Dimensional crossover in spin Hall oscillators

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons play an important role in suppression of the auto-oscillatory dynamics. Our measurements set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

Figure 1

(a) Schematic of Pt/Py/${\mathrm{AlO}}_x$ wire SHO device. Five devices with the wire width varying from 0.17 $\mu \mathrm{m}$ to 2.11 $\mu \mathrm{m}$ were studied. The active region length is 1.9 $\mu \mathrm{m}$ for all devices. Green arrows schematically show the electric current flow direction. (b) Scanning electron micrograph of the 0.51 $\mu \mathrm{m}$ wide SHO device. The magnetic field is applied in the plane of the sample at an angle $\theta$ with respect to the charge current flow direction. (c) Change in resistance of the five samples with different wire widths measured at 4.2 K for magnetic field applied at $5^{\circ }$ off the $y$ axis ($\theta ={85}^{\circ }$). (d) Saturation field $H_{\mathrm{sat}}$ of the wire for magnetic field applied at $\theta ={85}^{\circ }$ as a function of the wire width (solid line is a guide to the eye).

Figure 2

(a) Power spectral density (PSD) of the microwave signal generated by the 1.07 $\mu \mathrm{m}$ wide Pt/Py/${\mathrm{AlO}}_x$ wire SHO at the bias current density $J_{\mathrm{dc}}=2.0\times {10}^8$ A ${\mathrm{cm}}^{-2}$, bath temperature $T=4.2$ K, and magnetic field $H=470$ Oe applied at $5^{\circ }$ from y axis $\left(\theta ={85}^{\circ }\right)$. Three auto-oscillatory modes are excited. The non-Lorentzian peak line shapes are mainly due to standing waves in the microwave circuit. (b)–(f) Microwave emission spectra versus $J_{\mathrm{dc}}$ for five wires of different widths measured in fields exceeding $H_{\mathrm{sat}}$ by approximately 100 Oe and applied at $\theta ={85}^{\circ }$. The logarithmic color scale represents the emitted power normalized to the maximum power $P_{\max }$. The wire widths and the applied field values are shown in the figures. The low-frequency edge mode is seen for narrower wires (0.17 $\mu \mathrm{m}$ and 0.34 $\mu \mathrm{m}$ wide). The higher-frequency bulk modes are observed in wider wires (0.34 $\mu \mathrm{m}$, 0.53 $\mu \mathrm{m}$, 1.07 $\mu \mathrm{m}$, and 2.11 $\mu \mathrm{m}$ wide).

Figure 3

(a) Integrated microwave power emitted by all bulk modes of the wire $P_{\mathrm{b}}$ versus bias current density $J_{\mathrm{dc}}$. The data are shown for all four wires exhibiting bulk mode auto-oscillations. (b) Maximum value of the integrated microwave power emitted by all bulk modes of the wire $P_{\mathrm{bt}}$ as a function of the wire width. (c) Maximum integrated power of the largest-amplitude bulk mode $P_{\mathrm{bl}}$ as a function of the wire width.

Figure 4

Brillouin light scattering characterization of auto-oscillatory modes of the 1.07 $\mu \mathrm{m}$ wide wire device at room temperature ($T=300\mathrm{K}$). (a) Optical micrograph of the devices showing Pt/Py wire, Ti/Au leads, and laser spot of the BLS apparatus focused on one edge of the active region of the device. (b) BLS spectrum measured at the laser beam position at the edge of the active region shown in (a) for $J_{\mathrm{dc}}=9.77\times {10}^7$ A ${\mathrm{cm}}^{-2}$ and $H=495$ Oe applied at $\theta ={87}^{\circ }$. Spatially resolved BLS allows us to reveal the origin of the excitations: (c) Spatial profile of the BLS signal intensity at $f=4.3\mathrm{GHz}$—the center frequency of the low-frequency peak (edge mode). The rectangle denotes the approximate location of the active region of the device. This BLS spectral mapping reveals that this auto-oscillatory mode is an edge spin wave mode of the wire. (d) Spatial profile of the BLS signal intensity at $f=5.6\mathrm{GHz}$—the center frequency of the high-frequency peak (bulk mode). This BLS spectral mapping reveals that this auto-oscillatory mode is a bulk spin wave mode of the wire.

Figure 5

Micromagnetic simulations of spin wave spectra in the 1.07 $\mu \mathrm{m}$ wide wire with $H_{\mathrm{Oe}}=36$ Oe, $H=470$ Oe, and $\theta ={85}^{\circ }$. (a) Simulated spin Hall oscillator microwave emission spectra at ${\theta }_{\mathrm{SH}}=0.045$ (global average FFT). (b) Simulated cell-by-cell FFT spectra $\langle m_x^2\rangle$ at ${\theta }_{\mathrm{SH}}=0.045$ to be compared to BLS data. Note the scale of (b) is $2500\times$ the scale of (a). Inset shows a zoom of $50\times$ in amplitude. (c) Simulated spin wave eigenmode spectra (global average FFT).

Figure 6

Micromagnetic simulations of spin wave spatial profiles in the 1.07 $\mu \mathrm{m}$ wide wire. Amplitude (top) and phase (bottom) spatial profiles are shown for the auto-oscillatory modes with frequencies (a) 4.47, (b) 4.61, (c) 5.16, (d) 5.23, (e) 5.51, and (f) 5.63. The amplitude scales for (a)–(c) are the same, while the scales for (d), (e), and (f) are $2\times$, $100\times$, and $10\times$ larger, respectively. Amplitude (top) and phase (bottom) spatial profiles for spin wave eigenmodes with frequencies (g) 4.64, (h) 5.13, and (i) 5.18 GHz. Individual panel labels correspond to the peaks labeled $a$–$i$ in Fig. 5.

Figure 7

Temperature and angular dependence of auto-oscillatory dynamics in the 0.53 $\mu \mathrm{m}$ wide wire device. (a) Critical current density $J_{\mathrm{c}}$ (blue circles) and integrated power $P_{\mathrm{bt}}$ (red squares) versus bath temperature measured at $H=750$ Oe and $\theta ={85}^{\circ }$. (b) Critical current density (blue circles) and maximum emitted power $P_{\mathrm{bt}}$ (red squares) versus in-plane magnetic field angle $\theta$ measured at bath temperature of 56 K and magnetic field $H=1900$ Oe.