Giant supermagnonic Bloch point velocities in cylindrical ferromagnetic nanowires.

Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems without the Walker breakdown phenomenon. Here we demonstrate that the magnonic limit could be outstandingly surpassed in cylindrical nanowires with high magnetization, such as iron. Our numerical modeling shows the Bloch point domain wall velocities as high as 14 km s-1, well above the magnonic limit estimated in the interval 1.7-2.0 km s-1. The key ingredient is the three-dimensional conical shape of the domain wall, which elongates and breaks during the dynamics, expelling backwards pairs of Bloch points. This leads to domain wall acceleration, the effect, which resembles the "jet propulsion". This effect will be very important for three-dimensional networks based on cylindrical magnetic nanowires.

3D Magnetization Textures: Toroidal Magnetic Hopfion Stability in Cylindrical Samples.

Topologically non-trivial magnetization configurations in ferromagnetic materials on the nanoscale, such as hopfions, skyrmions, and vortices, have attracted considerable attention of researchers during the last few years. In this article, by applying the theory of micromagnetism, I demonstrate that the toroidal hopfion magnetization configuration is a metastable state of a thick cylindrical ferromagnetic nanodot or a nanowire of a finite radius. The existence of this state is a result of the competition among exchange, magnetostatic, and magnetic anisotropy energies. The Dzyaloshinskii-Moriya exchange interaction and surface magnetic anisotropy are of second importance for the hopfion stabilization. The toroidal hopfion metastable magnetization configuration may be reached in the process of remagnetizing the sample by applying an external magnetic field along the cylindrical axis.

Nutation Excitations in the Gyrotropic Vortex Dynamics in a Circular Magnetic Nanodot.

A significant activity is devoted to the investigation of the ultrafast spin dynamic processes, holding a great potential for science and applications. However, a challenge of the understanding of the mechanisms of underlying spin dynamics in nanomaterials at pico- and femtosecond timescales remains under discussion. In this article, we explore the gyrotropic vortex dynamics in a circular soft magnetic nanodot, highlighting the impacts given by nutations in the high-frequency part of the dot spin excitation spectrum. Using a modified Thiele equation of the vortex core motion with a nutation term, we analyze the dynamic response of the vortex to an oscillating magnetic field applied in the dot plane. It is found that nutations affect the trajectory of the vortex core. Namely, we show that the directions of the vortex core motion in the low-frequency gyrotropic mode and the high-frequency nutation mode are opposite. The resonant frequencies of gyrotropic and nutational vortex core motions reveal themselves on different scales: gigahertz for the gyrotropic motion and terahertz for the nutations. We argue that the nutations induce a dynamic vortex mass, present estimates of the nutational mass, and conduct comparison with the mass appearing due to moving vortex interactions with spin waves and Doering domain wall mass.

3D quasi-skyrmions in thick cylindrical and dome-shape soft nanodots.

Magnetic skyrmions are widely attracting researchers due to fascinating physics and novel applications related to their non-trivial topology. Néel skyrmions have been extensively investigated in magnetic systems with Dzyaloshinskii-Moriya interaction (DMI) and/or perpendicular magnetic anisotropy. Here, by means of micromagnetic simulations and analytical calculations, we show that 3D quasi-skyrmions of Néel type, with topological charge close to 1, can exist as metastable states in soft magnetic nanostructures with no DMI, such as in Permalloy thick cylindrical and dome-shaped nanodots. The key factor responsible for the stabilization of DMI-free is the interplay of the exchange and magnetostatic energies in the nanodots. The range of geometrical parameters where the skyrmions are found is wider in magnetic dome-shape nanodots than in their cylindrical counterparts. Our results open the door for a new research line related to the nucleation and stabilization of magnetic skyrmions in a broad class of nanostructured soft magnetic materials.

Spin-wave spectroscopy of individual ferromagnetic nanodisks.

The increasing demand for nanoscale magnetic devices requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of complex nano-architectures with applications in nanomagnetism, magnon spintronics, and superconducting electronics. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, an original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements with sample volumes down to about 10-3 µm3. The key component of the setup is a coplanar waveguide whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks which exhibit standing spin-wave resonances. The circular symmetry of the disks allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. A good correspondence between the results of analytical calculations and micromagnetic simulations is revealed, indicating a validity of the used analytical model going beyond the initial thin-disk approximation used in the theoretical derivation. The presented approach is especially valuable for the characterization of direct-write magnetic elements opening new horizons for 3D nanomagnetism and magnonics.

Half-hedgehog spin textures in sub-100 nm soft magnetic nanodots.

