Supplementary material for : Spindomain-wall transfer induced domain. perpendicular current injection. 1 ave A. Fresnel, Palaiseau, France

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1 SUPPLEMENTARY INFORMATION Vertical-current-induced Supplementary material for : Spindomain-wall transfer induced domain motion wallin MgO-based motion in MgO-based magnetic magnetic tunnel tunneljunctions controlled with by low current densities perpendicular current injection A. Chanthbouala, 1 R. Matsumoto, 1 J. Grollier, 1 V. Cros, 1 A. Anane, 1 A. Fert, 1 A. V. Khvalkovskiy, 1, 2, K.A. Zvezdin, 2, 3 K. Nishimura, 4 Y. Nagamine, 4 H. Maehara, 4 K. Tsunekawa, 4 A. Fukushima, 5 and S. Yuasa 5 1 Unité Mixte de Physique CNRS/Thales and Université Paris Sud 11, 1 ave A. Fresnel, Palaiseau, France 2 A.M. Prokhorov General Physics Institute of RAS, Vavilova str. 38, Moscow, Russia 3 Istituto P.M. s.r.l., via Cernaia 24, Torino, Italy 4 Process Development Center, Canon ANELVA Corporation, Kurigi 2-5-1, Asao, Kawasaki, Kanagawa , Japan 5 National Institute of Advanced Industrial Science and Technology (AIST) Umezono, Tsukuba, Ibaraki , Japan nature physics 1

2 supplementary information Supplementary note 1 : spin diode As illustrated on Fig.1 (a), the magnetic field is applied in plane along the hard axis of the ellipse, and is chosen large enough to saturate the magnetization of the free layer (experimental applied field range e, larger than the shape anisotropy field of 250 Oe). The dc current is swept between -0.9 and +0.9 ma. The microwave current (injected power -15 dbm) is modulated (on/off 1:1) in order to increase the precision. (a) H z m θ 0 θ M y (b) (frequency) 2 (GHz) hard axis magnetic field (T) (c) mixing voltage (µv) Oe -0.7 ma frequency (GHz) (d) mixing voltage (µv) Oe +0.7 ma frequency (GHz) FIG. 1: (a) Sketch of the sample geometry (b) Frequency square versus magnetic field determined from spin diode experiments at zero dc bias (c) and (d) black line : Experimental mixing voltage as a function of the frequency for two dc bias : and ma, with a fixed applied magnetic field of Oe. The background offset signal V background is substracted. Red line : Fit The Landau-Lifshitz-Gilbert (LLG) equation of motion including the two components of the spin torque is expressed as : dm dt = γm H eff + αm dm dt + T STT (1) with α the damping parameter. In our geometry where we apply the magnetic field H along the hard axis of the ellipse, the effective field H eff can be written as : H eff =(H H A ) u z H d m x u x (2) 2 nature physics

3 supplementary information u x and u z are the unit vectors along the large and small axis of the ellipse, H A and H d are the in plane shape anisotropy and out of plane demagnetizing fields. When a microwave current is injected, close to the resonant frequency, the magnetization is set into motion, an oscillatory resistance arise, and a rectifying voltage is built : we neglect the additional terms V θ and 1 2 V θ 2 θ 2 V mix = 2 V I θ (3) I θ [ θ 2 ]. Wang et al. [1] have shown that these corrective terms have a small effect on the determination of the out-of-plane field-like torque. Using the LLG equation, we calculate : V mix = 1 8 TMR R R AP R +2I R I i 2 hfsin 2 θ X (ω2 0 ω 2 )+Yω 2 (ω 2 0 ω 2 ) 2 + ( ω) 2 (4) By neglecting the changes of equilibrium position due to the dc spin torque (< 8 % in our case), and taking into account that the magnetization of the free layer is saturated along u z, the two amplitudes X and Y are given by : X γ 2 H d b J I Y γ a J I (5) γa J and γb J are respectively the amplitudes of the in-plane and out-of-plane torques. To determine H d we have performed additional spin diode measurements at zero bias while sweeping the magnetic field, shown on Fig.1 (b). The resultant frequency versus field curve is then fitted with the Kittel formula, which gives H d = 1 T., X and Y are determined for each bias by fitting the spin diode spectra. Fitting examples are given on Fig.1 (c) and (d). The background offset voltage V background was substracted from these curves. V background = 1 2 V 8 I 2 i2 hf (6) The injected microwave current of i hf = 40 µa corresponding to the source power of - 15 dbm was determined from this background offset signal of the spin diode spectra [2]. With our samples, two modes are systematically observed, as is often the case for magnetic tunnel junctions. While the lowest frequency mode is always attributed to the free layer excitation, the interpretation of the highest frequency peak is sometimes attributed to edge nature physics 3

