Current-Induced Nanomagnet Dynamics for Magnetic Fields Perpendicular to the Sample Plane

We present electrical measurements of high-frequency magnetic dynamics excited by spin-polarized currents in $\mathrm{C}\mathrm{o}/\mathrm{C}\mathrm{u}/{\mathrm{N}\mathrm{i}}_{80}{\mathrm{F}\mathrm{e}}_{20}$ nanopillar devices, with a magnetic field applied perpendicular to the sample layers. As a function of current and magnetic field, the dynamical phase diagram contains several distinguishable precessional modes and also static magnetic states. Using detailed comparisons with numerical simulations, we provide rigorous tests of the theory of spin-transfer torques.

Figure 1

(a) Measured room-temperature dynamical stability diagram for in-plane $H$. The dashed line separates static states with the free-layer moment parallel (P) and antiparallel (AP) to the fixed layer. Solid lines outline the region of microwave-frequency dynamics. Inset: Schematic of the sample geometry. (b) Magnetoresistance near $I=0$ for $H$ perpendicular to the sample layers. The measurement includes a lead resistance of $\sim 20\mathbf{\Omega }$. (c) Variations in $dV/dI$ and (d) in $R=V/I$ for perpendicular $H$ as a function of $I$.

Figure 2

(a) Measured small-amplitude signal frequency for perpendicular $H$ (circles) compared to numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation (black curve). The red line is a linear fit to Eq. (1). Inset: the small-amplitude signal frequency for in-plane $H$, with a fit to the Kittel formula. (b) Spectra for $H=18\mathrm{k}\mathrm{O}\mathrm{e}$ perpendicular to the sample plane, for $I=2.2–9.2\mathrm{m}\mathrm{A}$, in increments of 1 mA (offset vertically). (c),(e),(g) Color scale: measured spectra as a function of $I$ at selected values of $H$ perpendicular to the sample plane. The spectra are normalized as discussed in the text. $P_{\mathrm{J}\mathrm{N}}$ is the magnitude of room-temperature Johnson noise. White lines show $dV/dI$, plotted using different vertical scales. (d),(f),(h) Spectra predicted by the simulation described in the text. The diagrams illustrate the dynamical modes of the free layer within the simulations, for the values of $I$ marked by arrows. The vertical direction is normal to the sample plane.

Figure 3

Experimental room-temperature stability diagram for perpendicular $H$. Filled symbols indicate features that are reproducible between samples. Open symbols show transitions that can differ in number and position between samples. SLR (SHR) denotes a region of static low (high) resistance. Squares indicate the onset of small angle precession. Triangles denote the position of frequency steps. Diamonds show kinks in the dependence of $f$ on $I$. Circles denote points where the microwave signal drops below measurable values. Lines indicate peaks in $dV/dI$. (b) Theoretical room-temperature stability diagram obtained by numerical solution of the LLG equation with the Slonczewski spin-torque term [1]. Solid lines separate SLR, SHR, and dynamical states (precession $\mathrm{\text{angles}}>2°$). Dotted and dashed lines show the transition from small-angle precession about the $I=0$ equilibrium angle to large-angle precession about $H$, associated with a step in $f$ (dashed line) or a kink in $f$ vs $I$ (dotted line). At the $1\mu \mathrm{s}$ time scale in the simulations, transitions between the SLR and SHR states are hysteretic [18], with the boundary given by the black line for increasing $I$ and the gray line for decreasing $I$.