We report on the controllable pinning of domain walls in stripes with perpendicular magnetic anisotropy by magnetostatic coupling to magnetic vortices in disks located above the stripe. Pinning mechanisms and depinning fields are reported. This novel pinning strategy, which can be realized by current nanofabrication techniques, opens up new possibilities for the non-destructive control of domain wall mobility in domain wall based spintronic devices.
We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum-Hall regime, which is reached when the rotation frequency $Ω$ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency $ω$ and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are al…
Multi-quanta, or giant, 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 the formation of GVs. Using Bitter decoration to visualise vortices in small Nb disks, 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.
Antagonistic symmetries of superconducting polygons and their induced multi-vortex states in a homogeneous magnetic field may lead to appearance of antivortices in the vicinity of the superconducting/normal state boundary (where mesoscopic confinement is particularly strong). Resulting vortex-antivortex (V-Av) molecules match the sample symmetry, but are extremely sensitive to defects and fluctuations and remain undetected experimentally. Here we show that V-Av states can re-appear deep in the superconducting state due to an array of perforations in a polygonal setting, surrounding a central h…
Model of quantum depinning of magnetic vortex cores from line defects in a disk geometry and under the application of an in-plane magnetic field has been developed within the framework of the Caldeira-Leggett theory. The corresponding instanton solutions are computed for several values of the magnetic field. Expressions for the crossover temperature Tc and for the depinning rate Γ(T) are obtained. Fitting of the theory parameters to experimental data is also presented.
We report on the direct observation of vortex states confined in equilateral and isosceles triangular dots of weak pinning amorphous superconducting thin films with a scanning superconducting quantum interference device microscope. The observed images illustrate not only pieces of a triangular vortex lattice as commensurate vortex states, but also incommensurate vortex states including metastable ones. We comparatively analyze vortex configurations found in different sample geometries and discuss the symmetry and stability of commensurate and incommensurate vortex configurations against deform…
The persistence of the first-order transition line in the phase diagram of mesoscopic Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ vortex matter is detected down to a system size of less than hundred vortices. Precise and highly-sensitive to bulk currents AC magnetization techniques proved to be mandatory in order to obtain this information. The location of the vortex matter first-order transition lines are not altered by decreasing the sample size down to 20 $μ$m. Nevertheless, the onset of irreversible magnetization is affected by increasing the sample surface-to-volume ratio producing a noticeable enl…
We use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image individual vortices in amorphous superconducting MoSi thin films. Spatially resolved measurements of the magnetic field generated by both vortices and Meissner screening satisfy the Pearl model for vortices in thin films and yield values for the Pearl length and bulk penetration depth at 4.2 K. Flux pinning is observed and quantified through measurements of vortex motion driven by both applied currents and thermal activation. The effects of pinning are also observed in metastable vortex configuration…
Conventional superconductors have vortices carrying integer multiples of magnetic flux quantum while unconventional ones, with p- or d-wave order parameter, allow half-integer fluxes. Here we show that mesoscopic size effects stabilize fractional flux vortices in the thermodynamical ground state of s-wave two-gap superconductors. The value of these fluxes can be an arbitrary fraction of flux quantum and can be measured directly from distributions of magnetic fields on the samples.
Topological magnetic textures are of great interest in various scientific and technological fields. To allow for precise control of nanoscale magnetism, it is of great importance to understand the role of intrinsic defects in the host material. Here, we use conventional and time-resolved Lorentz microscopy to study the effect of grain size in polycrystalline permalloy films on the pinning and gyration orbits of vortex cores inside magnetic nanoislands. To assess static pinning, we use in-plane magnetic fields to shift the core across the island while recording its position. This enables us to …
In mesoscopic two-gap superconductors with sizes of the order of the coherence length noncomposite vortices are found to be thermodynamically stable in a large domain of the $T - H$ phase diagram. In these phases the vortex cores of one condensate are spatially separated from the other condensate ones, and their respective distributions can adopt distinct symmetries. The appearance of these vortex phases is caused by a non-negligible effect of the boundary of the sample on the superconducting order parameter and represents therefore a genuine mesoscopic effect. For low values of interband Jose…
Transport characteristics of nano-sized superconducting strips and bridges are determined by an intricate interplay of surface and bulk pinning. In the limiting case of a very narrow bridge, the critical current is mostly defined by its surface barrier, while in the opposite case of very wide strips it is dominated by its bulk pinning properties. Here we present a detailed study of the intermediate regime, where the critical current is determined, both, by randomly placed pinning centers and by the Bean-Livingston barrier at the edge of the superconducting strip in an external magnetic field. …
We present an approximate description of the giant vortex state in a thin mesoscopic superconducting disk within the phenomenological Ginzburg-Landau approach. Analytical asymptotic expressions for the energies of the states with fixed vorticity are obtained when a small magnetic flux is accumulated in the disk. The spectrum of the lowest Landau levels of such a disk is also discussed.
