Mechanisms limiting the coherence time of spontaneous magnetic oscillations driven by dc spin-polarized currents

The spin-transfer torque from a dc spin-polarized current can generate highly coherent magnetic precession in nanoscale magnetic-multilayer devices. By measuring linewidths of spectra from the resulting resistance oscillations, we argue that the coherence time can be limited at low temperature by thermal deflections about the equilibrium magnetic trajectory and at high temperature by thermally activated transitions between dynamical modes. Surprisingly, the coherence time can be longer than predicted by simple macrospin simulations.

Figure 1

(Color online) (a) The narrowest spectral peak for free-layer oscillations that we have observed in a nanopillar $(\mathrm{FWHM}=5.2\mathrm{MHz})$. The device has the same composition as device 3, described in the text. (Inset) Schematic of a nanopillar device. (b) Differential resistance of device 1 as a function of $I$ and $H$ at $T=4.2\mathrm{K}$, obtained by increasing $I$ at fixed $H$. AP denotes static antiparallel alignment of the two magnetic moments, P parallel alignment, P/AP a bistable region, SD small-angle dynamics, and LD large-angle dynamics.

Figure 2

Measured linewidths vs $T$ for (a) device 1 and (b) device 2. The dashed line is a fit of the low-$T$ data to Eq. (2) and the solid line is a combined linewidth from Eqs. (2, 3), obtained by convolution. (Inset) Dependence of linewidth on $I$ for device 1, with estimates of precession angles.

Figure 3

(Color online) (Main plot and lower inset) Squares: Linewidth calculated directly from the Fourier transform of $R\left(t\right)$ within a macrospin LLG simulation of the dynamics of device 1. Triangles: Linewidth calculated from the same simulation using the right-hand side of Eq. (2). Line in inset: Fit to a $T^{1∕2}$ dependence. (Top inset) Simulated probability distribution of the precession angle at $15\mathrm{K}$.

Figure 4

Measured (a) frequencies and (b) linewidths of large-angle dynamical modes in device 3 for $T=40\mathrm{K}$, ${\mu }_{0}H=63.5\mathrm{mT}$ applied in the exchange-bias direction, 45° from the free-layer easy axis. When two modes are observed in the spectrum simultaneously, both linewidths increase.