Micromagnetic model for studies on Magnetic Tunnel Junction switching dynamics, including local current density

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Micromagnetic model for studies on magnetic tunnel junction switching dynamics, including local current density Marek Frankowski, Maciej Czapkiewicz, Witold Skowroński, Tomasz Stobiecki

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S0921-4526(13)00538-3 http://dx.doi.org/10.1016/j.physb.2013.08.051 PHYSB307878

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Physica B

Cite this article as: Marek Frankowski, Maciej Czapkiewicz, Witold Skowroński, Tomasz Stobiecki, Micromagnetic model for studies on magnetic tunnel junction switching dynamics, including local current density, Physica B, http://dx.doi.org/10.1016/j.physb.2013.08.051 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Micromagnetic model for studies on magnetic tunnel junction switching dynamics, including local current density Marek Frankowski∗, Maciej Czapkiewicz, Witold Skowro´nski, Tomasz Stobiecki∗ Department of Electronics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krak´ow, Poland

Abstract We present a model introducing the Landau-Lifshitz-Gilbert equation with Slonczewski’s Spin-Transfer-Torque (STT) component in order to take into account spin polarized current influence on the magnetization dynamics, which was developed as Object Oriented MicroMagnetic Framework extension. We implement the following computations: magnetoresistance of vertical channels is calculated from the local spin arrangement, local current density is used to calculate the in-plane and perpendicular STT components as well as the Oersted field, which is caused by the vertical current flow. The model allows for an analysis of all listed components separately, therefore, the contribution of each physical phenomenon in dynamic behavior of Magnetic Tunnel Junction (MTJ) magnetization is discussed. The simulated switching voltage is compared with the experimental data measured in MTJ nanopillars. Keywords: micromagnetizm, simulation, OOMMF, STT, MTJ, switching

1. Introduction Magnetic Tunnel Junction (MTJ), consisting of two ferromagnetic nano-layers separated by a thin insulating barrier, has recently drawn a significant attention, due to their potential application as Spin-Transfer-Torque Random Access Memory (STT-RAM) [1], magnetic field sensors [2] and microwave oscillators [3]. The major advantage of MTJs is the possibility of the magnetization control of one of the ferromagnetic layers - called the Free Layer (FL) with a spin polarized current by means of the STT effect [4, 5]. Due to the STT, the applied spin polarized current can drive the magnetization of the FL into precession, laying typically in a microwave frequency regime [6] or, for sufficiently high current amplitudes, it can switch the FL between Parallel (P) and Anti-Parallel (AP) alignment with respect to the Reference Layer (RL) [7, 8]. The difference between the P and AP states can be detected using the Tunnel Magnetoresistance (TMR) effect [9]. In order to fully understand the magnetization switching process, micromagnetic simulations are commonly used, in order to derive the parameters not-accessible in the experiment, or to support the optimization of the MTJ design. In this paper we present model which was adopted to an extension of Object Oriented MicroMagnetic Framework (OOMMF) [15] that allows for accurate local current density calculation, which is crucial for the magnetization switching dynamics. We implement the feedback between the local magnetizations alignment, current density and the conductivity. Recent publications used either macrospin models [11, 10], or focused on the simulations with a fixed current density or a current pulse independent of the dynamic MTJ resistance [12, 13, 14]. 2. Implemented models In our MTJs model we assume that the current flows through channels perpendicular to the junction plane, which are connected in parallel. Each channel is considered as separate junction with the resistance R, which depends on ∗ [email protected]

Preprint submitted to Physica B: Condensed Matter

September 11, 2013

TMR effect given by formula:

RAP − RP (1 − cosθ), (1) 2 where θ is an angle between magnetization vectors of FL and RL, RP (for θ = 0) and RAP (for θ = 180◦ ) are resistances of the P and AP states, respectively. The idea of calculating local conductance is depicted in Fig. 1(a). The detailed specification of the OOMMF settings files, as well as the used source code can be found on one of the authors home page [16]. R = RP +

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Figure 1: (a) The idea of calculating local conductance. White cells represent the non-ferromagnetic material and grey cells represent the ferromagnetic material with its magnetization vector. Vertical arrows symbolize the current, whereas crosses stay for channels with the suppressed current. (b) The illustration to the Oersted field calculation. The contribution from the channel of length 2d is added to the cell located in the distance r from that channel.

