We demonstrate magnetic droplet soliton pairs in all-perpendicular spin-torque nano-oscillators (STNOs), where one droplet resides in the STNO free layer (FL) and the other in the reference layer (RL). Typically, theoretical, numerical, and experimental droplet studies have focused on the FL, with any additional dynamics in the RL entirely ignored. Here we show that there is not only significant magnetodynamics in the RL, but the RL itself can host a droplet driven by, and coexisting with, the FL droplet. Both single droplets and pairs are observed experimentally as stepwise changes and sharp peaks in the dc and differential resistance, respectively. While the single FL droplet is highly stable, the coexistence state exhibits high-power broadband microwave noise. Furthermore, micromagnetic simulations reveal that the pair dynamics display periodic, quasi-periodic, and chaotic signatures controlled by applied field and current. The strongly interacting and closely spaced droplet pair offers a unique platform for fundamental studies of highly non-linear soliton pair dynamics.

Magnetic droplets are a type of non-topological magnetic soliton, which are stabilised and sustained by spin-transfer torques for instance. Without this, they would collapse. Here Ahlberg et al show that by decreasing the applied magnetic field, droplets can be frozen, forming a static nanobubble Magnetic droplets are non-topological magnetodynamical solitons displaying a wide range of complex dynamic phenomena with potential for microwave signal generation. Bubbles, on the other hand, are internally static cylindrical magnetic domains, stabilized by external fields and magnetostatic interactions. In its original theory, the droplet was described as an imminently collapsing bubble stabilized by spin transfer torque and, in its zero-frequency limit, as equivalent to a bubble. Without nanoscale lateral confinement, pinning, or an external applied field, such a nanobubble is unstable, and should collapse. Here, we show that we can freeze dynamic droplets into static nanobubbles by decreasing the magnetic field. While the bubble has virtually the same resistance as the droplet, all signs of low-frequency microwave noise disappear. The transition is fully reversible and the bubble can be thawed back into a droplet if the magnetic field is increased under current. Whereas the droplet collapses without a sustaining current, the bubble is highly stable and remains intact for days without external drive. Electrical measurements are complemented by direct observation using scanning transmission x-ray microscopy, which corroborates the analysis and confirms that the bubble is stabilized by pinning.

We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane magnetic fields (mu H-0(IP) = 30-40 mT) and also investigate its angular dependence. We compare SHNOs with different nanoconstriction 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 magnetodipolar coupling between neighboring SHNOs.

We demonstrate the compositional effect on the magnetodynamic and auto-oscillation properties of Ni 100 - xFe(x)/Pt (x=10-40) nanoconstriction-based spin Hall nano-oscillators. Using spin-torque ferromagnetic resonance performed on microstrips, we measure a significant reduction in both damping and spin Hall efficiency with the increasing Fe content, which lowers the spin pumping contribution. The strong compositional effect on spin Hall efficiency is primarily attributed to the increased saturation magnetization in Fe-rich devices. As a direct consequence, higher current densities are required to drive spin-wave auto-oscillations at higher microwave frequencies in Fe-rich nanoconstriction devices. Our results establish the critical role of the compositional effect in engineering the magnetodynamic and auto-oscillation properties of spin Hall devices for microwave and magnonic applications.

Reliable in situ control of spin wave (SW) excitation between localized and propagating SW modes is of great interest for both fundamental and applied spintronics and magnonics. While spin-transfer-torque-generated SWs can typically be tuned directly via the driving current, the frequency of the highest intensity SWs, achieved in the strongly self-localized magnetic droplet soliton, is virtually current independent, as the droplet frequency is given by the intrinsic material properties. Here, we demonstrate, using micromagnetic simulations, how the droplet frequency can be efficiently tuned by an applied voltage through the effect of electric field (E-field)-dependent perpendicular magnetic anisotropy (PMA). It is found that as the PMA decreases, the droplet begins to distort and eventually collapses to give way to propagating SWs. However, due to the geometrically confined structures, the radially propagating SWs are reflected by the periphery boundary of the sample, and then the forward and backward SWs superpose to produce a series of standing SWs. The node number of the standing SWs strongly depends on the sample size as well as the applied E field. These findings provide a deeper understanding of magnetic excitation properties, which will be helpful for designing advanced spintronic devices.

