Dynamical Skyrmion State in a Spin Current Nano-Oscillator with Perpendicular Magnetic Anisotropy

We study the spectral characteristics of spin current nano-oscillators based on the $\mathrm{Pt}/[\mathrm{Co}/\mathrm{Ni}]$ magnetic multilayer with perpendicular magnetic anisotropy. By varying the applied magnetic field and current, both localized and propagating spin wave modes of the oscillation are achieved. At small fields, we observe an abrupt onset of the modulation sidebands. We use micromagnetic simulations to identify this state as a dynamical magnetic skyrmion stabilized in the active device region by spin current injection, whose current-induced dynamics is accompanied by the gyrotropic motion of the core due to the skew deflection. Our results demonstrate a practical route for controllable skyrmion manipulation by spin current in magnetic thin films.

Figure 1

Magnetic characteristics of the $\mathrm{Pt}(5)/[\mathrm{Co}(0.2)/\mathrm{Ni}(0.3){]}_6$ film at 295 K. (a) Anomalous Hall effect measured in a film patterned into a $4\times 14\mu \mathrm{m}$ Hall cross, with in-plane (triangles) and out-of-plane (circles) field. (b) Dependence of the SCAO resistance on the direction of in-plane field $H=1\mathrm{kOe}$, due to the AMR of the magnetic film. (c) $f_{\text{FMR}}$ versus in-plane field measured in the SCAO. Top inset: scanning electron micrograph of the device and the experimental layout. Bottom inset: ST-FMR voltage versus frequency $f_{\text{ex}}$ of the applied microwave current $I_{\text{ac}}=2\mathrm{mA}$, at $H=700\mathrm{Oe}$ [24]. The curve is the best fit with a sum of symmetric and antisymmetric Lorentzians, accounting for the effects of ST and the Oersted field.

Figure 2

Dependence of the microwave generation characteristics on current $I$ at $H=1.1\mathrm{kOe}$. (a) Pseudocolor plot of the spectra obtained at $I$ between 11 and 14.4 mA increased in 0.2 mA steps. (b) Symbols: power spectral density (PSD) at $I=14\mathrm{mA}$. The linewidth was determined by fitting the spectra with the Lorentzian function. (c) Dependence of the FWHM on current for the propagating mode at small $I<12.5\mathrm{mA}$ (squares), the bullet mode at $I>12.5\mathrm{mA}$ (circles), and the quasipropagating mode at $I>14\mathrm{mA}$ (triangles).

Figure 3

Dependence of the microwave generation characteristics on $H$ at $I=13\mathrm{mA}$. (a) Spectra obtained at $H$ between 100 Oe and 1.6 kOe increased in 100 Oe steps. (b) Spectrum obtained at $H=400\mathrm{Oe}$ exhibits sidebands around the main peak at $f_d=4.55\mathrm{GHz}$. (c) Dependence of the central generation frequency (solid symbols), $f_{\text{FMR}}$ (dashed curve), and total integral intensity (open symbols) on $H$.

Figure 4

(a)–(d) Time sequences of out-of-plane (in color) and in-plane (vector) magnetization components obtained from micromagnetic simulations at current $I=5\mathrm{mA}$ and field $H=300\mathrm{Oe}$. (e) The power spectrum of the averaged in-plane projection of magnetization along the current direction. Two arrows indicate sideband peaks. The material parameters used in the simulations are the exchange stiffness $A=10\mathrm{pJ}/\mathrm{m}$, the saturation magnetization $M_s=850\mathrm{kA}/\mathrm{m}$, the perpendicular anisotropy $K_u=0.65\mathrm{MJ}/{\mathrm{m}}^3$, the damping constant 0.02, and the spin Hall angle 0.05.