Droplet Solitons Research Articles

Effect of Temperature on Magnetic Solitons Induced by Spin-Transfer Torque

Spin-transfer torques in a nanocontact to an extended magnetic film can create spin waves that condense to form dissipative droplet solitons. Here we report an experimental study of the temperature dependence of the current and applied field thresholds for droplet soliton formation, as well as the nanocontact's electrical characteristics associated with droplet dynamics. Nucleation of droplet solitons requires higher current densities at higher temperatures, in contrast to typical spin-transfer torque induced switching between static magnetic states. Magnetoresistance and electrical noise measurements show that soliton instabilities become more pronounced with increasing temperature. These results are of fundamental interest in understanding the influence of thermal noise on droplet solitons, and in controlling their dynamics.

Eigenmodes of two-dimensional conservative droplet soliton

Droplet solitons are strongly nonlinear, dynamic structures in ferromagnets with perpendicular magnetic anisotropy. For experimental observation of such structures a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping is utilized. We analyze eigenmode of this droplet excitations in a simplest case of conservative droplet solitons, when both Gilbert damping in magnetic films and energy gain due to spin-polarized current can be neglected. As a result of such analysis eigenmode frequencies of conservative droplet are obtained. Among main features of conservative droplet eigenmode is azimuthal degeneration of mods and localization of mode frequencies in a finite region.

Dynamics of current induced nano-skyrmions

The dynamics of magnetic skyrmions is investigated in a composite free layer spin valve nano pillar for different coupling mechanisms in the absence of Dzyaloshinski-Moriya Interaction (DMI). Nano meter sized skyrmions and anti skyrmions are trapped with different helices in the free layer. The spin polarised current under specific choice of system parameters changes the droplet solitons into skyrmions and anti skyrmions. The current driven dynamics is studied and the condition at which an isolated skyrmion exists, is reported. We have optimised the current density (J) and spin wave vector (k) for which Skyrmion Hall Effect (SHE) completely vanishes and as a result the velocity, size and shape of skyrmions are preserved. When the coupling between the composite free layers is changed, skyrmion-anti skyrmion pair and radial skyrmion-chiral skyrmion pair emerge. For the specific values of ‘J’ and ‘k’ these pairs show coupled motion along the layer and hence these pairs could also be used as a bit in the data processing and storage devices. Our investigation ascertains that a single material can host all the localised magnetic structures if the current density, spin wave vector and coupling constant are suitably chosen and tuned. This study would really be of fundamental importance owing to the possible applications in information processing and data storage in skyrmion based logic circuits and magnetic sensors.

Parametric autoexcitation of magnetic droplet soliton perimeter modes

Recent experiments performed in current-driven nano-contacts with strong perpendicular anisotropy have shown that spin-transfer torque can drive self-localized spin waves [1, 2] that above a certain threshold intensity can condense into a highly nonlinear magnetodynamic and nano-sized state known as a magnetic droplet soliton [3]. Here we demonstrate analytically, numerically, and experimentally that at sufficiently large driving currents, and for a spin polarization that is tilted away from the film normal, the circular droplet soliton can become unstable to periodic excitations of its perimeter. We furthermore show that these perimeter excitation modes (PEMs) are parametrically excited when the fundamental droplet soliton precession frequency is close to twice the frequency of one or more of the PEMs. As a consequence, for increasing applied fields, progressively higher PEMs can be excited. Quantitative agreement with experiment confirms this picture.

Merging droplets in double nanocontact spin torque oscillators

We demonstrate how magnetic droplet soliton pairs, nucleated by two separated nanocontact (NC) spin torque oscillators, can merge into a single droplet soliton. A detailed description of the magnetization dynamics of this merger process is obtained by micromagnetic simulations: A droplet pair with a steady-state in-phase spin precession is generated through the spin-transfer torque effect underneath two separate NCs, followed by a gradual expansion of the droplets' volume and the out-phase of magnetization on the inner side of the two droplets, resulting in the droplets merging into a larger droplet. This merger occurs only when the NC separation is smaller than a critical value. A transient breathing mode is observed before the merged droplet stabilizes into a steady precession state. The precession frequency of the merged droplet is lower than that of the droplet pair, consistent with its larger size. Merged droplets can again break up into droplet pairs at high enough magnetic field with a strong hysteretic response.

Observation of droplet soliton drift resonances in a spin-transfer-torque nanocontact to a ferromagnetic thin film

Magnetic droplet solitons are non-linear dynamical modes that can be excited in a thin film with perpendicular magnetic anisotropy with a spin-transfer-torque. Although droplet solitons have been proved to be stable with a hysteretic response to applied currents and magnetic fields at low temperature, measurements at room temperature indicate less stability and reduced hysteresis width. Here, we report evidence of droplet soliton drift instabilities, leading to drift resonances, at room temperature that explains their lower stability. Micromagnetic simulations show that the drift instability is produced by an effective field asymmetry in the nanocontact region that can have different origins.

Magnetic droplet solitons in orthogonal spin valves

We review the recent experimental advancements in the realization and understanding of magnetic droplet solitons generated by spin transfer torque in orthogonal nanocontact based spin torque nanooscillators (STNOs) fabricated on extended spin valves and spin valve nanowires. The magnetic droplets are detected and studied using the STNO microwave signal and its resistance, the latter both quasistatically and time-resolved. The droplet nucleation current is found to have a minimum at intermediate magnetic field strengths and the nature of the nucleation changes gradually from a single sharp step well above this field, mode-hopping around the minimum, and continuous at low fields. The mode-hopping and continuous transitions are ascribed to droplet drift instability and re-nucleation at different time scales, which is corroborated by time-resolved measurements. We argue that the use of tilted anisotropy fixed layers could reduce the nucleation current further, move the nucleation current minimum to lower fields, and potentially remove the need for an applied magnetic field altogether. Finally, evidence of an edge mode droplet in a nanowire is presented.

