Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators

Magnetic droplet soliton pairs

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.

Freezing and thawing magnetic droplet solitons

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.

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

Generation and stability of dynamical skyrmions and droplet solitons

A spin-polarized current in a nanocontact to a magnetic film can create collective magnetic oscillations by compensating the magnetic damping. In particular, in materials with uniaxial magnetic anisotropy, droplet solitons have been observed-a self-localized excitation consisting of partially reversed magnetization that precesses coherently in the nanocontact region. It is also possible to generate topological droplet solitons, known as dynamical skyrmions (DSs). Here, we show that spin-polarized current thresholds for DS creation depend not only on the material's parameters but also on the initial magnetization state and the rise time of the spin-polarized current. We study the conditions that promote either droplet or DS formation and describe their stability in magnetic films without Dzyaloshinskii-Moriya interactions. The Oersted fields from the applied current, the initial magnetization state, and the rise time of the injected current can determine whether a droplet or a DS forms. DSs are found to be more stable than droplets. We also discuss electrical characteristics that can be used to distinguish these magnetic objects.

Investigation of magnetic droplet solitons using x-ray holography with extended references

A dissipative magnetic soliton, or magnetic droplet, is a structure that has been predicted to exist within a thin magnetic layer when non-linearity is balanced by dispersion, and a driving force counteracts the inherent damping of the spin precession. Such a soliton can be formed beneath a nano-contact (NC) that delivers a large spin-polarized current density into a magnetic layer with perpendicular magnetic anisotropy. Although the existence of droplets has been confirmed from electrical measurements and by micromagnetic simulations, only a few attempts have been made to directly observe the magnetic landscape that sustains these structures, and then only for a restricted set of experimental parameter values. In this work we use and x-ray holography technique HERALDO, to image the magnetic structure of the [Co/Ni]x4 multilayer within a NC orthogonal pseudo spin-valve, for different range of magnetic fields and injected electric currents. The magnetic configuration imaged at −33 mA and 0.3 T for devices with 90 nm NC diameter reveals a structure that is within the range of current where the droplet soliton exist based on our electrical measurements and have it is consistent with the expected size of the droplet (∼100 nm diameter) and its spatial position within the sample. We also report the magnetisation configurations observed at lower DC currents in the presence of fields (0–50 mT), where it is expected to observe regimes of the unstable droplet formation.

Direct Observation of Zhang-Li Torque Expansion of Magnetic Droplet Solitons

Magnetic droplets are nontopological dynamical solitons 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.

Generation and annihilation time of magnetic droplet solitons

Magnetic droplet solitons were first predicted to occur in materials with uniaxial magnetic anisotropy due to a long-range attractive interaction between elementary magnetic excitations, magnons. A non-equilibrium magnon population provided by a spin-polarized current in nanocontacts enables their creation and there is now clear experimental evidence for their formation, including direct images obtained with scanning x-ray transmission microscopy. Interest in magnetic droplets is associated with their unique magnetic dynamics that can lead to new types of high frequency nanometer scale oscillators of interest for information processing, including in neuromorphic computing. However, there are no direct measurements of the time required to nucleate droplet solitons or their lifetime-experiments to date only probe their steady-state characteristics, their response to dc spin-currents. Here we determine the timescales for droplet annihilation and generation using current pulses. Annihilation occurs in a few nanoseconds while generation can take several nanoseconds to a microsecond depending on the pulse amplitude. Micromagnetic simulations show that there is an incubation time for droplet generation that depends sensitively on the initial magnetic state of the nanocontact. An understanding of these processes is essential to utilizing the unique characteristics of magnetic droplet solitons oscillators, including their high frequency, tunable and hysteretic response.

Symmetry-broken dissipative exchange flows in thin-film ferromagnets with in-plane anisotropy

Planar ferromagnetic channels have been shown to theoretically support a long-range ordered and coherently precessing state where the balance between local spin injection at one edge and damping along the channel establishes a dissipative exchange flow, sometimes referred to as a spin superfluid. However, realistic materials exhibit in-plane anisotropy, which breaks the axial symmetry assumed in current theoretical models. Here, we study dissipative exchange flows in a ferromagnet with in-plane anisotropy from a dispersive hydrodynamic perspective. Through the analysis of a boundary value problem for a damped sine-Gordon equation, dissipative exchange flows in a ferromagnetic channel can be excited above a spin current threshold that depends on material parameters and the length of the channel. Symmetry-broken dissipative exchange flows display harmonic overtones that redshift the fundamental precessional frequency and lead to a reduced spin pumping efficiency when compared to their symmetric counterpart. Micromagnetic simulations are used to verify that the analytical results are qualitatively correct, even in the presence of non-local dipole fields. Simulations also confirm that dissipative exchange flows can be driven by spin transfer torque in a finite-sized region. These results delineate the important material parameters that must be optimized for the excitation of dissipative exchange flows in realistic systems.

A 20 nm spin Hall nano-oscillator

Spin Hall nano-oscillators (SHNOs) are an emerging class of pure spin current driven microwave signal generators. Through the fabrication of 20 nm nano-constrictions in Pt/NiFe bilayers, we demonstrate that SHNOs can be scaled down to truly nanoscopic dimensions, with the added benefit of ultra-low operating currents and improved power conversion efficiency. The lateral confinement leads to a strong shape anisotropy field as well as an additional demagnetizing field whose reduction with increasing auto-oscillation amplitude can yield a positive current tunability contrary to the negative tunability commonly observed for localized excitations in extended magnetic layers. Micromagnetic simulations corroborate the experimental findings and suggest that the active magnetodynamic area resides up to 100 nm outside of the nano-constriction.

Breaking of Galilean Invariance in the Hydrodynamic Formulation of Ferromagnetic Thin Films

Microwave magnetodynamics in ferromagnets are often studied in the small-amplitude or weakly nonlinear regime corresponding to modulations of a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned approximations are not applicable, have become experimentally accessible. By reinterpreting the governing Landau-Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are shown to, in general, break Galilean invariance. A magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHSs), which exhibit fluidlike behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpretation opens up novel possibilities in magnetic research.