Quenched Slonczewski-windmill in spin-torque vortex-oscillators

Spin-torque nano-oscillators (STNOs) typically consist of two single domain ferromagnetic layers separated by a metallic spacer or a tunnel barrier, one with its magnetization fixed (polarizing layer), the other one susceptible to torques (free layer). An electric current traversing the system perpendicular to the layers becomes spin-polarized and exerts torques on the magnetic moments [1-3], thereby inducing switching or steady-state dynamics. The pinning of the polarizing layer can be achieved by exchange coupling to an antiferromagnet [4] or by extending its thickness and lateral dimension [5]. In the absence of pinning, both ferromagnetic layers can be excited. For increasingly symmetric STNOs, this can lead to a dynamic equilibrium state called the Slonczewski-windmill [1,6], with the magnetic moments of both layers rotating in the same direction with a constant relative angle, resulting in a vanishing magnetoresistance (MR) time-dependence.
Here we investigate STNOs containing two stacked magnetic vortices, i.e., a system consisting of two ferromagnetic disks, each in a vortex state and separated by a metallic, nonmagnetic spacer. Employing analytical and numerical methods, we study the coupled spin torque-driven motion of the magnetizations in the two disks, which are not pinned by any of the above mentioned mechanisms. The theoretical findings are supported by our experimental data obtained from double-vortex Fe/Ag/Fe STNOs.
The motion of the magnetic vortex in each of the disks is governed by the Thiele equation [7] with an additional force expression arising from the transfer of spin angular momentum from the polarised current to the vortex. Assuming that in the double vortex system, each vortex is free to move while at the same time it serves as a polarizing layer for the other, we solve the system of Thiele equations coupled by the spin-polarized current. We use parabolic approximations to the magnetostatic potentials for each vortex, which are chosen to represent our Fe/Ag/Fe nanopillars with ferromagnetic layers with a thickness ratio of 5/3; the uncoupled top and bottom vortices’ eigenfrequencies are set to 1.0 and 1.7 GHz, respectively.
The solutions are obtained numerically using Maple's rkf45 implementation. The results can be summarized as follows: While the spin torque induces large orbit vortex gyration in one of the layers, the vortex motion in the other disk is strongly reduced, resulting in a quenching of the Slonczewski-windmill mode. Which of the two layers contributes dominantly to the magnetization dynamics is determined by the direction of the applied current. This effect results from an adaption of the motion of the constricted vortex according to the dominant one. The former acquires a stable phase to the dominant vortex, while the latter determines the frequency and sense of gyration of the whole system: If its core polarity is positive (negative), the system gyrates in the counterclockwise (clockwise) direction. If the dominating vortex is in the top disk, the gyration frequency is 1.0 GHz while for large orbit gyration in the bottom disk, we obtain 1.7 GHz. Figure 1 displays the relations between the phase, frequency and gyration radius of the bottom vortex in the case, where the top vortex is dominant. For an experimental confirmation of the frequency and phase adaption mechanism and the related quenching of the windmill modes, we study the current-induced magnetization dynamics of a Fe/Ag/Fe nanopillar with a Fe layer thickness ratio of 5/3. We apply current densities of 6.1x107 A/cm2 and investigate the resulting double vortex dynamics depending on the current polarity. At low external field, the ratio between the obtained frequencies is close to the ratio of the disk aspect ratios, which strongly supports our numerical findings.

References:

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