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

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Sharlene Robertson
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1 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 in the spin-torque diode experiment. Figure S1a shows the magnetoresistance curve of the sample. The resistance-area product of this sample is 2 Ω µm 2, which is the same as the value of the main text. The MR ratio of this sample, 162%, is slightly larger than the value in the main text, 154%, but such a difference is within the usual sample-to-sample variation among samples in our experiment. We applied sequential pulse currents with long pulse duration of 2 ms to measure the resistance under biases. We observed current-induced switching, as shown in Fig. S1b, which was obtained under an external field of -25 Oe. We changed the external field to check the symmetry of the switching current/voltage. Around the center of the minor loop (ca. -2 Oe), the switching voltage for P to AP state is about 3 mv; the reverse switching voltage is about -2 mv. These switching voltages were smaller than the intrinsic ones (-27 mv for AP to P, +38 mv for P to AP, which were obtained from the pulse duration dependence of the switching current in other sets of samples) because switching under long pulses is affected by thermal excitation.

2 Figure S1. Current induced magnetization switching in a CoFeB/MgO/CoFeb MTJ: a, magnetoresistance curve; b, a typical result of current-induced switching; c, switching voltage; and d, switching current as a function of an external magnetic field. The MTJ was prepared on the same wafer of the sample used in the spin-torque diode experiment described in the main text. The junction area, 7 nm 16 nm, was slightly smaller, but the switching current density and switching voltage are independent of the junction area.

3 S2. Determination of microwave current based on S 11 measurement. For STD effect measurements, we set a microwave power of -15 dbm for the signal generator output, which corresponds to a microwave current of about.8 ma for a load resistance of 5 Ω. Because of the wire and capacitance in the sample, the current attenuates at an MTJ, which is expressed as η. We performed a theoretical fit to complex reflectivity S 11 based on an equivalent circuit model to evaluate an actual value of the microwave current passing through the MTJ. Complex reflectivity S 11 is defined as S 11 =(Z-Z )/(Z+ Z ), where Z and Z respectively represent the impedance of the sample and characteristic impedance of the system (5 Ω). In addition, S 11 is measured using a vector network analyzer. Figure S2a depicts the frequency dependence of S 11. Dots are experimental values and lines show theoretical fits based on an equivalent circuit model, as illustrated in Fig. S2b. In addition, Z consists of an MTJ s resistance (R ) and parallel impedance (Z p ), which correspond to a capacitive current path through the thick SiO 2 layer in the vicinity of the MTJ. The resistance was measured using a two-point-probe method. Therefore, R is the sum of tunnel resistance of 233 Ω and electrical lead resistance of 177 Ω. Such a high lead resistance is attributable to the thin bottom electrode film and to the narrow width of the bottom and top electrode patterns. The values of C p and R p are fitting parameters, determined respectively as.7 pf and 19.4 Ω. In addition, η is expressed as η =(Z / R ) 2Z/(Z+Z ) 2. In the figure, η is shown as a blue line exhibiting a slight decrease with frequency. Around a resonance frequency of about 6.7 GHz, η is about.38.

4 Figure S2. Analysis of the S 11 properties using an equivalent circuit model. a, Complex reflectivity is shown as a function of the input rf frequency. Circles show experimental results and red lines show the theoretical fit. In the present experiment, R is much larger than Z ; the real part of S 11 is large at low frequencies. Both real and imaginary parts decrease with increased frequency because of the parallel impedance Z p. The blue line represents η, which is the rf correction. In addition, η =1 signifies that the rf currents do not attenuate until reaching the MTJ. In this result, η is rather small, but almost constant for the frequency examined. b, The equivalent circuit model used in the theoretical fit for S 11. Here, C p and R p correspond to a capacitive current path through the thick SiO 2 layer.

5 S3. Analysis of the spin-torque diode spectrum. The parameters used in fitting (Fig. 3 in main text) are shown as a function of the bias voltage in Fig. S3. The line width, Δ, decreases at the negative bias and is almost constant in the positive bias. The ω increases with the bias. The effective damping parameter (α eff = Δ /(ω aa + ω bb )) is also shown in Fig. S3c. To check the consistency of the fitting results, we calculated Δ and ω. The calculated Δ I ( = "(# aa + # bb ) $ ' b & ST % IdI cos 2 ( 12 ) are similar to the observed value. The discrepancy in the negative bias is likely to be caused by the imperfect subtraction of the background signal. The α, the zero bias value of α eff, is about.11, which is slightly larger than the value (ca..7) observed in conventional ferromagnetic resonance (FMR) experiments (frequency of ca. 9 GHz). Therefore, it is confirmed that the peak width is well reproduced. On the contrary, calculations of ω do not reproduce the experimental dependence. For calculations, we considered two cases: we took into account only STT (corresponds to Calc., STT in Fig. S3b, where " 2 = " aa " bb + " 2 ST ), and both STT and FLT (corresponds to Calc., STT+FLT in Fig. S2b, where " 2 I = (" aa + % b $ FT # IdI cos& 12 ) " + I ( $ # IdI bb % b FT cos& 12 ) + " 2 ST ). Therefore, the large shift of the resonance frequency is difficult to explain by considering STT and FLT only. Because the shift varies from sample to sample, it can be related to the micromagnetic character of samples. Further study is necessary to explain the bias dependence of the resonance frequency. Figure S3d shows the dependence of β ST and β FT on the bias: β ST depends slightly on bias at low biases V b <1 mv, but changes rapidly at large biases V b >1 mv. In addition, β ST is bias-dependent and cannot be treated as a constant to describe the motion of S 2 ; β FT is smaller than β ST, but is also bias dependent. It is interesting that β FT changes its sign depending on the bias voltage sign. We expect that these experimental data are useful to clarify the relation between the electronic band structure of the interface and the spin torque.

6 Figure S3. Bias dependence of the parameters used in fitting (Fig. 3): a, linewidth (Δ) I b ( ) % & (red, observed; black, calculated as " = # $ aa + $ bb ( ' ST IdI cos 2 ) 12 ); b, resonance angular frequency (ω ) (right axis, f =ω /2π) (red, observed) with calculation taking account of spin torque (black, only STT; blue, both STT and FLT); c, effective damping parameter (α eff = Δ /(ω aa + ω bb )) obtained from the observed linewidth (Δ, which corresponds to red in a); and d, torque coefficient (red, # ST " ; blue, # FT " ).

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION 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