Droplet Solitons Research Articles

Antiferromagnetic droplet soliton driven by spin current

We demonstrate that a spin current flowing through a nanocontact into a uniaxial antiferromagnet with first- and second-order anisotropy can excite a self-localized dynamic magnetic soliton, known as a spin-wave droplet in ferromagnets. The droplet nucleates at a certain threshold current with the frequency of the Néel vector precession laying below the antiferromagnetic resonance. The frequency exhibits nonlinear behavior with the increase in the applied current. At the high value of the applied torque, the soliton mode transforms, and the oscillator emits spin waves propagating in the antiferromagnetic layer.

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.

Field-Free High-Frequency Exchange-Spring Spin-Torque Nano-Oscillators.

Spin-torque nano-oscillators (STNOs) are a type of nanoscale microwave auto-oscillators utilizing spin-torque to generate magnetodynamics with great promise for applications in microwaves, magnetic memory, and neuromorphic computing. Here, we report the first demonstration of exchange-spring STNOs, with an exchange-spring ([Co/Pd]-Co) reference layer and a perpendicular ([Co/Ni]) free layer. This magnetic configuration results in high-frequency (>10 GHz) microwave emission at a zero magnetic field and exchange-spring dynamics in the reference layer and the observation of magnetic droplet solitons in the free layer at different current polarities. Our demonstration of bipolar and field-free exchange-spring-based STNOs operating over a 20 GHz frequency range greatly extends the design freedom and functionality of the current STNO technology for energy-efficient high-frequency spintronic and neuromorphic applications.

Generation and routing of nanoscale droplet solitons without compensation of magnetic damping

A magnetic droplet soliton is a localized dynamic spin state which can serve as a nanoscale information carrier and nonlinear oscillator. The present opinion is that the formation of droplet solitons requires the compensation of magnetic damping by a torque created by a spin-polarized electric current or pure spin current. Here, we demonstrate theoretically that nanoscale droplet solitons can be generated and routed in ferromagnetic nanostructures with voltage-controlled magnetic anisotropy in the presence of uncompensated magnetic damping. Performing micromagnetic simulations for the MgO/Fe/MgO trilayer with almost perpendicular-to-plane magnetization, we reveal the formation of the droplet soliton under a nanoscale gate electrode subjected to a subnanosecond voltage pulse. The soliton lives up to 50 ns at room temperature and can propagate over micrometer distances in a ferromagnetic waveguide due to nonzero gradient of the demagnetizing field. Furthermore, we show that electrical routing of the soliton to different outputs of a spintronic device can be realized with the aid of an additional semiconducting nanostripe electrode creating controllable gradient of the perpendicular magnetic anisotropy.

Effect of Oersted field on the localized droplet mode and propagating spin waves mode excited in spin-torque nano-oscillator

Magnetic droplets are self-localized spin wave solitons that can be excited in spin valves with perpendicular magnetic anisotropy by using spin-transfer torque generated by a dc current through a nano-contact. Using micromagnetic simulations, we demonstrate that the droplet soliton mode could be switched to a localized spiral precession mode due to the resistance effect of current-induced Oersted fields whose rotation direction is opposite to the precession direction of droplet. This spiral mode can switch back to the droplet mode by increasing current. With an assistance of electric field, both the localized droplet and spiral modes can develop to the radially propagating spin waves. The frequencies of all these localized spiral and droplet as well as the propagating spin wave modes show linear increase relationship with a magnetic field applied in out-of-plane direction. These results are of fundamental interest in understanding the rich dynamics of magnetic excitation properties, which will be helpful for the droplet-based spintronic devices.

Tuning the dynamics of magnetic droplet solitons using dipolar interactions

Magnetic droplets are dissipative magnetodynamical solitons that can form under current driven nanocontacts in magnetic layers with large perpendicular magnetic anisotropy. Here, we extend the original droplet theory by studying the impact of the dipolar interactions on the dynamics of droplet solitons. By varying the thickness of the free layer of a spin torque nano-oscillator, we systematically tune the internal field of the free layer to investigate the dynamics of droplet solitons. Our numerical results show that increasing the free layer thickness increases the droplet threshold current, decreases the droplet frequency and diameter, enlarges the current hysteresis and also modifies the structure of the droplet. The Oersted field of the current breaks the phase coherency and deteriorates the stability of the droplet in free layers with larger thicknesses. Moreover, our findings show a simple relation to determine the impact of the free layer thickness on the droplet nucleation boundaries. Our study presents the missing brick on the physics behind magnetic droplet solitons, and further illustrates that magnetic droplets in thinner layers possess more promising characteristics for spintronic applications and enable devices with higher speed of operation.

