Elementary pinning forces measured using low temperature scanning electron microscopy

Magnetic flux penetrating Josephson tunnel junctions parallel and transverse to the tunnel barrier has been imaged using low temperature scanning electron microscopy. Employing this technique we have studied the behavior of magnetic flux quanta under the influence of external forces. The strength of pinning centers acting on vortices existing within the barrier has been determined by measuring the turning angle of these flux quanta in rotating magnetic fields. Trapped transverse flux quanta could be depinned by applying a sufficient Lorentz force or electron beam irradiation. The strength of the pinning centers has been determined.     

Vortices in Bose-Einstein condensates: A review of the experimental results

Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity. Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature, (d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures, nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature; (d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations (Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed.     

Pinning-induced formation of vortex clusters and giant vortices in mesoscopic superconducting disks

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.     

Traces of vortices in superfluid helium droplets

We report on the observation of vortices in superfluid 4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.     

Non-monotonic driven vortex noise in HTSC

We present noise measurements on YBCO thin films in different conditions of magnetic field and driving current. Noise spectra for non-driven and driven cases (in the flux-creep region) evidence deep differences in vortex dynamics between these two regimes. For the driven case, the effect of applying magnetic field is a reduction in noise, which can be explained by the increase in the fraction of vortices that undergo flux-flow. For the non-driven case, magnetic field has no significative influence on noise, probably due to the absence of Lorentz force that causes coherent movement of vortices. For all magnetic fields studied in this work (0-154 mT) the effect of increasing current is an increase of noise, which is in contrast to the results from other authors. This behavior can be explained by an increase of current induced vortex-antivortex annihilation events. We propose that driven noise has a non-monotonic behavior due to the competition between annihilation events and driving force which causes opposite effects on noise.     

Active control of coaxial jet mixing with manipulation of primary vortical structures by arrayed micro flap actuators

Active mixing control of a methane/air isothermal coaxial jet was achieved using micro magnetic flap actuators arranged on the inner surface of the outer annular nozzle. The spatio-temporal evolution of vortical structures and the scalar mixing were studied through the particle image velocimetry and planar laser-induced fluorescence methods. In contrast to studies on jet control using acoustic forcing, the mechanical movement of the flap directly generated large-scale intense vortices. The mixing was enhanced significantly by the vortices formed in the inner shear layer, although the control input was given to the outer shear layer. It was found that the primary vortex rings dominated the near-field mixing, while streamwise vortices were responsible for the downstream mixing. It was also demonstrated that the radial range of the inner fuel transportation could be manipulated flexibly by adjusting the shedding interval of the vortices. Especially, the mixing was enhanced most significantly when the primary vortices were most densely populated near the nozzle exit at the control Strouhal number of unity.     

Structure of the wake of a magnetic obstacle

We use a combination of numerical simulations and experiments to elucidate the structure of the flow of an electrically conducting fluid past a localized magnetic field, called magnetic obstacle. We demonstrate that the stationary flow pattern is considerably more complex than in the wake behind an ordinary body. The steady flow is shown to undergo two bifurcations (rather than one) and to involve up to six (rather than just two) vortices. We find that the first bifurcation leads to the formation of a pair of vortices within the region of magnetic field that we call inner magnetic vortices, whereas a second bifurcation gives rise to a pair of attached vortices that are linked to the inner vortices by connecting vortices.     

Magnetic vortex gyration mediated by point-contact position

Micromagnetic simulation is employed to study the gyration motion of magnetic vortices in distinct permalloy nanodisks driven by a spin-polarized current. The critical current density for magnetic vortex gyration, eigenfrequency, trajectory, velocity and the time for a magnetic vortex to obtain the steady gyration are analyzed. Simulation results reveal that the magnetic vortices in larger and thinner nanodisks can achieve a lower-frequency gyration at a lower current density in a shorter time. However, the magnetic vortices in thicker nanodisks need a higher current density and longer time to attain steady gyration but with a higher eigenfrequency. We also find that the point-contact position exerts different influences on these parameters in different nanodisks, which contributes to the control of the magnetic vortex gyration. The conclusions of this paper can serve as a theoretical basis for designing nano-oscillators and microwave frequency modulators.     

