Large-amplitude coherent spin waves excited by spin-polarized current in nanoscale spin valves

We present spectral measurements of spin-wave excitations driven by direct spin-polarized current in a free layer of nanoscale ${\mathrm{Ir}}_{20}{\mathrm{Mn}}_{80}∕{\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}∕\mathrm{Cu}∕{\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ spin valves. The measurements reveal that large-amplitude coherent spin-wave modes are excited over a wide range of bias current. The frequency of these excitations exhibits a series of jumps as a function of current due to transitions between different localized nonlinear spin-wave modes of the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ nanomagnet. We find that micromagnetic simulations employing the Landau-Lifshitz-Gilbert equation of motion augmented by the Slonczewski spin-torque term (LLGS) accurately describe the frequency of the current-driven excitations including the mode transition behavior. However, LLGS simulations give qualitatively incorrect predictions for the amplitude of excited spin waves as a function of current.

Figure 1

(Color online) (a) Schematic side view of the nanopillar spin valve used for studies of magnetization dynamics. (b) Schematic top view of the spin valve with approximate directions of magnetizations of the pinned, $M_P$, and the free, $M_F$, nanomagnets as well as the direction of positive external magnetic field $H$ and exchange bias field $H_{\mathrm{EB}}$. (c) Experimentally measured resistance of the nanopillar as a function of the external magnetic field (circles) and a macrospin Stoner-Wohlfarth fit to the data (solid line) with the parameters described in text. (d) Resistance versus field obtained from micromagnetic simulations using the giant magnetoresistance (GMR) asymmetry parameter $\chi =0.5$, the exchange bias field magnitude $H_{\mathrm{EB}}=1600\mathrm{Oe}$ and its direction ${\theta }_{\mathrm{EB}}=30°$ obtained from the macrospin fit shown in (c). (e) Differential resistance of the sample as a function of bias current measured at $H=0\mathrm{Oe}$ (red) and $H=680\mathrm{Oe}$ (blue). (f) dc resistance of the sample as a function of bias current obtained from the data in (e) by numerical integration.

Figure 2

(Color online) (a) Circuit schematic for measurements of magnetization dynamics driven by a direct current. (b) Normalized rms amplitude spectral density $S\left(f\right)$ (defined in text) generated by the spin valve under a dc bias of $6.15\mathrm{mA}$. (c) $S\left(f\right)$ as a function of current for the nanopillar spin valve measured at $H=680\mathrm{Oe}$. (d) $S\left(f\right)$ at $3.7\mathrm{mA}$ and $H=680\mathrm{Oe}$.

Figure 3

(Color online) (a) Dependence of the frequency of magnetization oscillations, $f$, on spin-torque amplitude $a_J$ calculated in the “minimal model” (see text for details). Gray-scale maps represent spatial distributions of the oscillation power for chosen $a_J$ values (bright corresponds to maximal oscillation power). (b) Oersted field effect: $f\left(a_J\right)$ without (open circles) and with (open triangles) the Oersted field included in the simulations; arrows indicate the positions of frequency jumps, and straight lines are guides to the eye. (c) Effect of the torque asymmetry: $f\left(a_J\right)$ for the symmetric ($\Lambda =1.0$, open triangles) and asymmetric (${\Lambda }^2=1.5$, solid triangles) spin torque.

Figure 4

(Color online) (a) Effect of thermal fluctuations on the frequency of magnetization oscillations: $f\left(a_J\right)$ for $T=0$ (triangles) and for $T\propto I\propto a_J$ (crosses). Simulated rms-amplitude spectral densities $S\left(f\right)$ for oscillations (b) before the first frequency jump, (c) between the first and second frequency jumps, and (d) after the second frequency jump. The linewidth of the peaks marked with $\delta$ is below the resolution limit of our numerical simulations. See the text for the detailed analysis of these spectra.

Figure 5

(Color online) (a) Dependence of the frequency of oscillations on spin torque amplitude $a_J$ for different polarization angles of the spin current, ${\theta }_p$, as defined in Fig. 1b. (b) The same frequencies plotted as functions of the normalized spin torque amplitude $a_J∕a_J^{\mathrm{cr}}$.

Figure 6

(Color online) (a), (c), (e) Examples of hysteresis loops of resistance versus field of different nominally identical samples. (b), (d), (f) Frequency of persistent magnetization dynamics as a function of current for the samples in (a), (c), (e) measured at $H=600\mathrm{Oe}$.

Figure 7

(Color online) (a) Comparison of the experimentally measured (solid triangles) and simulated (open circles) dependence of the frequency of oscillations on current. (b) Experimentally measured (solid triangles) and simulated (open circles) integrated rms-amplitude spectral density $S_{\mathit{int}}$ as a function of current.