Two-dimensional overdamped simulations of droplet solitons activated by spin transfer torque

We present overdamped micromagnetic simulations of the time evolution of magnetic droplet solitons which are formed in a thin film with perpendicular magnetic anisotropy by injecting a spin polarized current through a circular nanocontact. The overdamped dynamics help explore the effective energy landscape of these structures and permit identification of stationary states that are either energy extrema or saddle configurations. Our micromagnetic simulations start with configurations that are numerical solutions of a one-dimensional model where the magnetization depends only on the radial distance to the center of the nanocontact. We verify that these solutions correspond either to energy minima or saddle states, and use them to estimate thermal activation barriers for various current strengths. From the two-dimensional micromagnetic simulations, we identify a new persistent state which does not appear in the one-dimensional model.

Tuning Magnetic Droplets in Nanocontact Spin-Torque Oscillators Using Electric Fields

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.

Magnetic droplet solitons

Magnetic droplet solitons are dynamical magnetic textures that form due to an attractive interaction between spin waves in thin films with perpendicular magnetic anisotropy. Spin currents and the spin torques associated with these currents enable their formation as they provide a means to excite non-equilibrium spin-wave populations and compensate their decay. Recent years have seen rapid advances in experiments that realize and study magnetic droplets. Important advances include the first direct x-ray images of droplets, determination of their threshold and sustaining currents, measurement of their generation and annihilation time, and evidence for drift instabilities, which can limit their lifetime. This perspective discusses these studies and contrasts these solitons to other types of spin-current excitations, such as spin-wave bullets, and static magnetic textures, including magnetic vortices and skyrmions. Magnetic droplet solitons can also serve as current controlled microwave frequency oscillators with potential applications in neuromorphic chips as nonlinear oscillators with memory.

Thermal activation barriers for creation and annihilation of magnetic droplet solitons in the presence of spin transfer torque

We study noise-induced creation and annihilation of magnetic droplet solitons in experimental parameter regions in which they are linearly stable against drift. Exploiting the rotational symmetry of the problem, we transform to the reference frame rotating with the droplet soliton and introduce an effective potential energy that accounts for the work done against spin-transfer torque to rotate the magnetization between two different orientations. We use this function to compute the activation barrier in both directions between the uniform magnetization state and the droplet soliton state for a variety of nanocontact radii and currents. We investigate droplet soliton structures with both zero and nonzero spin-torque asymmetry parameter. Our approach can be applied to estimate activation barriers for dynamical systems where non-gradient terms can be absorbed by changes of reference frames, and suggests a technique applicable to extended systems that may not be uniformly magnetized.

Propagating Magnetic Droplet Solitons as Moveable Nanoscale Spin-Wave Sources with Tunable Direction of Emission

Magnetic droplets are strongly nonlinear and localized spin-wave solitons that can be formed in current-driven nanocontacts. Here, we propose a simple way to launch droplets in an inhomogeneous nanoscopic waveguide. We use the drift motion of a droplet and show that in a system with broken translational symmetry, the droplet acquires a linear momentum and propagates. We find that the droplet velocity can be tuned via the strength of the break in symmetry and the size of the nanocontact. In addition, we demonstrate that the launched droplet can propagate up to several micrometers in a realistic system with reasonable damping. Finally, we demonstrate how an annihilating droplet delivers its momentum to a highly nonreciprocal spin-wave burst with a tunable wave vector with nanometer wavelengths. Such a propagating droplet can be used as a moveable spin-wave source in nanoscale magnonic networks. The presented method enables full control of the spin-wave emission direction, which can largely extend the freedom to design integrated magnonic circuits with a single spin-wave source.

Chiral excitations of magnetic droplet solitons driven by their own inertia

The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We reveal the role of the spin torque on the excitation of these chiral modes and we show how to control these modes using the current and the field.