In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth Δ f is governed by white noise, the signal quality factor, Q= f∕ Δ f, increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing.

We experimentally study the auto-oscillating spin-wave modes in Ni(80)Fc(20)/beta-W constriction-based spin Hall nano-oscillators as a function of bias current, strength of the in-plane applied field, and azimuthal field angle in the low-field range of 40-80 mT. We observe two different spin-wave modes: (i) a linearlike mode confined to the internal field minima near the edges of the nanoconstriction, and only weakly dependent on the bias current and the applied-field angle, and (ii) a second, lower-frequency mode with significantly higher threshold current and stronger dependence on both the bias current and the externalfield angle. Micromagnetic modeling qualitatively reproduces the experimental data and reveals that the second mode is a spin-wave bullet and that the spin Hall nano-oscillator mode hops between the two modes, resulting in a substantial increase in linewidths. In contrast to the linearlike mode, the bullet is localized in the middle of the constriction and shrinks with increasing bias current. Using intrinsic frequency doubling at zero field angle, we can reach frequencies above 9 GHz in fields as low as 40 mT, which is important for the development of low-field spintronic oscillators with applications in microwave-signal generation and neuromorphic computing.

We demonstrate low-operational-current W/Co20Fe60B20/MgO spin Hall nano-oscillators (SHNOs) on highly resistive silicon (HiR-Si) substrates. Thanks to a record high spin Hall angle of the beta-phase W (theta(SH) = -0.53), a very low threshold current density of 3.3 x 10(7) A/cm(2) can be achieved. Together with their very wide frequency tunability (7-28GHz), promoted by a moderate perpendicular magnetic anisotropy, HiR-Si/W/CoFeB based SHNOs are potential candidates for wide-band microwave signal generation. Their CMOS compatibility offers a promising route towards the integration of spintronic microwave devices with other on-chip semiconductor microwave components.

Magnetic droplets are nontopological dynamical soli tons that can be nucleated in nanocontact based spin torque nano-oscillators (STNOs) with perpendicular magnetic anisotropy free layers. While theory predicts that the droplet should be of the same size as the nanocontact, its inherent drift instability has thwarted attempts at observing it directly using microscopy techniques. Here, we demonstrate highly stable magnetic droplets in all-perpendicular STNOs and present the first detailed droplet images using scanning transmission X-ray microscopy. In contrast to theoretical predictions, we find that the droplet diameter is about twice as large as the nanocontact. By extending the original droplet theory to properly account for the lateral current spread underneath the nanocontact, we show that the large discrepancy primarily arises from current-in-plane Zhang-Li torque adding an outward pressure on the droplet perimeter. Electrical measurements on droplets nucleated using a reversed current in the antiparallel state corroborate this picture.

We investigate the effect of hafnium (Hf) dusting on the magnetodynamical properties of NiFe/Pt bilayers using spin-torque-induced ferromagnetic resonance measurements on 6 μm wide microstrips on high-resistive Si substrates. Based on two series of NiFe(t_NiFe)/Hf(t_Hf)/Pt(5) stacks, we first demonstrate that the zero-current magnetodynamic properties of the devices benefit from Hf dusting: (i) the effective magnetization of the NiFe layer increases by 4%–8% with Hf present and (ii) the damping α decreases linearly with t_Hf by up to 40%. The weaker anisotropic magnetoresistance (AMR≈0.3%–0.4%) of the 3 nm NiFe series is largely unaffected by the Hf, while the stronger AMR of the 5 nm NiFe series drops from 0.7% to 0.43% with increasing t_Hf. We find that the spin Hall efficiency ξ_SH is independent of the NiFe thickness, remaining unaffected (ξ_SH = 0.115) up to t_Hf = 0.4 nm and then decreasing linearly for higher t_Hf. The different trends of α and ξ_SH suggest that there is an optimum Hf thickness (≈0.4 nm) for which the threshold current for auto-oscillation should have a minimum, while the much lower damping should improve mutual synchronization. Our results also indicate that the spin-orbit torque is entirely damping-like with no field-like torque component. Finally, the internal spin Hall angle of Pt is estimated to be θ_SH = 0.22 by calculating the transparency of the interface.