Topologically non-trivial structures such as magnetic skyrmions are nanometric spin textures of outstanding potential for spintronic applications due to their unique features. It is well known that Néel skyrmions of definite chirality are stabilized by the Dzyaloshinskii-Moriya exchange interaction (DMI) in bulk non-centrosymmetric materials or ultrathin films with strong spin-orbit coupling at the interface. In this work, we show that soft magnetic (permalloy) hemispherical nanodots are able to host three-dimensional chiral structures (half-hedgehog spin textures) with non-zero tropological charge. They are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. Micromagnetic simulations corroborate the experimental data. Our work implies the existence of a new degree of freedom to create and manipulate complex 3D spin-textures in soft magnetic nanodots and opens up future possibilities to explore their magnetization dynamics.

Single Chiral Skyrmions in Ultrathin Magnetic Films.

The stability and sizes of chiral skyrmions in ultrathin magnetic films are calculated accounting for the isotropic exchange, Dzyaloshinskii⁻Moriya exchange interaction (DMI), and out-of-plane magnetic anisotropy within micromagnetic approach. Bloch skyrmions in ultrathin magnetic films with B20 cubic crystal structure (MnSi, FeGe) and Neel skyrmions in ultrathin films and multilayers Co/X (X = Ir, Pd, Pt) are considered. The generalized DeBonte ansatz is used to describe the inhomogeneous skyrmion magnetization. The single skyrmion metastability/instability area, skyrmion radius, and skyrmion width are found analytically as a function of DMI strength d . It is shown that the single chiral skyrmions are metastable in infinite magnetic films below a critical value of DMI d c , and do not exist at d > d c . The calculated skyrmion radius increases as d increases and diverges at d → d c - 0 , whereas the skyrmion width increases monotonically as d increases up to d c without any singularities. The calculated skyrmion width is essentially smaller than the one calculated within the generalized domain wall model.

Magnetization Reversal Modes in Short Nanotubes with Chiral Vortex Domain Walls.

Micromagnetic simulations of magnetization reversal were performed for magnetic nanotubes of a finite length, L, equal to 1 and 2 µm, 50 and 100 nm radii, R, and uniaxial anisotropy with "easy axis" parallel to the tube length. I.e., we considered relatively short nanotubes with the aspect ratio L/R in the range 10-40. The non-uniform curling magnetization states on both ends of the nanotubes can be treated as vortex domain walls (DW). The domain wall length, Lc, depends on the tube geometric parameters and the anisotropy constant Ku, and determines the magnetization reversal mode, as well as the switching field value. For nanotubes with relative small values of Lc (Lc/L < 0.2) the magnetization reversal process is characterized by flipping of the magnetization in the middle uniform state. Whereas, for relative large values of Lc, in the reverse magnetic field, coupling of two vortex domain walls with opposite magnetization rotation directions results in the formation of a specific narrow Néel type DW in the middle of the nanotube. The nanotube magnetization suddenly aligns to the applied field at the switching field, collapsing the central DW.

Information processing in patterned magnetic nanostructures with edge spin waves.

Low dissipation data processing with spins is one of the promising directions for future information and communication technologies. Despite a significant progress, the available magnonic devices are not broadband yet and have restricted capabilities to redirect spin waves. Here we propose a breakthrough approach to spin wave manipulation in patterned magnetic nanostructures with unmatched characteristics, which exploits a spin wave analogue to edge waves propagating along a water-wall boundary. Using theory, micromagnetic simulations and experiment we investigate spin waves propagating along the edges in magnetic structures, under an in-plane DC magnetic field inclined with respect to the edge. The proposed edge spin waves overcome important challenges faced by previous technologies such as the manipulation of the spin wave propagation direction, and they substantially improve the capability of transmitting information at frequencies exceeding 10 GHz. The concept of the edge spin waves allows to design a broad of logic devices such as splitters, interferometers, or edge spin wave transistors with unprecedented characteristics and a potentially strong impact on information technologies.

Nonlinear magnetic vortex dynamics in a circular nanodot excited by spin-polarized current.

We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots.

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50-100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

Nano-structured magnetic metamaterial with enhanced nonlinear properties.

Nano-structuring can significantly modify the properties of materials. We demonstrate that size-dependent modification of the spin-wave spectra in magnetic nano-particles can affect not only linear, but also nonlinear magnetic response. The discretization of the spectrum removes the frequency degeneracy between the main excitation mode of a nano-particle and the higher spin-wave modes, having the lowest magnetic damping, and reduces the strength of multi-magnon relaxation processes. This reduction of magnon-magnon relaxation for the main excitation mode leads to a dramatic increase of its lifetime and amplitude, resulting in the intensification of all the nonlinear processes involving this mode. We demonstrate this experimentally on a two-dimensional array of permalloy nano-dots for the example of parametric generation of a sub-harmonic of an external microwave signal. The characteristic lifetime of this sub-harmonic is increased by two orders of magnitude compared to the case of a continuous magnetic film, where magnon-magnon relaxation limits the lifetime.

