Interplay of Voltage Control of Magnetic Anisotropy, Spin-Transfer Torque, and Heat in the Spin-Orbit-Torque Switching of Three-Terminal Magnetic Tunnel Junctions

We use three-terminal magnetic tunnel junctions (MTJs) designed for field-free switching by spin-orbit torques (SOTs) to systematically study the impact of dual voltage pulses on the switching performance. We show that the concurrent action of an SOT pulse and an MTJ bias pulse allows for reducing the critical switching energy below the level typical of spin-transfer-torque while preserving the ability to switch the MTJ on the subnanosecond time scale. By performing dc and real-time electrical measurements, we discriminate and quantify three effects arising from the MTJ bias: the voltage-controlled change of the perpendicular magnetic anisotropy, current-induced heating, and the spin-transfer torque. The experimental results are supported by micromagnetic modeling. We observe that, depending on the pulse duration and the MTJ diameter, different effects take a lead in assisting the SOTs in the magnetization-reversal process. Finally, we present a compact model that allows for evaluating the impact of each effect due to the MTJ bias on the critical switching parameters. Our results provide input to optimize the switching of three-terminal devices as a function of time, size, and material parameters.

Figure 1

(a) The schematics of the three-terminal device allowing for field-free SOT switching, with an illustration of the effects at play when applying a bias voltage on the MTJ: STT, current-induced heating, and the VCMA effect add to the SOT driven by $V_{\mathrm{SOT}}$. The purple arrows represent the stray field produced by the magnetic hard mask (MHM) that enables zero-field switching. (b) The simplified schematics of the circuitry used for real-time (black) and dc (purple) detection of switching induced by SOT- (bottom) and MTJ-bias (top) pulses.

Figure 2

Representative voltage time traces ($V_{\mathrm{sw}}$) recorded during AP-P reversal, smoothed with a 0.5 ns window, at $V_{\mathrm{SOT}}=0.27$ V with (a) $V_{\mathrm{MTJ}}=-1.3V_{\mathrm{SOT}}$ and (b) $V_{\mathrm{MTJ}}=-2.1V_{\mathrm{SOT}}$. The black lines are examples of individual time traces. (c) Statistical distributions of the activation delay ($t_0$) and transition time ($\mathrm{\Delta }t$) derived from the $V_{\mathrm{sw}}$ traces fitted to a piecewise linear function. The distributions are compiled from 500 switching events, 50 of which are displayed in (a) and (b).

Figure 3

The field-induced switching assisted by a dc voltage bias. (a) The schematics of an $R$-$H$ loop, showing the switching fields ($H_{\mathrm{sw}}$), the offset field ($H_{\mathrm{offset}}$), and the coercive field ($H_c$). The block arrows show the direction of the magnetization of the free and reference layers at different fields. (b) $R$-$H$ loops measured at different $V_{\mathrm{dc}}$ applied to the MTJ with a diameter of 60 nm. The measurements are offset along the $y$ axis for clarity. (c) $H_{\mathrm{sw}}$ corresponding to P-AP and AP-P reversals of the free (black lines) and reference (gray lines) layer extracted from (b). (d) Variation of the offset field $\mathrm{\Delta }{H}_{\mathrm{offset}}=H_{\mathrm{offset}}(V_{\mathrm{dc}})-H_{\mathrm{offset}}(0)$ and (e) the coercive field $\mathrm{\Delta }{H}_c=H_c(V_{\mathrm{dc}})-H_c(0)$ as a function of $V_{\mathrm{dc}}$ and the MTJ diameter. The solid lines in (e) are fits to the data (see text).

Figure 4

The probability of AP-P (open symbols) and P-AP (full symbols) switching measured postpulse as a function of $V_{\mathrm{SOT}}$. (a) Switching at $V_{\mathrm{MTJ}}=0$ for different pulse widths and (b) switching at different $V_{\mathrm{MTJ}}$ for $t_{\mathrm{pulse}}=0.33$ ns.

Figure 5

The dependence of the critical switching parameters for STT (black diamonds) and SOT (colored hexagons). The purple data set, $|V_{\mathrm{MTJ}}/V_{\mathrm{SOT}}|=4.4$, represents the borderline between SOT- and STT-dominated switching. The main panels refer to P-AP switching and the insets to AP-P switching. (a) The critical voltage as a function of $t_{\mathrm{pulse}}$. $V_c$ corresponds to the pulse amplitude for which $P_{\mathrm{sw}}=0.5$, $V_{\mathrm{SOT}}$ for the SOT-dominated switching, and $V_{\mathrm{MTJ}}$ for STT switching. (b) The critical current density $j_c$ and (c) the critical energy $E_c$ as a function of $t_{\mathrm{pulse}}$.

Figure 6

(a) The median (symbols) and interquartile range (shaded areas) of the statistical distributions of $t_0$ and $\mathrm{\Delta }t$ as a function of $V_{\mathrm{MTJ}}/V_{\mathrm{SOT}}$. The data have been obtained by measuring 500 single-shot switching traces for each point using a fixed pulse amplitude $|V_{\mathrm{SOT}}|=305$ mV, which is equivalent to $1.1V_c$ for AP-P switching at $V_{\mathrm{MTJ}}=0$. The dashed lines are a guide to the eye. (b) $t_0$ and $\mathrm{\Delta }t$ obtained from micromagnetic simulations including the combined impact of SOT and MTJ bias. The SOT pulse amplitude is defined by a current density of $81\mathrm{MA}/{\mathrm{cm}}^2$. (c) $t_0$ and $\mathrm{\Delta }t$ obtained from the simulations by considering only one of the three effects of $V_{\mathrm{MTJ}}$ in each plot. Full (open) symbols correspond to the P-AP (AP-P) reversal.

Figure 7

Simulated switching traces for AP-P reversal induced by $j_{\mathrm{SOT}}=81\mathrm{MA}/{\mathrm{cm}}^2$ without (black line) and with (yellow line) MTJ bias given by $V_{\mathrm{MTJ}}/V_{\mathrm{SOT}}=-0.9$ and taking into account only one bias-induced effect at a time (orange-red lines).

Figure 8

(a) The median value of $t_0$ (top) and $\mathrm{\Delta }t$ (bottom) obtained from single-shot measurements of SOT-induced switching as a function of $|V_{\mathrm{SOT}}|$ and $V_{\mathrm{MTJ}}$. P-AP (AP-P) switching is induced by positive (negative) $V_{\mathrm{SOT}}$. (b) $t_0$ and $\mathrm{\Delta }t$ derived from micromagnetic simulations of the switching by the combined impact of currents flowing through the SOT line and MTJ. The shading represents $t_0$ or $\mathrm{\Delta }t$ in nanoseconds, according to the scale on the right. The white lines are isocurves of $t_0$ and $\mathrm{\Delta }t$. The white areas at the bottom of the diagrams delimit the undercritical switching conditions.

Figure 9

(a) The normalized critical switching voltage $v_c$ as a function of $V_{\mathrm{MTJ}}/V_{\mathrm{SOT}}$ in the 60-nm MTJ device. P-AP (AP-P) reversal is shown in a blue (orange) color palette for different $t_{\mathrm{pulse}}$. (b) Fits of $v_c$ obtained for different $t_{\mathrm{pulse}}$ using Eqs. (3) and (4). (c) The fitting coefficients $c_{\mathrm{\Delta }T}$, $c_{\mathrm{VCMA}}$, and $c_{\mathrm{STT}}$ as a function of $t_{\mathrm{pulse}}$ for three MTJ devices with different diameters. The coefficients represent the relative contribution of Joule heating, VCMA, and STT to the reduction of $v_c$.