Multiscale modeling of current-induced switching in magnetic tunnel junctions using ab initio spin-transfer torques

There exists a significant challenge in developing efficient magnetic tunnel junctions with low write currents for nonvolatile memory devices. With the aim of analyzing potential materials for efficient current-operated magnetic junctions, we have developed a multi-scale methodology combining ab initio calculations of spin-transfer torque with large-scale time-dependent simulations using atomistic spin dynamics. In this work we introduce our multiscale approach, including a discussion on a number of possible schemes for mapping the ab initio spin torques into the spin dynamics. We demonstrate this methodology on a prototype Co/MgO/Co/Cu tunnel junction showing that the spin torques are primarily acting at the interface between the Co free layer and MgO. Using spin dynamics we then calculate the reversal switching times for the free layer and the critical voltages and currents required for such switching. Our work provides an efficient, accurate, and versatile framework for designing novel current-operated magnetic devices, where all the materials details are taken into account.

Figure 1

The Co/MgO MTJ stack studied in this work. Panel (a) shows a schematic of the scattering region for the smeagol calculation, while panels (b) and (c) present the atomic resolved ab initio STT for ${90}^{\circ }$ misalignment at 1 V and the atomic spin moments profiles, respectively. In (b) and (c) the first 4 Co and last 4 Cu atoms are omitted, since in the calculations these are replaced with the semi-infinite leads.

Figure 2

The angular dependence of (a) the current density and (b) the total torque at 0.5 V. The solid line in (a) is a fit to the current density using $J\left(\theta \right)=A+Bcos\left(\theta \right)$. The solid lines in (b) are a fit using the Slonczewski angular dependence given in Eq. (9). In both cases the fits agree well with the data, indicating that the empirical forms can be used.

Figure 3

The voltage dependence of the in-plane (open squares) and out-of-plane (filled circle) torque, and the in-plane torkance (solid line). The in-plane torque shows a linear behavior up to approximately 1.4 V. Within this range the torkance is a good approximation of the finite-bias torque. The out-of-plane torque shows a quadraticlike behavior, for which the zero-bias torkance is not sufficient to describe.

Figure 4

The resulting current density for an applied bias voltage in the Co/MgO/Co/Cu MTJ. The solid circles show the current density in the antiparallel configuration, while the open squares show the parallel configuration. Up to approximately 1 V there is a significant TMR, but above this value more current flows in the antiparallel state and the TMR drops.

Figure 5

Magnetization switching for a junction kept at (a) constant voltage and (b) constant current for $\lambda =0.01$ and $k=0.1\mathrm{meV}$. At constant voltage the switching is uniform above the critical voltage, while at constant current the torque has an additional angular dependence given by the variation of the conductivity (hence the voltage at constant current) with angle.

Figure 6

The switching time for a Co free layer as a function of bias voltage for three values of the anisotropy and a damping coefficient of $\lambda =0.1$. The open points are for calculations performed with the full interpolation, while the solid lines are for the torkance method and the dotted ones are a guide to the eye. The arrow indicates the difference between the torkance and full interpolation methods for the $k=0.1$ meV case.

Figure 7

The critical (a) voltage and (b) current required to switch the free layer for a given anisotropy and damping at $T=0$ K. Three alternative methods for interpolating the STT are shown for each case: torkance (solid lines), full interpolation (filled circles), and semifunctional (open circles). The dotted lines are a guide to the eye.

Figure 8

Inverse switching time with (a) $k=0.1$ meV and (b) 0.5 meV at $T=0$ K (solid blue line), 100 K (orange circles) and 300 K (green triangles). Filled and open symbols represent simulations run by using the angle calculated for the total magnetization or for each individual spin, respectively. The dashed lines indicate the inverse reversal time at $T=0$ K using a scaled anisotropy constant.