Reduction of intrinsic critical current density under a magnetic field along the hard axis of a free layer in a magnetic tunnel junction

We investigated the effect of a magnetic field along a hard in-plane axis $H_{\mathrm{hard}}$ on a current-induced magnetization switching (CIMS) in magnetic tunnel junctions (MTJs). Since $H_{\mathrm{hard}}$ causes the effective field to tilt away from the easy axis, we evaluated the $H_{\mathrm{hard}}$ dependence of two contributing factors in CIMS [the intrinsic critical current density ($J_{c0}$) and the thermal stability factor ($E/k_{B}T$)] as functions of the tilting angle (${\theta }_H$). Both measurements and numerical simulations showed that the presence of $H_{\mathrm{hard}}$ can reduce $J_{c0}$ by more than the amount estimated by Slonczewski's polarization function $g$($\theta$) by an order of magnitude and that $E/k_{B}T$ is independent of ${\theta }_H$. These findings suggest that the effect of $H_{\mathrm{hard}}$ mainly appears in the dynamic properties due to the nonconservative force of the spin-transfer torque based on the Slonczewski's model. A simple stability analysis demonstrated that the tilt of the magnetization direction away from the easy axis caused by the presence of $H_{\mathrm{hard}}$ induces an imbalance between the spin-transfer and damping torques and that applying a current achieves the further tilted stable state. Achievement of this stable state can be interpreted as the suppression of the effect of the effective demagnetization field ($H_d^{*}$). Therefore the major reduction in $J_{c0}$ is due to the suppression of $H_d^{*}$ caused by the presence of $H_{\mathrm{hard}}$.

Figure 1

(a) Dependence of $R$ on $H_{\mathrm{easy}}$ at $H_{\mathrm{hard}}=0$ from which we obtained $R_P$ of 3.2 k$\Omega$, $R_{\mathrm{AP}}$ of 5.4 k$\Omega$, and the TMR ratio of 69$\%$. (b) Asteroid curves of MTJ. Open (solid) circles represent fields for switching from AP to P (P to AP) state. Extra magnetic field at origin of asteroid curves is small because center of asteroid curves corresponds approximately to origin. (c) Dependencies of $R_P$ and $R_{\mathrm{AP}}$ on $H_{\mathrm{hard}}$ at the applied current of 10 $\mu$A were used to determine ${\theta }_{\mathrm{free}}$ and ${\theta }_{\mathrm{pin}}$. Open (solid) circles represent $R_P$ ($R_{\mathrm{AP}}$). (d) ${\theta }_{\mathrm{free}}$ and ${\theta }_{\mathrm{pin}}$ as functions of $H_{\mathrm{hard}}$.

Figure 2

Map of $P$ as a function of applied current density $J$ with ${\tau }_p=100$ ns for various $H_{\mathrm{hard}}$ from which $J_{c0}$ and $E/k_{B}T$ were determined.

Figure 3

$J_{c0}$ obtained from fitting of probability curves as a function of ${\theta }_H$.

Figure 4

$E/k_{B}T$ obtained from fitting of probability curves as a function of ${\theta }_H$.

Figure 5

(a) Schematic diagram of MTJ device consisting of pinned layer (P), insulating barrier (I), and free layer (F). (b) Polar coordinates of magnetization vector $\mathbf{m}$ and applied field ${\mathbf{H}}_{\mathrm{hard}}$.

Figure 6

(a) $J_c$ as a function of $t_p$ of “AP-to-P” CIMS as a function of $J$ for various $h_{\mathrm{hard}}$. (b) Extracted $J_{c0}$ as a function of ${\theta }_H$.

Figure 7

$\theta$ dependence of damping torque ($-\alpha \langle \partial \varepsilon /\partial \theta \rangle$: solid line), STT ($j\sin \theta$: dash-dotted line), potential energy (dashed line), and the resulting equilibrium positions of magnetization including stable (solid circles) and saddle points (open circles). (a) $j=0$ and $h_{\mathrm{hard}}=0$, (b) $j=0$ and $h_{\mathrm{hard}}\ne 0$, (c) $j\ne 0$ and $h_{\mathrm{hard}}=0$, and (d) $j\ne 0$ and $h_{\mathrm{hard}}\ne 0$.

Figure 8

Equilibrium positions $\theta$ of magnetization as functions of $J$ in the limiting case of ${\varphi }_0\to 0$ from Eqs. (7) and (8). Solid and dash-dotted lines show stable states and saddle points for hard in-plane axis applied field at ${\theta }_H={10}^{\circ }$ in limit of ${\varphi }_0=0^{\circ }$. Dashed line represents saddle point at $h_{\mathrm{hard}}=0$.

Figure 9

Time-averaged distribution of degree of freedom $\varphi$ for ${\theta }_H=2.5^{\circ }$, 10${}^{\circ }$, and 20${}^{\circ }$ immediately below $J_c$. Schematic trajectory with tilting of ${\mathbf{H}}_{\mathrm{eff}}$ accompanied by limited ${\varphi }_0$ is shown on the left, and its projection onto the $m_{\mathrm{x}}$$m_{\mathrm{y}}$-plane is shown on the right.

Figure 10

$J_{c0}$ as a function of ${\theta }_H$.