Stochastic ejection of nanocontact droplet solitons via drift instability

The magnetic droplet soliton is a large amplitude, coherently precessing wave state that exists in ferromagnetic thin films with perpendicular magnetic anisotropy. To effectively sustain a droplet, magnetic damping can be locally compensated in a nanocontact region that imparts spin-transfer torque; this has been successfully deployed in experiment to directly image the droplet and probe its dynamics electrically. However, theory predicts and experiments indicate the existence of a drift instability whereby the droplet is ejected from the spin-transfer-torque-active region and subsequently decays, an effect that may be enhanced or possibly induced by thermal fluctuations. Using soliton perturbation theory and large deviation theory, this work determines the soliton ejection rate and the most likely path an ejected soliton tracks in the presence of thermal fields. These results lead to an effective lower bound on the stability of magnetic droplet solitons in spin-transfer torque nanocontact devices operating at finite temperature and point to ways in which droplets can be made more robust.

Multiple magnetic droplet soliton modes

Droplet solitons are large amplitude localized spin-wave excitations that can be created in magnetic thin films with uniaxial anisotropy by a spin-polarized current flowing through an electrical nanocontact. Here, we report a low-temperature (4 K) experimental study that shows there are multiple and, under certain conditions, combinations of droplet modes, each mode with a distinct high-frequency spin precession (tens of gigahertz). Low-frequency ($\ensuremath{\lesssim}1\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$) voltage noise is used to assess the stability of droplet modes. It is found that droplets are stable only in a limited range of applied field and current, typically near the current and field at which they nucleate, in agreement with recent predictions. Applied fields in the film plane favor multiple droplet modes, whereas fields perpendicular to the film plane tend to stabilize a single droplet mode. Micromagnetic simulations are used to show that spatial variation in the energy landscape in the nanocontact region (e.g., spatial variation of magnetic anisotropy or magnetic field) can lead to quantized droplet modes and low-frequency mode modulation, characteristics observed in our experiments.

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.

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.

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.

Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy

Stripe domains are narrow, elongated, reversed regions that exist in magnetic materials with perpendicular magnetic anisotropy. Stripe domains appear as a pair of domain walls that can exhibit topology with a nonzero chirality. Recent experimental and numerical investigations identify an instability of stripe domains in the long direction as a means of nucleating isolated magnetic skyrmions. Here, the onset and nonlinear evolution of transverse instabilities for a dynamic stripe domain known as the bion stripe are investigated. Both non-topological and topological variants of the bion stripe are shown to exhibit a long-wavelength transverse instability with different characteristic features. In the former, small transverse variations in the stripe's width lead to a neck instability that eventually pinches the non-topological stripe into a chain of two-dimensional breathers composed of droplet soliton pairs. In the latter case, small variations in the stripe's center results in a snake instability whose topological structure leads to the nucleation of dynamic magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets. Quantitative, analytical predictions for both the early, linear evolution and the long-time, nonlinear evolution are achieved using an averaged Lagrangian approach that incorporates both exchange (dispersion) and anisotropy (nonlinearity). The method of analysis is general and can be applied to other filamentary structures.

Designing magnetic droplet soliton nucleation employing spin polarizer

We show by means of micromagnetic simulations that spin polarizer in nano-contact (NC) spin torque oscillators as the representative of the fixed layer in an orthogonal pseudo-spin valve can be employed to design and to control magnetic droplet soliton nucleation and dynamics. We found that using a tilted spin polarizer layer decreases the droplet nucleation time which is more suitable for high speed applications. However, a tilted spin polarizer increases the nucleation current and decreases the frequency stability of the droplet. Additionally, by driving the magnetization inhomogenously at the NC region, it is found that a tilted spin polarizer reduces the precession angle of the droplet and through an interplay with the Oersted field of the DC current, it breaks the spatial symmetry of the droplet profile. Our findings explore fundamental insight into nano-scale magnetic droplet soliton dynamics with potential tunability parameters for future microwave electronics.

Magnetic droplet solitons generated by pure spin currents

Magnetic droplets are dynamical solitons that can be generated by locally suppressing the dynamical damping in magnetic films with perpendicular anisotropy. To date, droplets have been observed only in nanocontact spin-torque oscillators operated by spin-polarized electrical currents. Here, we experimentally demonstrate that magnetic droplets can be nucleated and sustained by pure spin currents in nanoconstriction-based spin Hall devices. Micromagnetic simulations support our interpretation of the data, and indicate that in addition to the stationary droplets, propagating solitons can be also generated in the studied system, which can be utilized for the information transmission in spintronic applications.