Magnetisation switching dynamics induced by combination of spin transfer torque and spin orbit torque

Abstract

We present a theoretical investigation of the magnetisation reversal process in CoFeB-based magnetic tunnel junctions (MTJs). We perform atomistic spin simulations of magnetisation dynamics induced by combination of spin orbit torque (SOT) and spin transfer torque (STT). Within the model the effect of SOT is introduced as a Slonczewski formalism, whereas the effect of STT is included via a spin accumulation model. We investigate a system of CoFeB/MgO/CoFeB coupled with a heavy metal layer where the charge current is injected into the plane of the heavy metal meanwhile the other charge current flows perpendicular into the MTJ structure. Our results reveal that SOT can assist the precessional switching induced by spin polarised current within a certain range of injected current densities yielding an efficient and fast reversal on the sub-nanosecond timescale. The combination of STT and SOT gives a promising pathway to improve high performance CoFeB-based devices with high speed and low power consumption.

Figure 1

(a) Sketch illustrating the investigated system. Brass colour depicts the heavy metal (HM), red and light blue represent the free layer (FL) and reference layer (RL) of the MTJ respectively, light grey refers to the MTJ barrier. $j_e^{\mathrm{SOT}}$ and $j_e^{\mathrm{STT}}$ (yellow arrows) are the current densities injected in the HM and MTJ, respectively. $j_e^{\mathrm{STT}}$ is injected along the y-direction, $j_e^{\mathrm{STT}}$ is perpendicular to the structure along the z-direction. (b) Simulation protocol: initially both $j_e^{\mathrm{SOT}}$ (dashed light blue line) and $j_e^{\mathrm{STT}}$ (solid black line) are injected for 0.5 ns. After 0.5 ns $j_e^{\mathrm{SOT}}$ is switched off and only $j_e^{\mathrm{STT}}$ is injected into the system in the next 3.5 ns.

Figure 2

Time evolution of the magnetisation components of a 20 nm diameter MTJ for $j_e^{\mathrm{STT}}$ $1\times {10}^{12},2\times {10}^{12}\text{and}3\times {10}^{12}{\text{Am}}^{-2}$.

Figure 3

(a) Plot of the critical current density for STT switching $j_c^{\mathrm{STT}}$ as a function of MTJ diameter for different pulse widths. (b) Plot of the critical current density for SOT switching $j_c^{\mathrm{SOT}}$ as a function of different strengths of the SOT field-like component ($A_{\mathrm{F}}$) with respect to the damping-like term ($A_{\mathrm{D}}$). For $A_{\mathrm{F}}=0\%$ and 10% $j_c^{\mathrm{SOT}}$ could not be determined. Time evolution of the magnetisation components of a 20 nm diameter MTJ as a function of $A_{\mathrm{F}}$ for $j_e^{\mathrm{SOT}}$ $1\times {10}^{12}{\text{Am}}^{-2}$ (c) and $5\times {10}^{12}{\text{Am}}^{-2}$ (d) in absence of $j_e^{\mathrm{STT}}$.

Figure 4

(a) Time evolution of the reduced z-component of the magnetisation as a function of $j_e^{\mathrm{SOT}}$ for $j_e^{\mathrm{STT}}=1\times {10}^{11},1\times {10}^{12}\text{and}5\times {10}^{12}{\text{Am}}^{-2}$. In this case $A_{\mathrm{F}}=A_{\mathrm{D}}$ and the diameter is 20 nm. (b) Write energy and c) write energy $\times$ total switching time as a function of $j_e^{\mathrm{STT}}$ and $j_e^{\mathrm{SOT}}$ for $A_{\mathrm{F}}=A_{\mathrm{D}}$ and diameter of 20 nm. The palette represents the energy in (b) and energy $\times$ switching time in (c), and ranges from blue (low) to yellow (high). White regions correspond to combinations of $j_e^{\mathrm{STT}}$ and $j_e^{\mathrm{SOT}}$ that yield no switching.

Figure 5

(a) Time evolution of the magnetisation components as a function of $A_{\mathrm{F}}$ for $j_e^{\mathrm{SOT}}=j_e^{\mathrm{STT}}=1\times {10}^{12}{\text{Am}}^{-2}$ for a 20 nm MTJ. Plot of total switching time (colour) as a function of $j_e^{\mathrm{STT}}$ and $j_e^{\mathrm{SOT}}$ for $A_{\mathrm{F}}$ = 0, 0.1, 0.5 and 1 $A_{\mathrm{D}}$ for a 20 nm MTJ in panel (b–e) respectively. The colour scheme shows the switching time from immediate switching (blue) to no switching (yellow) within 4 ns. Dark grey lines represent mark points with switching time 0.5, 1, 2 and 3 ns.

Figure 6

(a) Calculated amplitudes of the coherent excitation mode $m_0$ of the free layer of a 20 nm MTJ as a function of $j_e^{\mathrm{SOT}}$ for different $j_e^{\mathrm{STT}}$ and $A_{\mathrm{F}}=0.5A_{\mathrm{D}}$. (b) and (c) show the calculated amplitudes of $m_0$, $m_1$ (vortex) and $m_{-1}$ (antivortex) modes of a 30 nm MTJ FL for $A_{\mathrm{F}}=0.5A_{\mathrm{D}}$, $j_e^{\mathrm{STT}}=1\times {10}^{12}{\text{Am}}^{-2}$ and $j_e^{\mathrm{SOT}}=0$, $1\times {10}^{12}{\text{Am}}^{-2}$, respectively. Insets show snapshots of the z-component of the magnetisation with palette blue (+ 1), green (0), red (− 1).