Vortex dynamics mediated by exchange coupling in permalloy double disks

The dynamics of magnetic vortices in double disks coupled with a bridge are studied by micromagnetic simulations. There are three types of magnetic configurations being found, which depend on the size of the bridge and the chiralities of the vortices. The exchange coupling between the vortices, which is mediated by the magnetizations in the bridge, influences the trajectories and oscillation frequencies of the vortices. Moreover, the frequency depends on the configurations of the double disks and the bridge size.     

Direct Observation of Magnetic Vortices in Superconductors Using Electron Waves

The development of a coherent field-emission electron beam has made it possible to observe microscopic magnetic lines of force by detecting the electron-wave phase shifts that are due to vector potentials. Electron-holographic interference microscopy has been used to observe magnetic lines of force of magnetic vortices in superconductors, and Lorentz microscopy has been used to observe the dynamics of the vortices. The observation of vortices not only helps us understand the microscopic mechanism of flux pinning, which holds the key to practical applications of superconductors, but also clarifies fundamental phenomena of superconductivity which have implications for more general physical phenomena.     

Vortex flux channeling in magnetic nanoparticle chains

A detailed understanding of the formation of magnetic vortices in closely spaced ferromagnetic nanoparticles is important for the design of ultra-high-density magnetic devices. Here, we use electron holography and micromagnetic simulations to characterize three-dimensional magnetic vortices in chains of FeNi nanoparticles. We show that the diameters of the vortex cores depend sensitively on their orientation with respect to the chain axis and that vortex formation can be controlled by the presence of smaller particles in the chains.     

Josephson vortices and intrinsic Josephson junctions in the layered iron-based superconductor Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5

Modulated electronic state due to the layered crystal structures brings about moderate anisotropy of superconductivity in the iron-based superconductors and thus Abrikosov vortices are expected in the mixed state. However, based on the angular and temperature dependent transport measurements in iron-based superconductor Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{0.9}$Pt$_{0.1}$)$_2$As$_2$)$_5$ with $T_{\rm c} \simeq 12$ K, we find clear evidences of a crossover from Abrikosov vortices to Josephson vortices at a crossover temperature $T^{\star} \simeq 7 $ K, when the applied magnetic field is parallel to the superconducting FeAs layers, i.e., the angle between the magnetic field and the FeAs layers $\theta = 0^\circ$. This crossover to Josephson vortices is demonstrated by an abnormal decrease (increase) of the critical current (flux-flow resistance) below $T^{\star}$, in contrast to the increase (decrease) of the critical current (flux-flow resistance) above $T^{\star}$ expected for Abrikosov vortices. Furthermore, when $\theta$ is larger than $0.5^\circ$, the flux-flow resistance and critical current have no anomalous behaviors across $T^{\star}$. These anomalous behaviors can be understood in terms of the distinct transition from the well-pinned Abrikosov vortices to the weakly-pinned Josephson vortices upon cooling, when the coherent length perpendicular to the FeAs layers $\xi_\bot$ becomes shorter than half of the interlayer distance $d/2$. These experimental findings indicate the existence of intrinsic Josephson junctions below $T^{\star}$ and thus quasi-two-dimensional superconductivity in Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{0.9}$Pt$_{0.1}$)$_2$As$_2$)$_5$, similar to those in the cuprate superconductors.     

Critical field for complete vortex expulsion from narrow superconducting strips

We have measured the maximum field for which vortices are completely expelled from a thin-film superconducting strip. Niobium strips of width W were field cooled and imaged with a scanning Hall-probe microscope. Below a critical field B(m) approximately Phi(0)/W(2) all flux was expelled; above this field vortices were observed with a density increasing approximately linearly with field. The small value of the critical field, which is orders of magnitude less than in the bulk, implies that superconducting devices should be designed with narrow wires to eliminate the generation of noise from vortex motion.     

