Thermally Assisted Spin Torque Switching in Magnetic Random Access Memory
Authors: Taniguchi Tomohiro , Fukushima Akio , Yakushiji Kay , Kubota Hitoshi 
Published: February 2020

Magnetic random access memory (MRAM) consisting of magnetic tunnel junctions (MTJs) is a fascinating candidate for high-density nonvolatile memory. An MTJ has two ferromagnetic metals called free and pinned layers separated by nonmagnetic spacer. The free layer in the MTJ shows two energetically stable states corresponding to the parallel and antiparallel alignments of the magnetizations. These magnetization alignments are distinguished by tunnel magnetoresistance (TMR) effect, i.e., the resistance at the antiparallel alignment is higher than that at the parallel alignment. The free layer is switched between these two stable states by spin torque effect [1], where the transfer of the spin angular momentum from the conducting electrons to the free layer excites the spin torque and induces the magnetization dynamics. The observation of the high TMR ratio more than 100% in CoFeB/MgO-based MTJ [2] has motivated both experimental and theoretical researchers to develop practical MRAM.
The free layer should stay one of the stable states to keep information in MRAM. Unfortunately, however, the thermal fluctuation induces probabilistic switching of MTJ. Therefore, high thermal stability is required to guarantee the MRAM performance. Thermal stability of the MTJ is defined by the energy barrier of the free layer separating the two stable states divided by the thermal energy, k
B
T. Since the retention time of MRAM is exponentially proportional to the thermal stability, a small error in the evaluation of the thermal stability affects the estimation of the retention time significantly. Thus, an accurate evaluation of the thermal stability is necessary. The thermal stability has been evaluated by analyzing the switching probability of the free layer’s magnetization in the thermally activated region assisted by the spin torque. The fitting function of the switching probability is P=1-exp[-ft exp[-Δ(1-I/I
c)
b
]], where f, Δ, I, and I
c are the attempt frequency, thermal stability, current, and switching current at zero temperature, respectively. The switching exponent, b, is assumed to be one [3].
In this study, we study the thermally assisted spin torque switching in an in-plane magnetized MTJ theoretically. The theoretical formula of the switching probability is derived from the Fokker-Planck equation. We find that the switching exponent is larger than one and depends on the applied electric current. The assumption that the switching exponent is one used in previous works is approximately valid only near the low current region, while relatively large current is applied in experiments to obtain the switching probability efficiently. In the high current region, the switching exponent is almost two. We also perform the numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation with stochastic torque. Figure 1(a) shows the dependence of the probability density, dP/dt, on the current pulse time for several temperatures. As shown, the probability density shows a peak at certain time. We call this time the switching time. Figure 1(b) shows the temperature dependence of the switching time on the temperature. It should be noted that the curvature of the switching time reflects the switching exponent [4]. The nonlinear dependence of the switching time is another evidence that the switching exponent is larger than one. The fact that the switching exponent is larger than one indicates that the previous works have underestimated the thermal stability. The presented formula enables us to evaluate the thermal stability with high accuracy. We also notice that the switching current at zero temperature, I
c, can also be evaluated from the switching probability and our formula. We will talk the details of the theoretical analysis of the switching probability and numerical simulation. A comparison with latest experiments will also be presented.
(Figure caption) Figure 1: (a) The dependence of the switching probability density on the current pulse time for several temperatures. (b) The temperature dependence of the switching time.
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[4] T. Taniguchi and H. Imamura, J. Nanosci. Nanotechnol. 12, 7520 (2012). T. Taniguchi, M. Shibata, M. Marthaler, Y. Utsumi, and H. Imamura, Appl. Phys. Express 5, 063009 (2012).

Figure 1