Interplay between Nonequilibrium and Equilibrium Spin Torque Using Synthetic Ferrimagnets

We discuss the current induced magnetization dynamics of spin valves ${\mathrm{F}}_0|\mathrm{N}|\mathrm{SyF}$ where the free layer is a synthetic ferrimagnet $\mathrm{SyF}$ made of two ferromagnetic layers ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ coupled by RKKY exchange coupling. When the magnetic moment of the outer layer ${\mathrm{F}}_2$ dominates the magnetization of the $\mathrm{SyF}$, the sign of the effective spin torque exerted on the layer ${\mathrm{F}}_1$ is controlled by the coupling’s strength: for weak coupling the spin torque tends to antialign ${\mathrm{F}}_1$’s magnetization with respect to the pinned layer ${\mathrm{F}}_0$. At large coupling the situation is reversed and tends to align ${\mathrm{F}}_1$ with respect to ${\mathrm{F}}_0$. At intermediate coupling, numerical simulations reveal that the competition between these two incompatible limits leads generically to spin torque oscillator (STO) behavior. The STO is found at zero magnetic field, with very significant amplitude of oscillations and frequencies up to 50 GHz or higher.

Figure 1

Panel (a) is a cartoon of the magnetic multilayer stack, in which ${\mathbf{M}}_i$ is the magnetization of the layer ${\mathrm{F}}_i$. The angle between ${\mathbf{M}}_1$ and ${\mathbf{M}}_0$ (${\mathbf{M}}_2$) is respectively $\theta$ ($\alpha$). Panels (b), (c), and (d) show the stationary magnetization $m_1^z$ along ${\mathbf{M}}_0$ as a function of the current density $j$ in $\mathrm{A}·{\mathrm{cm}}^{-2}$, for a stack with $d_1=2.\mathrm{nm}$, $d_2=4d_1$ and three different coupling strengths $J$; (b) weak coupling limit ($J=0$), (c) Intermediate coupling limit ($J=-{10}^{-3}\mathrm{J}·{\mathrm{m}}^{-2}$). (d) Strong coupling limit ($J=-6\times {10}^{-3}\mathrm{J}·{\mathrm{m}}^{-2}$). Upper (Lower) inset: Sketch of the torque ${\mathit{\tau }}_1$ action on ${\mathbf{M}}_1$ (${\mathbf{M}}_{\mathrm{SyF}}$) for the weak (strong) coupling regime.

Figure 2

Upper panel: phase diagram of the system as a function of the current density $j$ and the thickness $d_1$ for a fixed $\delta =4$ and $J=-5\times {10}^{-3}\mathrm{J}·{\mathrm{m}}^{-2}$. The various symbols indicate the observed stationary states in the corresponding region (defined by different colors): $\uparrow$ ($\downarrow$) stands for $m_1^z=1$ ($m_1^z=-1$), while STO corresponds to the presence of a precessional state. In the 2 STO region, two different STO states can be observed depending on the hysteresis history. Lower panels: Resistance $R$ as a function of time $t$ for a pillar surface of $1000{\mathrm{nm}}^2$ and $d_1=3\mathrm{nm}$. Upper (lower) plots correspond to initial conditions in the up (down) configuration. Left panels: $j=2.8\times {10}^7\mathrm{A}·{\mathrm{cm}}^{-2}$. Right panels: $j=5.8\times {10}^7\mathrm{A}·\mathrm{c}{\mathrm{m}}^{-2}$. The amplitude of the oscillation with the up initial condition is small and invisible on the scale of the graphics.

Figure 3

Upper plot: Amplitude (in %) of the time dependent signal of the resistance as a function of $d_1$ for fixed $j=6\times {10}^7\mathrm{A}·{\mathrm{cm}}^{-2}$. Lower plot: Idem for the main oscillating frequency of the resistance. Insets: Corresponding color plots in the ($j$, $d_1$) plane. $\delta =4$ and $J=-5\times {10}^{-3}\mathrm{J}·{\mathrm{m}}^{-2}$.