Single-element objective lens for soft x-ray differential interference contrast microscopy

High-resolution soft x-ray differential interference contrast (DIC) imaging was demonstrated through the use of a single-element objective, the XOR pattern, in a full-field soft x-ray microscope. DIC images of the magnetic domains in a 59 nm thick amorphous Gd25Fe75 layer were obtained and magnetic phase contributions were directly imaged. With its elemental, chemical, and magnetic specificity, compatibility with various sample environments, and ease of implementation, we expect this soft x-ray DIC technique to become one of the standard modes of operation for existing full-field soft x-ray microscopes.     

Dynamic and static phases of vortices under an applied drive in a superconducting stripe with an array of weak links

Static and dynamic properties of superconducting vortices in a superconducting stripe with a periodic array of weakly-superconducting (or normal metal) regions are studied in the presence of external magnetic and electric fields. The time-dependent Ginzburg-Landau theory is used to describe the electronic transport, where the anisotropy is included through the spatially-dependent critical temperature T _c . Superconducting vortices penetrating into the weak-superconducting region with smaller T _c are more mobile than the ones in the strong superconducting regions. We observe periodic entrance and exit of vortices which reside in the weak link for some short interval. The mobility of the weakly-pinned vortices can be reduced by increasing the uniform applied magnetic field leading to distinct features in the voltage vs. magnetic field response of the system.     

Interaction between superconducting vortices and a Bloch wall in ferrite garnet films

A theoretical model for how Bloch walls occurring in in-plane magnetized ferrite garnet films can serve as efficient magnetic micromanipulators is presented. As an example, the walls' interaction with Abrikosov vortices in a superconductor in close contact with a garnet film is analyzed within the London approximation. The model explains how vortices are attracted to such walls, and excellent quantitative agreement is obtained for the resulting peaked flux profile determined experimentally in NbSe(2) using high-resolution magneto-optical imaging of vortices. In particular, this model, when generalized to include charged magnetic walls, explains the counterintuitive attraction observed between vortices and a Bloch wall of opposite polarity.     

Attraction between pancake vortices in the crossing lattices of layered superconductors

The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancake vortices, forming the AVs and JVs, produces the deformation of the AV line. It is demonstrated that, as a result of this deformation, a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chain formation. The vortex structure in the weak perpendicular magnetic field is the vortex chain phase, where only a small part of JVs is occupied by AVs.     

Topological vortices in a two-gap superconductor

Based on the ϕ-mapping theory, we derive a new rigorous equation describing the distribution of the magnetic field for vortices in a two-gap superconductor, of which the so-called modified London equation is just a special case in a one-flavor limit. We explicitly investigate the London penetration depth, the Meissner and mixed states and Josephson effect. A magnetic flux quantization condition for vortices in a two-gap superconductor is also derived, from which it follows that in a two-gap superconductor there exist vortices which carry an arbitrary fraction of magnetic flux quantum. The branch processes during the evolution of the vortices in a two-gap superconductor are discussed.     

Lorentz transmission electron microscopy studies on topological magnetic domains

Lorentz transmission electron microscopy(TEM) is a powerful tool to study the crystal structures and magnetic domain structures in correlation with novel physical properties. Nanometric topological magnetic configurations such as vortices, bubbles, and skyrmions have received enormous attention from the viewpoint of both fundamental science and potential applications in magnetic logic and memory devices, in which understanding the physical properties of magnetic nanodomains is essential. In this review article, several magnetic imaging methods in Lorentz TEM including the Fresnel and Foucault modes, electron holography, and differential phase contrast(DPC) techniques are discussed, where the novel properties of topological magnetic domains are well addressed. In addition, in situ Lorentz TEM demonstrates that the topological domains can be efficiently manipulated by electric currents, magnetic fields, and temperatures, exhibiting novel phenomena under external fields, which advances the development of topological nanodomain-based spintronics.