4 supplementary information modes [3], higher order spin-wave modes [4] or to oscillations of the synthetic antiferromagnet [1, 4]. All the results we give correspond to the lowest frequency mode of the free layer. Supplementary note 2 : current-induced heating In order to evaluate the current-induced temperature increase in our samples, we have measured the saturation fields H SAT of the synthetic antiferromagnet (SAF) spin-flop switch as a function of the applied current for the largest samples size (type 1). H SAT is determined from the resistance versus field curves measured at room temperature (inset in Fig.2 (a)). The resulting plot H SAT versus current is shown on Fig.2 (a). Various works have shown that the SAF coupling strengh is strongly temperature-dependent and follows the relationship: H SAT = H 0 T \T 0 sinht \T 0 [5, 6]. The experimental datas obtained for the same sample as a function of temperature have been plotted and fitted using this equation (blue symbols and red curve in Fig.2 (b)). By comparing H SAT (T ) and H SAT (I) (open symbols in Fig.2 (b)) we estimate that the temperature increase for the largest applied bias is 20 K. The inset in Fig.2 (b) shows the depinning field of the domain wall as a function of temperature. The red line is a linear fit of the data, which gives a coercive field variation of about 0.06 Oe/K. A temperature increase of 20 K has a negligible impact on the DW depinning ( 1 Oe). saturation field (ka/m) (a) resistance (Ω) Hsat magnetic field (Oe) dc current (ma) (b) saturation field (ka/m) depinning field (Oe) temperature (K) Spin-Flop measurements Fit Transport measurements temperature (K) FIG. 2: (a) Saturation field of the synthetic antiferromagnet as a function of the injected dc bias determined by transport measurements at room temperature. Inset : resistance versus field at room temperature. (b) Blue symbols : Saturation field of the synthetic antiferromagnet as a function of the temperature. Red line : Fit. The open black symbols correspond to H SAT (I). Inset : depinning field of the domain wall as a function of temperature. 4 4 nature physics

5 supplementary information Supplementary note 3 : micromagnetic simulations For the micromagnetic simulations, we use our finite-difference micromagnetic code SpinPM, developed by Istituto P.M. The simulated free layer has the geometry of the S.E.M. image of sample 2, with a thickness of 5 nm. The mesh cell size is set to nm 3. We took the following magnetic parameters: α = 0.01 for the Gilbert damping, M s (CoF e/nif e) = 1 T for the magnetization of the free layer. The spin polarization has been set to P spin = 0.5 and the amplitude of the OOP field like torque to 40 % of the in-plane torque. 210 nm 500 nm H(Oe) (a) (b) (c) 120 nm 500 nm H(Oe) (d) (e) (f) FIG. 3: (a) and (d) S.E.M. images of the two junction sizes before adding the top electrode. (b) and (e) micromagnetic simulations of the Oersted field distribution in both type of samples, for a current density of A.cm 2. (c) and (f) micromagnetic simulations showing the initial DW position at zero applied magnetic field and zero current. Two sample sizes have been studied, corresponding to the S.E.M. images of Fig.3 (a) and (d). The Oersted field distribution for each kind of sample is shown in Fig.3 (b) and (e). As expected, the Oersted field amplitude is larger for the larger area samples. The curves of the equivalent field versus current densities have been obtained with the DW initially pinned at the position shown Fig.3 (c) and (f). The micromagnetic simulations exactly follow the experimental procedure. Starting from these initial configurations, the depinning fields H + dep and H dep are determined at zero bias by sweeping the field either to positive or negative nature physics 5

6 supplementary information applied, the DW position is stabilized, and the current is applied, which allows to determine I + dep and I dep. The SpinPM program allows to separate the different contributions of the IP, OOP and Oersted torques. Now at Grandis, Inc., 1123 Cadillac Court, Milpitas, CA 95035, USA [1] Wang, C., Cui, Y.-T., Sun, J.Z., Katine, J.A., Buhrman, R.A., & Ralph, D.C., Bias and angular dependence of spin-transfer torque in magnetic tunnel junctions Phys. Rev. B. 79, (2009). [2] Sankey, J.C., Cui, Y.-T., Sun, J.Z., Slonczewski, J.C., Buhrman, R.A., & Ralph, D.C., Measurement of the spin-transfer-torque vector in magnetic tunnel junctions Nature Physics 4, (2007). [3] Deac, A.M., Fukushima, A., Kubota, H., Maehara, H., Suzuki, Y., Yuasa, S., Nagamine, Y., Tsunekawa, K., Djayaprawira, D.D., & Watanabe, N., Bias-driven high-power microwave emission from MgO-based tunnel magnetoresistance devices Nature Physics 4, 803 (2008). [4] Helmer, A., Cornelissen, S., Devolder, T., Kim, J.-V., van Roy, W., Lagae, L., & Chappert, C., Quantized spin-wave modes in magnetic tunnel junction nanopillars Phys. Rev. B 81, (2010). [5] Wiese, N., Dimopoulos, T., Ruhrig, M., Wecker, J., Reiss, G., Sort, J., & Nogues, J., Strong temperature dependence of antiferromagnetic coupling in CoFeB/Ru/CoFeB EPL 78, (2007). [6] Zhang, Z., Zhou, L., Wigen, P.E., & Ounadjela, K., Using ferromagnetic resonance as a sensitive method to study temperature dependence of interlayer exchange coupling Phys. Rev. Lett. 73, 336 (1994). 6 nature physics