Microstructural and magnetic properties of CoCu nanoparticles prepared by wet chemistry.

Co(10)Cu(90) nanopowder alloys have been prepared by the sonochemical wet method. In this way, Cu/Co bimetallic nanocrystallites with average diameter of 10-20 nm, presenting a homogeneous metastable solid solution of Co in Cu, were produced. Their structural characterization by X-ray diffraction, transmission electron microscopy and inductive coupled plasma-atomic emission spectrometry techniques has been used. Temperature dependences of the sample magnetization show two characteristic (blocking) temperatures associated to the typical deviation of the zero-field cooling and field-cooling magnetization curves at T1 approximately 15 and T2 approximately 310 K, respectively. This effect can be attributed to the fact that the samples consist of either superparamagnetic and/or ferromagnetic nanoparticles of different sizes. The samples were annealed at 300 degrees C and 450 degrees C and the observed evolution of their magnetic properties was explained in relation to decomposition of the metastable Co/Cu solid solution.

Dynamic origin of azimuthal modes splitting in vortex-state magnetic dots.

A spin-wave theory explaining experimentally observed frequency splitting of dynamical spin excitations with azimuthal symmetry of a magnetic dot in a vortex ground state is developed. It is shown that this splitting is a result of the dipolar hybridization of three spin-wave modes of a dot having azimuthal indices |m|=1: two high-frequency azimuthal dipolar modes of the in-plane part of the vortex with indices m = +/-1 and a low-frequency (Goldstone-like) gyrotropic mode, describing translational motion of the vortex core and having index m = +1. The analytically calculated magnitude of the frequency splitting is proportional to the ratio of the dot thickness to its radius and quantitatively agrees with the results of time-resolved Kerr experiments.

Dynamic origin of vortex core switching in soft magnetic nanodots.

The magnetic vortex with in-plane curling magnetization and out-of-plane magnetization at the core is a unique ground state in nanoscale magnetic elements. This kind of magnetic vortex can be used, through its downward or upward core orientation, as a memory unit for information storage, and thus, controllable core switching deserves some special attention. Our analytical and micromagnetic calculations reveal that the origin of vortex core reversal is a gyrotropic field. This field is induced by vortex dynamic motion and is proportional to the velocity of the moving vortex. Our calculations elucidate the physical origin of the vortex core dynamic reversal, and, thereby, offer a key to effective manipulation of the vortex core orientation.

Universal criterion and phase diagram for switching a magnetic vortex core in soft magnetic nanodots.

The universal criterion for ultrafast vortex-core switching between the up- and down-core bistates in soft magnetic nanodots is investigated by micromagnetic simulations along with vortex-core switching that occurs whenever the velocity of vortex-core motion reaches its critical velocity, upsilon cri = (1.66 +/- 0.18) gamma mean square root of Aex (e.g., upsilon cri = 330 +/- 37 m/s for Permalloy), with the exchange stiffness Aex and the gyromagnetic ratio gamma. On the basis of the universality of upsilon cri, phase diagrams for the vortex-core switching event and switching time with respect to both the amplitude and frequency of a circularly rotating magnetic field are calculated.

Strong radiation of spin waves by core reversal of a magnetic vortex and their wave behaviors in magnetic nanowire waveguides.

We conducted micromagnetic numerical studies on the strong radiation of spin waves (SWs) produced by the magnetic-field-induced reversal of a magnetic vortex core, as well as their wave behaviors in magnetic nanowires. It was found that the radial SWs can be emitted intensively from a vortex core in a circular dot by virtue of localized large torques employed at the core, and then can be injected into a long nanowire via their contact. These SWs exhibit wave characteristics such as propagation, reflection, transmission, interference, and dispersion. These results offer a preview of the generation, delivery, and manipulation of SWs in magnetic elements, which are applicable to information-signal processing in potential SW devices.

Field evolution of tilted vortex cores in exchange-biased ferromagnetic dots.

We developed an analytical model for the magnetization reversal via vortex nucleation and annihilation in double-layer ferromagnetic/antiferromagnetic cylindrical dots. The coupling of the ferromagnet to the antiferromagnet is modeled by means of an interfacial exchange field. The nonuniformity of the magnetization reversal mode perpendicular to the layers is explicitly included and results in a tilted vortex core (tilted Bloch line). The vortex core tilt results in an asymmetry of the nucleation and annihilation fields, which are calculated as a function of the dot geometry.