Figure 1

(Color online) Effect of spin transfer torque within a pinned layer. (a) General structure of a pinned layer. Due to exchange coupling, an AFM layer pins the direction of magnetization ${\mathbf{p}}_{\text{cur}}$ of the adjacent FM layer. In turn, the FM layer polarizes the spin current flowing to AFM. (b) Transfer of spin torques ${\mathbf{T}}_{1,2}$ from free electrons $\left(e^{-}\right)$ to sublattice magnetizations ${\mathbf{M}}_1$ and ${\mathbf{M}}_2$ (solid arrows, before and dotted arrows, after an interaction with the conduction electrons). STT produces small FM moment $\mathbf{m}$ which, in turn, sets up a solidlike rotation of ${\mathbf{M}}_1$, ${\mathbf{M}}_2$ around $\mathbf{m}$ (arc arrows), according to Eq. (6). [(c) and (d)] Sketch of eigenmodes of an AFM vector for different orientations of the external magnetic field. Easy axes (EA) are parallel to the film plane.Reuse & Permissions

Figure 2

(Color online) Stable magnetic configurations with different macroscopic properties. In FM/AFM bilayer [(a) and (b)] the magnetization $\left(\parallel {\mathbf{p}}_{\text{cur}}\right)$ of FM layer is fixed, AFM vector can be switched from (a) parallel to (b) perpendicular orientation with respect to ${\mathbf{p}}_{\text{cur}}$ by application of the external magnetic field $H_0\ge H_{\text{s-f}}$ within an AFM layer. In FM/FM bilayer [(c) and (d)] the magnetization of free layer can be switched from (c) parallel to (d) antiparallel orientation with respect to ${\mathbf{p}}_{\text{cur}}$ by the external magnetic field ${\mathbf{H}}_0$ applied antiparallel to ${\mathbf{p}}_{\text{cur}}$. In both cases (c) and (d) the switching can be also induced by current.Reuse & Permissions

Figure 3

(Color online) Dynamics of AFM vector induced by steady spin-polarized current. (a) Stability diagram under combined action of field and current. Static states of the bilayer (schematically shown with an arrow for ${\mathbf{p}}_{\text{cur}}$ and double arrow for AFM vector) are stable within the shaded area. Strong current $\left(\left|J\right|>\left|J_{\text{cr}}\right|\right)$ induces precession of an AFM vector around the current polarization ${\mathbf{p}}_{\text{cur}}$, direction of rotation depends on the sign of $J$. Strong field $\left(\left|H_0\right|>H_{\text{s-f}}\right)$ induces spin-flop transition combined with the current-induced precession. (b) Three-dimensional evolution of AFM vector $\mathbf{l}$ in overcritical regime $\left(J>J_{\text{cr}}\right)$ in the presence of magnetic field ${\mathbf{H}}_0$. In the initial state the AFM vector is slightly misaligned from $Z$ axis. Under the action of STT the vector $\mathbf{l}$ spirals away from $Z$ axis with a steadily increasing precession angle and the angular frequency $\Omega$. Final state corresponds to precession with the stable frequency within $XY$ plane $\left(l_Z=0\right)$. [(c) and (d)] Time dependence of the angular frequency $\Omega$ and $l_Z$ projection. Arrows indicate the moment, $t_{\text{min}}$, at which monotonic decrease in $l_Z$ switches to the decaying oscillations. Envelope (dash line) corresponds to relaxation $\left[\propto \text{exp}\left(-{\gamma }_{\text{AFM}}t\right)\right]$ caused by internal damping. AFM vector is normalized as $\left|\mathbf{l}\right|=1$. $t$ and $\Omega$ are expressed in the dimensionless units as explained in text.Reuse & Permissions

Figure 4

(Color online) Switching between the different configurations of (a) FM/FM and (b) FM/AFM bilayers. Magnetization of the fixed layer is shown with magenta (thick) arrow, that of the free layer with violet (thin arrow), double arrow shows orientation of AFM vector. (a) Switching between P and AP states can be achieved by the field or current applied in two opposite directions. (b) Transition from parallel to perpendicular configuration can be induced by current (arbitrary direction) and field applied along initial orientation of AFM vector. Transition from perpendicular to parallel configuration can be induced by the field only.Reuse & Permissions

Figure 5

(Color online) Profile of the effective potential well, Eq. (21), arbitrary units. $1-\Omega \le {\Omega }_0$ and $2-\Omega >{\Omega }_0$. Arrows indicate static solution $\left(\theta =0\right)$ unstable in overcritical regime and stable stationary solution $\left(\theta =\pi /2\right)$.Reuse & Permissions

Figure 6

(Color online) Relaxation dynamics of slow amplitude $l_Z$ at $t\ge t_{\text{min}}$. Points, numerical simulation, solid line—approximation according to Eq. (23), dashed line, envelope $\propto \text{exp}\left(-{\gamma }_{\text{AFM}}t\right)$ Both $l_Z$ and $t$ are dimensionless as explained in text.Reuse & Permissions

Figure 7

(Color online) Switching time from parallel to perpendicular configurations shown in Figs. 2a, 2b. (a) Current dependence of the calculated switching time, $t_{\text{min}}$ (dimensionless, as explained in text), and the effective pumping coefficient $\tau \propto {\left|J-J_{\text{cr}}\right|}^{-1}$, external magnetic field $H_0=0.2H_{\text{s-f}}$ is parallel to $Z$. Inset shows correlation between $\tau$ and $t_{\text{min}}$. (b) Field dependence of switching time $t_{\text{min}}$ at fixed bias current (points). Solid line shows approximation $\propto {\left|H_{\text{s-f}}+H_0\right|}^{-1}$.Reuse & Permissions

Figure 8

(Color online) Dynamics of AFM vector induced by a pulse of spin-polarized current. (a) Time dependence of $l_Z$ (thick or blue line) under the rectangular current pulse (thin or red line). Pulse duration close to $t_{\text{min}}$ is enough to ensure maximal deflection of $l_Z$ from the initial value. (b) High frequency rotation of AFM vector persists as long as current induces STT, as seen from time dependence of $\Omega$. Just after the current is switched off the frequency of rotation goes down to zero and AFM vector lies down to $XY$ plane. Relaxation time $\left(=1/{\gamma }_{\text{AFM}}\right)$ of both $\Omega$ and $l_Z$ is due to internal damping. (c) Magnetic field applied parallel to the initial orientation of $\mathbf{l}$ induces $90°$ switching, the final state of AFM vector is parallel to $XY$ plane. (d) In isotropic AFM in the absence of field a spin-polarized current may induce $180°$ switching. AFM vector is normalized as $\left|\mathbf{l}\right|=1$. $t$ and $\Omega$ are expressed in the dimensionless units as explained in text.Reuse & Permissions

Figure 9

(Color online) Current dependence of the exchange-bias field. (a) Exchange-bias spin-valve structure with multidomain AFM layer. AFM vector in some of domains deflects from the initial orientation due to STT. (b) The shift of bias for typical spin transfer (AFM layer is not affected by current). (c) The shift of bias in the case when spin torque is transferred to AFM layer.Reuse & Permissions