Micromagnetic model for studies on Magnetic Tunnel Junction switching dynamics, including local current density Marek Frankowski n , Maciej Czapkiewicz, Witold Skowron ́ ski, Tomasz Stobiecki Department of Electronics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland article info Available online 13 September 2013 Keywords: Micromagnetism Simulation OOMMF STT MTJ Switching abstract We present a model introducing the Landau–Lifshitz–Gilbert equation with a 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 an 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. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Magnetic Tunnel Junction (MTJ), consisting of two ferromag- netic nano-layers separated by a thin insulating barrier, has recently drawn a significant attention, due to their potential applications such as Spin-Transfer-Torque Random Access Memory (STT-RAM) [1], magnetic field sensors [2] and microwave oscilla- tors [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 a 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, the current density and the conductivity. Recent publications used macrospin models [11,10], or focused on the simulations with a fixed current density or a current pulse independent of the dynamic MTJ resistance [12–14]. 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 the TMR effect given by the formula: R ¼ R P þ R AP  R P 2 ð1  cos θÞ; ð1Þ where θ is an angle between magnetization vectors of FL and RL, R P (for θ ¼ 0) and R AP (for θ ¼ 1801) 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]. 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 contribu- tions 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 the simulated ferromagnetic MTJ trilayer. Assuming that current channel protrudes symmetrically from simulated area, Oersted field contributions are calculated Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physb Physica B 0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.08.051 n Corresponding author. Tel.: þ48 126174474. E-mail address: mfrankow@agh.edu.pl (M. Frankowski). Physica B 435 (2014) 105–108