.5 in the longer pulse duration interval owing to influence of thermal fluctuation. These observations are in good agreement with the results discussed in main text (Fig. 4). In the case of CIMS, H s,perp was assumed as a constant (1400 Oe), and a spin-transfer torque that was calculated using the spin-transfer efficiency obtained (as mentioned above) was added for a pulse current, I = -3.8 ma. Since no switching was observed for both polarities (not shown), we also calculated spin-transfer switching in a sample with a spin-transfer efficiency that was enhanced by a factor of 2, although it may exceed the maximum error in our estimation (red circles in Figs. S3a, b). There is no P to AP switching; however, AP to P switching occurs. The switching probability is still less than 1 within 8 ns, and it reaches 1 with pulse durations of more than 20 ns (not shown). From these calculations, we conclude that the effects of the spin-transfer torque on the magnetization switching are negligibly small in our experiments. In particular, in very short time regions, the phenomena are governed by voltage-induced anisotropy change. a P switch AP to P τ pulse (ns) VIMS CIMS b P switch P to AP VIMS CIMS τ pulse (ns) Fig. S3 Switching probability as a function of pulse duration. a, from AP to P switching and b, from P to AP switching. Red and blue circles indicate VIMS and CIMS. NATURE MATERIALS 5

6 Supplementary References: 27 Petit, S. et al. Spin-torque influence on the high-frequency magnetization fluctuations in magnetic tunnel junctions. Physical Review Letters 98, (2007). 28 C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, New York, 2005). 29 Schreiber, F., Pflaum, J., Frait, Z., Mühge, T. & Pelzl, J. Gilbert damping and g-factor in FexCo1-x alloy films. Solid State Communications 93, (1995). 30 Schumacher, H. W. et al. Phase coherent precessional magnetization reversal in microscopic spin valve elements. Physical Review Letters 90, (2003). 31 Koch, R. H., Katine, J. A. & Sun, J. Z. Time-resolved reversal of spin-transfer switching in a nanomagnet. Physical Review Letters 92, (2004). 6 NATURE MATERIALS

S1. Current-induced switching in the magnetic tunnel junction.

S1. Current-induced switching in the magnetic tunnel junction. Current-induced switching was observed at room temperature at various external fields. The sample is prepared on the same chip as that used