In addition to the local conductance channels, the Oersted field caused by the current flow was integrated in our model. The Oersted field calculations are performed by adding the contributions from current channels extended beyond the simulation space. This method is justified because the non-ferromagnetic parts of the real device, i.e., the buffer and capping layers, are usually much thicker than simulated ferromagnetic MTJ trilayer. Assuming that current channel protrude symmetrically from simulated area, Oersted field contributions are calculated using the formula: I √ d H = 2πr , where I is the current in the channel, r is the distance between the channel and considered simulation r2 +d2 cell, d is half of the total channel length. See Fig. 1(b). After adding contributions from all channels, the Oersted field can be treated as the contribution to the effective magnetic field in a particular cell. For a simulation of the magnetization dynamics, we use the Landau-Lifshitz-Gilbert equation with the STT component: d⃗ m ∂⃗ m ⃗ e f f + α⃗ ⃗ ×H ⃗ × (⃗ ⃗ × ⃗p. = −γ0 m m× + γ0 a J m m × ⃗p) + γ0 b J m (2) dt ∂t First term of equation 2 corresponds to the magnetization precession, second corresponds to damping, third and forth ⃗ is the normalized magnetization vector of the correspond to in-plane and perpendicular torques, respectively, where m m ⃗ e f f is the effective field derived by minimizing the local energy FL, γ0 = 2.21 · 105 As is the gyromagnetic factor, H densities, α is the damping factor, and ⃗p is the normalized RL magnetization vector. The in-plane torque factor is written as: a J = 2eµ~0 Ms t ηJ, where t is the FL thickness, η is the spin polarization, J is the current density, whereas perpendicular torque is implemented as: b J = b1 J + b2 J 2 , where b1 = 2.7 · 10−9 m, b2 = 2.8 · 10−19 m3 /A are the quadratic function components, taken from the experimental data [3]. Our model allows to adjust the following parameters: η, b1 , b2 , α, RP , RAP , while the applied time dependent voltage is the stimulus vector. By setting η or b1 and b2 to zero, the contribution from the in-plane torque or the perpendicular torque can be ignored, respectively. In addition, the model enables performing the micromagnetic simulations with the current density that depends on the local magnetization vectors alignment. 3. Results and discussion In order to compare simulation results to the real devices, we investigated exchange biased MTJ with a following multilayer structure (thickness in nm): Ta(5) / CuN(50) / Ta(3) / CuN(50) / Ta(3) / PtMn(16) / Co70 Fe30 (2) / Ru(0.9) / Co20 Fe40 B20 (2.3) / MgO(0.95) / Co20 Fe40 B20 (2.3) / Ta(10) / CuN(30) / Ru(7), described in detail in Ref. [3]. Nano-structured pillars with an elliptical cross-section of 250 × 150 nm were parametrized for our model purposes in the following way: cell size of 2 × 2 × 1 nm, FL with the anisotropy constant of KFL = 0.1 kJ/m3 , saturation magnetization of MFL = 1100kA/m and the damping constant equals α = 0.017, coupled to the RL with the coupling 2

energy of J MgO = 0.006 mJ/m3 . The RL was antiferromagnetically coupled to the CoFe pinned layer with the energy of JRu = −0.019 mJ/m3 . The implemented feedback between the local current density and magnetization involves dynamic decrease of the MTJ resistance. Therefore, for applied bias voltage, the current increases with the conductivity and the switching process can be accomplished faster. Figure 2 presents the dynamic behavior of the MTJ normalized magnetization vector during the switching process from the AP to P state with the fixed current (a) and the current-resistance feedback (b)

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(b). The difference confirms that this feedback has an influence on switching dynamics and should be taken into account in the simulations. Simulated Current Induced Magnetization Switching (CIMS) loops, with (a) in-plane torque component alone, (b) both in-plane and perpendicular torque components, (c) both torque components and Oersted field, are presented in Fig. 3(a-c). In addition, Figs (d-f) depict the MTJ resistance during the voltage sweep as a function of time. Note that for the Oersted field applied (Fig. 3(f)) the CIMS switching is accomplished for the shortest time. Moreover, for sufficiently high voltage amplitude, the perpendicular torque can overcome the in-plane torque and can cause indeterministic switching between the AP and P states. This phenomenon has been already observed experimentally and has been referred to as the back-hopping effect [17]. 450

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Figure 3: The example of CIMS loop simulation with taking into account: (a) in-plane torque alone (b) both torque components, (c) both torque components and Oersted field, (d-f) depict the MTJ resistance during the voltage sweep as a function of time, corresponding to graphs (a-c), respectively.