Perturbation theory for propagating magnetic droplet solitons

Droplet solitons are strongly nonlinear, inherently dynamic structures in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have the approximate form of a circular domain wall sustained by precession and, in contrast to single magnetic vortices, are predicted to propagate in an extended, homogeneous magnetic medium. In this work, multiscale perturbation theory is used to develop an analytical framework for investigating the impact of additional physical effects on the behaviour of a propagating droplet. After first developing soliton perturbation theory in the general context of Hamiltonian systems, a number of physical phenomena of current interest are investigated. These include droplet–droplet and droplet–boundary interactions, spatial magnetic field inhomogeneities, spin transfer torque induced forcing in a nanocontact device and damping. Their combined effects demonstrate the fundamental mechanisms for a previously observed droplet drift instability and under what conditions a slowly propagating droplet can be supported by the nanocontact, important considerations for applications. This framework emphasizes the particle-like dynamics of the droplet, providing analytically tractable and practical predictions for modern experimental configurations.

Stable magnetic droplet solitons in spin-transfer nanocontacts.

Magnetic thin films with perpendicular magnetic anisotropy have localized excitations that correspond to reversed, dynamically precessing magnetic moments, which are known as magnetic droplet solitons. Fundamentally, these excitations are associated with an attractive interaction between elementary spin-excitations and have been predicted to occur in perpendicularly magnetized materials in the absence of damping. Although damping suppresses these excitations, it can be compensated by spin-transfer torques when an electrical current flows in nanocontacts to ferromagnetic thin films. Theory predicts the appearance of magnetic droplet solitons in nanocontacts at a threshold current and, recently, experimental signatures of droplet nucleation have been reported. However, to date, these solitons have been observed to be nearly reversible excitations, with only partially reversed magnetization. Here, we show that magnetic droplet solitons exhibit a strong hysteretic response in field and current, proving the existence of bistable states: droplet and non-droplet states. In the droplet soliton state we find that the magnetization in the contact is almost fully reversed. These observations, in addition to their fundamental interest, are important to understanding and controlling droplet motion, nucleation and annihilation.

Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering

The interaction behavior of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.

Spin transfer torque generated magnetic droplet solitons (invited)

We present recent experimental and numerical advancements in the understanding of spin transfer torque generated magnetic droplet solitons. The experimental work focuses on nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has an easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The NC-STO resistance and microwave signal generation are measured simultaneously as a function of drive current and applied perpendicular magnetic field. Both exhibit dramatic transitions at a certain current dependent critical field value, where the microwave frequency drops 10 GHz, modulation sidebands appear, and the resistance exhibits a jump, while the magnetoresistance changes sign. We interpret these observations as the nucleation of a magnetic droplet soliton with a large fraction of its magnetization processing with an angle greater than 90°, i.e., around a direction opposite that of the applied field. This interpretation is corroborated by numerical simulations. When the field is further increased, we find that the droplet eventually collapses under the pressure from the Zeeman energy.

Analytical theory of modulated magnetic solitons

Droplet solitons are coherently precessing solitary waves that have been recently realized in thin ferromagnets with perpendicular anisotropy. In the strongly nonlinear regime, droplets can be well approximated by a slowly precessing, circular domain wall with a hyperbolic tangent form. Utilizing this representation, this work develops a general droplet modulation theory and applies it to study the long-range effects of the magnetostatic field and a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping. An analysis of the dynamical equations for the droplet's center, frequency, and phase demonstrates a negative precessional frequency shift due to long-range dipolar interactions, dependent on film thickness. Further analysis also demonstrates the onset of a saddle-node bifurcation at the minimum sustaining current for the NC-STO. The basin of attraction associated with the stable node demonstrates that spin torque enacts a restoring force to excursions of the droplet from the nanocontact center, observed previously in numerical simulations. Large excursions lead to the droplet's eventual decay into spin waves.

Magnetic droplet solitons in orthogonal nano-contact spin torque oscillators

We study microwave signal generation as a function of drive current and applied perpendicular magnetic field in nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has strong easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The orthogonal NC-STOs exhibit a dramatic transition from the conventional ferromagnetic resonance-like spin wave mode to a magnetic droplet soliton mode. In particular, the field and current dependence of the droplet soliton near threshold are discussed. Near threshold the droplet soliton undergoes complex dynamics that include mode hopping, as evident in the experimental frequency domain and magnetoresistance response.

Propagation and control of nanoscale magnetic-droplet solitons

The propagation and controlled manipulation of strongly nonlinear, two-dimensional solitonic states in a thin, anisotropic ferromagnet are theoretically demonstrated. It has been recently proposed that spin-polarized currents in a nanocontact device could be used to nucleate a stationary dissipative droplet soliton. Here, an external magnetic field is introduced to accelerate and control the propagation of the soliton in a lossy medium. Soliton perturbation theory corroborated by two-dimensional micromagnetic simulations predicts several intriguing physical effects, including the acceleration of a stationary soliton by a magnetic field gradient, the stabilization of a stationary droplet by a uniform control field in the absence of spin torque, and the ability to control the soliton's speed by use of a time-varying, spatially uniform external field. Soliton propagation distances approach 10 $\mu$m in low loss media, suggesting that droplet solitons could be viable information carriers in future spintronic applications, analogous to optical solitons in fiber optic communications.

Theory for a dissipative droplet soliton excited by a spin torque nanocontact

A distinct type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet against various perturbations that are likely in experiments, including tilting of the applied field, nonzero spin torque asymmetry, and nontrivial Oersted fields. Under certain conditions, the droplet experiences a drift instability in which it propagates away from the nanocontact and is then destroyed by damping.