Quenched Slonczewski windmill in spin-torque vortex oscillators

We present a combined analytical and numerical study on double-vortex spin-torque nano-oscillators and describe a mechanism that suppresses the windmill modes. The magnetization dynamics is dominated by the gyrotropic precession of the vortex in one of the ferromagnetic layers. In the other layer, the vortex gyration is strongly damped. The dominating layer for the magnetization dynamics is determined by the sign of the product between sample current and the chiralities. Measurements on Fe/Ag/Fe nanopillars support these findings. The results open up a new perspective for building high quality-factor spin-torque oscillators operating at selectable, well-separated frequency bands.

Figure 1

Coordinate system (a) and sample structure (b) used in the calculation. The sample consists of two ferromagnetic disks (1 and 2), each containing a vortex characterized by its chirality and core polarity (illustrated by the white arrows). The two ferromagnetic layers are separated by a metallic, nonmagnetic spacer (transparent). The positive technical current direction is shown, corresponding to an electron flow from the top to the bottom layer. (c) Scanning electron micrograph of a nanocontact after ion beam etching.

Figure 2

Spin-torque magnitudes exerted by disk 2 on the vortex in disk 1 and their dependence on the lateral core-core separation. The torque arising from the polarizer core, $F_1^c$ is negligible at large distances, explaining the results obtained by micromagnetic simulations and presented in Ref. 26.

Figure 3

Vortex dynamics obtained for the case of equal chiralities, represented by the time variation of the respective $X$ coordinates of the vortex cores. (a) For positive and negative current, the system gyrates at $1.0\mathrm{GHz}$ (solid) and $1.67\mathrm{GHz}$ (dotted), respectively. The $X$ coordinate of the vortex cores is shown in the lower panels for positive (b) and negative (c) currents. The thin line corresponds to the top, the thick line to the bottom vortex. In (b), both cores have positive polarity, while in (c) they are antiparallel with the bottom core pointing down.

Figure 4

Trajectory radius $r$ (a) and frequency $f$ [(b) and (c)] of the bottom vortex as functions of the phase $\varphi$ with respect to the top vortex which gyrates at the same frequency. The solid and dashed lines correspond to positive and negative bottom vortex core polarity, respectively. The dash-dotted lines mark the eigenfrequency $f^0$ of the uncoupled bottom vortex for positive (b) and negative (c) core polarity.

Figure 5

$X$ components of the top (thin line) and bottom (thick line) core coordinates versus time for the case of symmetric disks. The cores are aligned parallel in (a) and antiparallel in (b). In the parallel case, a windmill mode only appears in a transient time interval, but is hindered afterwards. The oscillation decays due to the low core separation and the related decrease of the spin-transfer torque-induced force.

Figure 6

Resistance vs field measurements at sample currents of $+21\mathrm{mA}$ [(d) and (f)] and for $-21\mathrm{mA}$ (e). Simultaneously to the resistance measurements, the high-frequency spectra resulting from the magnetization dynamics were recorded. The square symbols on the MR curves indicate data points at which the corresponding spectrum displayed a peak (regardless of whether or not the sample was in a double vortex state). The top panels (a)–(c) display the peak frequencies. The insets to (a)–(c) show single spectra recorded at a field magnitude of about $70\mathrm{mT}$. Arrows indicate the sweep directions. The second sweep belonging to negative current is not shown, since no magnetization dynamics was visible in the double vortex state.