The discussed MTJ experimental CIMS loop is depicted in Fig. 4 (a) - resistance measured after voltage pulse 3

and (b) - during the pulse. In our simulations we are interested in the switching of the MTJ, so we assume that the resistance of AP state equals value at the switching voltage obtained by the experiment in Fig. 4(b).

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The simulated switching voltage from the AP to P state agrees quantitatively with the experimental value of V s = 0.75 V, in contrary for the opposite switching polarity, where the discrepancy between simulated and measured value is observed. Such asymmetry in the simulated switching voltages presented in Fig. 3(c) originates from the Oersted field effect, that favours the AP to P switching direction. This phenomenon is suppressed in the experiment due to the thermal effects, as was shown in Ref. [12]. 4. Summary In summary, we have presented a model, that allows for simulation of the switching dynamics in MTJ with both the external magnetic field and the spin polarized current. We have investigated an influence of the resistance-current feedback which decreases critical voltage value and affects the dynamic behavior of magnetization vector switching trajectory. If perpendicular component of STT is included in simulation, effect of back-hopping can be observed. Oersted field helps distort magnetization from equilibrium state and speeds-up switching process. Developed software allows quantitative reconstruction of experimental results of switching form AP to P state. Acknowledgements This project is supported by the Polish Ministry of Science and Higher Education - Diamond Grant DI2011001541 and statutory activity 11.11.230.016. M.C. and T.S. acknowledge the NANOSPIN Grant No. PSPB-045/2010 from Switzerland through the Swiss Contribution. W.S. acknowledges the Foundation for Polish Science MPD Programme co-financed by the EU European Regional Development Fund. Numerical calculations were supported in part by PL-Grid Infrastructure. [1] Y. Huai, F. Albert,P. Nguyen, M. Pakala, and T. Valet, Appl. Phys. Lett. 84, 3118 (2004). [2] W. Skowronski, P. Wisniowski, T. Stobiecki, S. Cardoso, Paulo P. Freitas, S. van Dijken, Appl. Phys. Lett. 101, 192401 (2012). [3] W. Skowronski, M. Czapkiewicz, M. Frankowski, J. Wrona, T. Stobiecki, G. Reiss, K. Chalapat, G. S. Paraoanu, S. van Dijken, Phys. Rev. B, 87:094419, (2013). [4] L. Berger, Phys. Rev. B 54, 9353 (1996). [5] J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996). [6] A. M. Deac, A. Fukushima, H. Kubota, H. Maehara, Y. Suzuki, S. Yuasa, Y. Nagamine, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe, Nature Phys. 4, 803 (2008). [7] Y.W. Liu, Z. Z. Zhang, P. P. Freitas, J. L. Martins, Appl. Phys. Lett., vol. 82, no. 17, pp. 28712873, (2003). [8] W. Skowronski, T. Stobiecki, J. Wrona, K. Rott, A. Thomas, G. Reiss, and S. van Dijken, J. Appl. Phys. 107, 093917 (2010). [9] Y. Huai, F. Albert, P. Nguyen, M. Pakala, T. Valet, Appl. Phys. Lett. 84, 3118 (2004). [10] P. Ogrodnik, M. Wilczynski, J. Barnas, R. Swirkowicz, IEEE Trans. On Magn., Vol. 47, No. 6, (2011). [11] WS. Zhao, E. Belhaire, Q. Mistral, C. Chappert, V. Javerliac, B. Dieny, E. Nicolle, IEEE Inter. BMAS 40-43 (2006). [12] T. Devolder, A. Tulapurkar, Y. Suzuki, C. Chappert, P. Crozat, K. Yagami, J. Appl. Phys. 98, 053904 (2005). [13] K. Ito, T. Devolder, C. Chappert, M. J. Carey, J. A. Katine, J. Phys. D: Appl. Phys. 40 1261 (2007). [14] Ch.-Y. You, J. of Magn. 17(2) 73-77 (2012). [15] M. J. Donahue, D. G. Porter, NIST report (1999). [16] M. Frankowski, http://layer.uci.agh.edu.pl/M.Frankowski (2013). [17] T. Min, J. Z. Sun, R. Beach, D. Tang, P. Wang, J. Appl. Phys. 105, 07D109 (2009).

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