Power and linewidth of propagating and localized modes in nanocontact spin-torque oscillators

The integrated power and linewidth of a propagating and a self-localized spin-wave mode excited by spin-polarized current in an obliquely magnetized magnetic nanocontact are studied experimentally as functions of the angle ${\theta }_e$ between the external bias magnetic field and the nanocontact plane. It is found that the power of the propagating mode increases monotonically with ${\theta }_e$, while the power of the self-localized mode has a broad maximum near ${\theta }_e={40}^{\circ }$ and exponentially vanishes near the critical angle ${\theta }_e={58}^{\circ }$, at which the localized mode disappears. The linewidth of the propagating mode in the interval of angles ${58}^{\circ }<{\theta }_e<{90}^{\circ }$, where only this mode is excited, is adequately described by the existing theory, while in the angular interval where both modes can exist the observed linewidth of both modes is substantially broadened due to the telegraph switching between the modes. Numerical simulations and an approximate analytical model give a good semiquantitative description of the observed results.

Figure 1

Power spectral density at $I_{\mathrm{dc}}=-12.6$, $-14$, and $-16$ mA, for two directions of the external magnetic field. (a) For ${\theta }_e={30}^{\circ }$, two distinct peaks can be identified: a red-shifted lower frequency peak, identified as a localized soliton mode, and a blue-shifted higher frequency peak, identified as the propagating mode. (b) At ${\theta }_e={70}^{\circ }$, only the propagating mode is observed.

Figure 2

(a) Averaged experimentally measured integrated power of both modes as a function of the angle of the applied magnetic field. The asymmetric error bars at each data point represent the upper and lower range of the data set, which is made up of the integrated power at different current values. (b) Nonlinear power of both modes computed from micromagnetic simulations using Eq. (1).

Figure 3

Experimentally measured linewidth of propagating (filled symbols) and localized (open symbols) modes as a function of the angle of the applied magnetic field. Solid line: calculated linewidth using the analytical model of Ref. 28. Dashed line: calculated linewidth using the partial coherence model described in the text.

Figure 4

Precession orbit of the magnetization for the propagating mode (top row) and the localized mode (bottom row), at different applied field directions, indicated by the filled arrow. The magnitude of the field is the same in all cases.

Figure 5

Time profile of individual mode oscillations in the bimodal regime of nanocontact spin-torque oscillator generation (schematically). The time profile consists of a series of “bursts” of approximately the same shape at the moments $t_n$. The oscillation phase at each burst is ${\phi }_n$.

Figure 6

Effective spectrum of phase fluctuations ${\sigma }_{\phi }\left(\omega \right)$ for several values of the phase variance $\Delta \phi$.