Driven energy transfer between coupled modes in spin-torque oscillators

The mutual interaction between the different eigenmodes of a spin-torque oscillator can lead to a large variety of physical mechanisms from mode hopping to multimode generation, that usually reduce their performances as radio-frequency devices. To tackle this issue for the future applications, we investigate the properties of a model spin-torque oscillator that is composed of two coupled vortices with one vortex in each of the two magnetic layers of the oscillator. In such double-vortex system, the remarkable properties of energy transfer between the coupled modes, one being excited by spin transfer torque while the second one being damped, result into an alteration of the damping parameters. As a consequence, the oscillator nonlinear behavior is concomitantly drastically impacted. This efficient coupling mechanism, driven mainly by the dynamic dipolar field generated by the spin transfer torque induced motion of the vortices, gives rise to an unusual dynamical regime of self-resonance excitation. These results show that mode coupling can be leveraged for controlling the synchronization process as well as the frequency tunability of spin-torque oscillators.

Figure 1

(a) Schematic of an hybrid magnetic tunnel junction: a Cu based spin-valve system with the two vortex Py layers (20 nm at the top, 6 nm at the bottom) above a 1-nm MgO barrier and a CoFeB based synthetic antiferromagnet. (b) Sketch of the hybridized gyrotropic modes of the double vortex system. The thin (thick) vortex layer and its associated coupled mode are excited (damped) by STT. (c) Evolution of the frequency $f_{\mathrm{exc}}$, the linewidth and the power of the excited mode as a function of the external perpendicular field for $I_{\mathrm{dc}}=+11$ mA. The frequency of the mode that is damped by STT is called $f_{\mathrm{damp}}$ $(H_1,H_2$, and $H_3$ correspond to the fields that we study by time domain measurements in Fig. 2).

Figure 2

(a) Noise power spectral density of the excited mode as a function of the offset frequency (for $I_{\mathrm{dc}}=+8$ mA and $H_{\mathrm{perp}}=-15$ kA/m). The dark line corresponds to the intrinsic phase noise $\mathrm{\Delta }{f}_0/\pi f^2$ (b) Evolution of the nonlinear parameters with $I_{\mathrm{dc}}$ at three different fields: nonlinear dimensionless parameter $\nu$, the linear linewidth $\mathrm{\Delta }{f}_0$, the amplitude relaxation rate ${\mathrm{\Gamma }}_p$ and the nonlinear frequency shift $N$. The different fields are either close $(H_1=-55$ kA/m), far $(H_3=-15$ kA/m) from an harmonic crossing or between two crossings $(H_2=-30$ kA/m).

Figure 3

(a) Frequency spectrum of the output emitted signal (associated with the dynamics in the bottom thick vortex layer close to the MgO barrier) at zero field for $I_{\mathrm{dc}}=-16$ mA. The coupled mode mainly dominated by the thin layer is excited by STT while the coupled mode mainly dominated by the thick layer is damped by STT and only thermally activated (b) $\mu \mathrm{Max}$ micromagnetic simulations representing gyration radii of the mode excited by STT in the two vortex layers at zero field, $I_{\mathrm{dc}}=-16$ mA. The simulations are performed at 0 K. The absence of thermal fluctuations explains that only the mode excited by STT is observed.

Figure 4

Evolution of the frequencies (a), linewidths (b), powers (c) of both the excited (red dot) and damped (blue dots) coupled modes as a function of the applied perpendicular field $H_{\mathrm{perp}}$. $I_{\mathrm{dc}}$ is kept fixed at $-15$ mA.

Figure 5

Experimental power spectrum and instantaneous frequency time traces for three values of field: out of $-10$ kA/m (a) and $+20$ kA/m (c) and within $+3$ kA/m (b), the self-resonance region. $I_{\mathrm{dc}}$ is kept fixed to $-15$ mA. (d) Evolution of the self-synchronization bandwidth as a function of the dc current.