Auto-oscillating Spin-Wave Modes of Constriction-Based Spin Hall Nano-oscillators in Weak In-Plane Fields

Abstract

We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane fields (µ0HIP = 30-40 mT) and also investigate its angular dependence. We compare SHNOs with different nano-constriction spacings of 300 and 900 nm. In all devices, mutual synchronization occurs below a certain critical angle, which is higher for the 300 nm spacing than for the 900 nm spacing, reflecting the stronger coupling at shorter distances. Alongside the synchronization, we observe a strong second harmonic consistent with predictions that the synchronization may be mediated by the propagation of second harmonic spin waves. However, although Brillouin Light Scattering microscopy confirms the synchronization, it fails to detect any related increase of the second harmonic. Micromagnetic simulations instead explain the angular dependent synchronization as predominantly due to magneto-dipolar coupling between neighboring SHNOs.

Interplay of Linear and Nonlinear Localization Mechanisms in Spin-Torque Oscillators with a Field Well

“…This means that the excitation thresholds of both these modes are close to each other. Similar hoppings were observed in a constriction-based SHO [27].…”

“…Recently, it was shown that the excited spin-wave mode in a nanoconstriction SHO, in which a ferromagnetic layer is patterned, is often a linearly localized mode independent of the static magnetization direction. It is a consequence of the strong nonuniformity of the internal magnetic field and different nonlinear properties of the edge modes compared to the bulk ones [26][27][28]. In [29], the mode hopping between linearly localized and bullet modes in an SHO with extended active area was found.…”

Controllable excitation of quasi-linear and bullet modes in a spin-Hall nano-oscillator

“…33 Therefore, the simultaneous presence of two spectral peaks in our experiments likely indicates random hopping of the SHNO between these modes. 21,34 This random switching cannot be observed in the temporal dependences in Fig. 4(b), obtained by averaging over multiple pulses of the driving current.…”

“…For instance, the SHNOs formed by a nano-constriction in the ferromagnet/spin Hall material bilayer 9 typically exhibit the quasi-linear auto-oscillation mode, 12,13,20 while the bullet mode has been observed only at low bias magnetic fields and large currents. 21 Meanwhile, SHNOs formed by a nano-gap between sharp electrodes on top of the extended ferromagnet/spin Hall bilayer 22 exhibit bullet-mode auto-oscillations, [23][24][25] while the quasi-linear mode was found in this geometry only at cryogenic temperatures. 8 In contrast, the recently demonstrated SHNOs based on magnetic insulators, 15 whose geometry is close to that of the nano-gap devices, were shown to exhibit only the quasi-linear auto-oscillation mode.…”

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

“…Multimodal dynamics is also commonly observed in an alternative SHNO configuration based on an F/N nanowire [21], due to the small frequency separation among the dynamical modes in a relatively large magnetic system. Meanwhile, SHNO layouts based on bow tie-shaped nanoconstrictions in extended F/N bilayers [22] or tapered nanowires [23][24][25] suffer from strong mode localization by the dipolar edge fields, diminishing their thermal stability. The same dipolar effects also make it challenging to utilize such layouts for the gen- eration of propagating SWs in magnonic circuits.…”