Magnetic Droplet Mode in a Vertical Nanocontact-Based Spin Hall Nano-Oscillator at Oblique Fields

We experimentally demonstrate an alternative type of spin Hall nano-oscillator based on a vertical nanocontact fabricated on a $\mathrm{Pt}$/($\mathrm{Co}$/$\mathrm{Ni}$) multilayer. We analyze the spectral characteristics of the nano-oscillator as a function of current, magnetic field, and temperature. At sufficiently large currents, the oscillator exhibits dynamics at a frequency far below the ferromagnetic resonance, which at large fields exhibits a redshift with increasing current. At smaller fields and low temperatures, the frequency becomes nearly independent of current, with a well-defined threshold current. These distinct spectral characteristics of the demonstrated nano-oscillator can be explained by the formation of the magnetic droplet—a dissipative magnetic soliton stabilized by the local injection of spin current produced by the spin Hall effect in $\mathrm{Pt}$. The minimum linewidth exhibits a linear temperature dependence, suggesting single-mode dynamics, and enabling coherent magnetization auto-oscillation at room temperature. The demonstrated nano-oscillator geometry provides alternative opportunities for the development of active nanomagnetic devices and for optimization of their spectral characteristics for applications in microwave technology and spin-wave logic.

Figure 1

Structure and electronic characteristics of the VNC SHNO based on a $\mathrm{Pt}$/($\mathrm{Co}$/$\mathrm{Ni}$) bilayer. (a) The device structure and the experimental setup including dc current source, bias tee, microwave amplifier, and spectrum analyzer (SA). (b)–(d) Color maps of the current distribution in the $\mathrm{Pt}$ layer (b), the in-plane Oersted field in the $\mathrm{Co}$/$\mathrm{Ni}$ layer (c), and the spin current injected from $\mathrm{Pt}$ into $\mathrm{Co}$/$\mathrm{Ni}$ (d) calculated with comsol multiphysics. The scales are indicated to the right of the corresponding plots. The dotted circle marks the nanocontact, and arrows show the directions of the corresponding vector quantities. (e) Calculated magnitude of the current density and the in-plane Oersted field at current $I=14\mathrm{mA}$ along the section shown by the dashed lines in (b),(c).

Figure 2

(a) Microwave-generation spectra (symbols) obtained at $I=14\mathrm{mA}$, $T=295\mathrm{K}$, and the labeled values of the magnetic field $H$. The curves are the results of fitting with the Lorentzian function. (b) Auto-oscillation frequency $f_c$ (solid circles) and the FMR frequency $f_{\mathrm{FMR}}$ (squares) versus field $H$. $f_{\mathrm{FMR}}$ is measured by the ST-FMR technique.

Figure 3

Dependence of the microwave-generation characteristics on current at $T=295\mathrm{K}$. (a)–(c). Pseudocolor plots of the spectra obtained at $I$ varied between 9 and 15 mA in 0.3-mA steps at fields $H=800\mathrm{Oe}$ (a), $H=960\mathrm{Oe}$ (b), and $H=1090\mathrm{Oe}$ (c). (d)–(f) Dependence of the central generation frequency $f_c$ (d), FWHM (e), and integral intensity $P_{\mathrm{int}}$ (f) on current at $H=800\mathrm{Oe}$ (squares), $H=960\mathrm{Oe}$ (circles), and $H=1090\mathrm{Oe}$ (triangles). $f_c$, the FWHM, and $P_{\mathrm{int}}$ are determined by fitting the power spectra with the Lorentzian function. (g) Dependence of the auto-oscillation-onset current $I_{\mathrm{on}}$ of the SHNO on the external field $H$.

Figure 4

Dependence of the microwave-generation characteristics on current at $T=60\mathrm{K}$. (a)–(e) Pseudocolor plots of the spectra obtained at $I$ varied between 10.6 and 17.2 mA in 0.3-mA steps and fields $H=620\mathrm{Oe}$ (a), $H=800\mathrm{Oe}$ (b), $H=960\mathrm{Oe}$ (c), $H=1090\mathrm{Oe}$ (d), and $H=1200\mathrm{Oe}$ (e). (f)–(h) The center frequency $f_c$ (f), FWHM (g), and integral intensity $P_{\mathrm{int}}$ (h) of the low-frequency mode $m_l$ versus $I$ extracted from the spectra in (a)–(e) at the labeled fields. (i)–(k) Field dependence of the threshold current $I_{\mathrm{th}}$ (i), the minimum FWHM (j), and $P_{\mathrm{int}}$(k) of mode $m_l$ obtained at the current $I_p$ defined in the main text.

Figure 5

Minimum linewidth versus $T$ for $H=1090\mathrm{Oe}$ (squares) and $H=1200\mathrm{Oe}$ (circles). The dashed lines are linear fits to the data.

Figure 6

Micromagnetic simulation of the VNC SHNO. (a) Representative calculated auto-oscillation spectrum showing a single oscillating mode and its second harmonic obtained by micromagnetic simulation at $H=1000\mathrm{Oe}$ applied at angle $\phi ={85}^{\circ }$ relative to the plane and $I=14\mathrm{mA}$. (b),(c) Normalized spatial maps of the square of the simulated dynamical magnetization component $m_x^2$ and $m_z^2$ of the fundamental mode at $f=1.24\mathrm{GHz}$. The large solid circle represents the boundary of the active simulation region, the dotted circle marks the nanocontact, and the arrow shows the direction of the in-plane component of the applied oblique field.