Spin-transfer dynamics in spin valves with out-of-plane magnetized CoNi free layers

We have measured spin-transfer-induced dynamics in magnetic nanocontact devices having a perpendicularly magnetized Co/Ni free layer and an in-plane magnetized CoFe fixed layer. The frequencies and powers of the excitations agree well with the predictions of the single-domain model and indicate that the excited dynamics correspond to precessional orbits with angles ranging from zero to $90°$ as the applied current is increased at a fixed field. From measurements of the onset current as a function of applied field strength we estimate the magnitude of the spin torque asymmetry parameter $\Lambda \approx 1.5$. By combining these with spin torque ferromagnetic resonance measurements, we also estimate the spin-wave radiation loss in these devices.

Figure 1

(Color online) (a) Two-dimensional plot showing the device oscillation frequency and output power as a function of $I_{dc}$ for an external field of 0.25 T applied perpendicular to the film plane. The power spectral density (PSD) is shown in a linear color scale. The second harmonic signal (see text) does persist up to the highest current values, but at significantly reduced power density, as shown in the inset. The magnitude has been corrected for amplifier gain and cable loss. All spectral data were taken on a time scale of roughly 1 s. (b) Oscillation frequency and (c) and line width (FWHM) of the first harmonic peak from the data shown in part (a) as determined by Lorentzian fits to the spectra. The frequencies and line widths of the second harmonic signal are not shown for reasons of clarity, but have been verified as to having both twice the frequency and line width of the first harmonic single.

Figure 2

(Color online) (a) Magnetization trajectories from the single-domain simulations for several current values. (b) and (c) Simulated time traces showing each component of the magnetization for $I_{dc}=5.5$ and 18 mA, respectively. The effects of the trajectories canting away from the $z$ axis can be seen through the time variation in $M_z$ and the Fourier transforms of $M_x$ (insets), the relevant component for the GMR readout mechanism. For currents less than roughly 10 mA, the time traces show nominally sinusoidal variations of $M_x$ (as is evidenced by the $I_{dc}=5.5\text{mA}$ example, where all higher harmonics are less than 3% of the fundamental). As the current is increased the time dependence significantly deviates from sinusoidal, as seen in (c) for $I_{dc}=18\text{mA}$, where the second harmonic is roughly 20% of the fundamental. The simulations are for a device having dimensions of $100\times 100\times 3{\text{nm}}^3$, an external field of 0.25 T applied along the $z$ axis, a damping parameter $\alpha =0.03$ and a simulated temperature of 5 K.

Figure 3

(Color online) (a) Onset frequencies of the dc driven dynamics (circles) along with the resonance frequencies (squares) determined through ST-FMR measurements as a function of applied field. (Inset) Plot showing an example of a frequency swept ST-FMR scan taken in an external field of 0.2 T and $I_{dc}=1\text{mA}$.

Figure 4

(a) Mapping of the measured device oscillation frequency to the derived oscillation amplitude $\theta$, which is shown as a function of $I_{dc}$. The error bars are determined through standard error propagation techniques and the uncertainty in the experimentally determined value of the ${\mu }_{0}H=0\text{T}$ intercepts of the fits to the dc driven and ST-FMR data in Fig. 3. The increased error bars at small angles reflect the sensitivity of the error propagation associated with the arc-cosine function near $0°$. (b) Calculated values of amplitude fluctuations $\Delta \theta$ as a function of precessional amplitude $\theta$. The values are calculated through Eq. (2) in which $\Delta f$ is taken as the FWHM values reported in Fig. 1c.

Figure 5

(Color online) Plots of the measured and theoretical output power as functions of $I_{dc}$. The theoretical plot is determined through Eq. (3) and the data shown in Fig. 4a, as described in the text. The maximum $\Delta R$ for this device is $100\text{m}\Omega$.

Figure 6

(Color online) The measured onset current $I_c$ as a function of the external field applied perpendicular to the film plane along with a linear fit to the data. The error bars determined by the current interval between adjacent spectral measurements are $\pm 0.05\text{mA}$ and are smaller than the data points in the plot.