(Invited) Spin Torque Switching in Magnetic Random Access Memory
The research on MRAM has required not only the technical development but also advances in fundamental physics. An important problem for realization of MRAM is the accurate evaluation of the thermal stability. The thermal stability in MRAM is defined as the uniaxial anisotropy energy of the ferromagnet divided by the temperature. A high thermal stability is necessary to keep retention time of MRAM longer than ten years. Experimentally, the thermal stability has been evaluated by measuring the dependence of the switching probability on the current magnitude. Here, the current magnitude is sufficiently small, and thus, the thermal fluctuation plays a key role to switch the magnetization, making the switching probabilistic. The value of the thermal stability was obtained by fitting the switching probability with the Arrhenius formula , which has been a conventional and traditional method to evaluate thermal stability in several physical, chemical, and biological systems. The spin torque switching current at zero-temperature, which determines the power of the writing in MRAM, was also determined from the switching probability. However, recently, we pointed out problems in the analysis. The Arrhenius law assumes that the force acting on a Brownian particle is conservative, i.e., the force is a gradient of a potential. On the other hand, the spin torque is a non-conservative force. Therefore, it is unclear whether the evaluation of the thermal stability in MRAM with the Arrhenius law provides the accurate evaluation. Also, nonlinearity of the magnetization dynamics has been neglected in the previous work by focusing on only a small fluctuation near the equilibrium.
In my study, we show recent our progress on theoretical study of magnetization dynamics in MRAM in the presence of both spin torque and thermal fluctuation . We noticed that, in the thermally activated region, the magnetization precesses almost on the constant energy curve many times during the switching. This fact allows us to average the equation of motion, called the Landau-Lifshitz-Gilbert (LLG) equation, on the constant energy curve. Deriving the Fokker-Planck equation from the LLG equation, we develop the general theory of the probabilistic switching by the spin torque. We also quantitatively calculate the spin torque switching rate by using both analytical and numerical methods, which enables us to take into account the nonlinearity of the magnetization dynamics. We found that, the switching probability can be written in the form of Arrhenius formula. However, its scaling with respect to the current is unconventional because of the non-conservative nature of the spin torque. This results indicate that both the thermal stability and the switching current at zero temperature had been underestimated in the previous work. The former is preferable for MRAM study because it guarantees a high thermal stability in the currently succeeded structures. On the other hand, the latter will be a problem from the view point of the low-power consumption. In this talk, we will show the introduction, the points of the problems, and the details of our theory. We will also discuss about future direction of MRAM study.
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