The competition between intrinsic disorder in superconducting YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) thin films and an ultradense triangular lattice of cylindrical pinning centers spaced at 30 nm intervals results in an ordered Bose glass phase of vortices. The samples were created by scanning the focused beam of a helium-ion microscope over the surface of the YBCO thin film to form columns of point defects where superconductivity was locally suppressed. The voltage-current isotherms reveal critical behavior and scale in the vicinity of the second-order glass transition. The latter exhibits a disti…
Recently completely new types of domain walls (DWs) have been discovered in helical magnets, consisting generically of a regular array of {\it pairs} of magnetic vortex lines \cite{Li+12}. Only for special orientations DWs are free of vortices. In this article we calculate their elastic and pinning properties, using the pitch angle $θ$ as a small parameter. In particular we show that vortex free DWs exhibit long range elasticity which makes them very stiff and suppresses their pinning by impurities. Their roughening transition temperature is of the order of the Néel temperature. DWs including …
Direct observation of vortices by the scanning SQUID microscopy was made on large mesoscopic disks of an amorphous MoGe thin film. Owing to the weak pinning nature of the amorphous film, vortices are able to form geometry induced, (quasi-)symmetric configurations of polygons and concentric shells in the large disks. Systematic measurements made on selected disks allow us to trace not only how the vortex pattern evolves with magnetic field, but also how the vortex polygons change in size and rotate with respect to the disk center. The results are in good agreement with theoretical consideration…
Magnetic fields penetrate a type-II superconductor as magnetic flux quanta, called vortices. In a clean superconductor they arrange in a hexagonal lattice, while by adding periodic artificial pinning centers many other arrangements can be realized. Using the focused beam of a helium ion microscope we have fabricated periodic patterns of dense pinning centers with spacings as small as 70 nm in thin films of the cuprate superconductor YBa$_{2}$Cu$_{3}$O$_{7-δ}$. In these ultradense kagomé-like patterns, the voids lead to magnetic caging of vortices, resulting in unconventional commensurability e…
Direct observation of vortex states confined in mesoscopic regular triangle dots of amorphous MoGe thin films was made with a scanning superconducting quantum interference device microscope. The observed magnetic images illustrate clearly how vortices are distributed over the triangle dots by forming not only commensurate triangular clusters, but also unique patterns imposed by incommensurability. We discuss the results in terms of vortex shells and construct the packing sequence of vortices in the multiple shell structure.
We study a high-TC superconducting (YBa2Cu3O7-d) / ferromagnetic (Co/Pt multilayer) hybrid which exhibits resistance switching driven by the magnetic history: depending on the direction of the external field, a pronounced decrease or increase of the mixed-state resistance is observed as magnetization reversal occurs within the Co/Pt multilayer. We demonstrate that stray magnetic fields cause these effects via i) creation of vortices/antivortices and ii) magnetostatic pinning of vortices that are induced by the external field.
We investigated configurational changes in mesoscopic vortex matter with less than thousand vortices during flux penetration in freestanding 50 $μ$m diameter disks of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 +δ}$. High-resolution AC and DC local magnetometry data reveal oscillations in the transmittivity echoed in peaks in the third-harmonics magnetic signal fainting on increasing vortex density. By means of extra experimental evidence and a simple geometrical analysis we show that these features fingerprint the discretized entrance of single-shells of vortices having a shape that mimics the sample edg…
Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50 ξ). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ~ 230 vor…
The response of mesoscopic superconductors to an ac magnetic field is investigated both experimentally and with numerical simulations. We study small square samples with dimensions of the order of the penetration depth. We obtain the ac susceptibitity $χ=χ'+iχ''$ at microwave frequencies as a function of the dc magnetic field $H_{dc}$. We find that the dissipation, given by $χ''$, has a non monotonous behavior in mesoscopic samples. In the numerical simulations we obtain that the dissipation increases before the penetration of vortices and then it decreases abruptly after vortices have entered…
The nucleation of superconductivity in a superconducting disk with a Co/Pt magnetic triangle was studied. We demonstrate that when the applied magnetic field is parallel to the magnetization of the triangle, the giant vortex state of vorticity three splits into three individual F0-vortices, due to a pronounced influence of the C3 symmetry of the magnetic triangle. As a result of a strong pinning of the three vortices by the triangle, their configuration remains stable in a broad range of applied magnetic fields. For sufficiently high fields, F0-vortices merge and the nucleation occurs through …
We investigate anisotropy in the vortex pinning in thin superconducting films with a square array of rectangular submicron holes ("antidots"). The size of the antidots is chosen in such a way that it corresponds to a saturation number n_s=1, i.e. each antidot can trap at most one flux quantum. Therefore, interstitial vortices, appearing when the magnetic field exceeds the first matching field, are "caged" at the interstitial positions by the repulsion from the saturated antidots. We observe an overall higher critical current Ic(H) when it is measured parallel to the long side of the antidots t…
We investigated vortex dynamics in a single-crystal sample of type-II superconductor NbSe$_{2}$ using scanning tunneling microscopy at 4.2 K. The decay of the magnetic field at a few nT/s in our superconducting magnet induced the corresponding motion of vortices at a few pm/s. Starting with an initial magnetic field of 0.5 T, we continued to observe motion of vortices within a field of view of 400$\times$400 nm$^2$ subject to decay of the magnetic field over a week. Vortices moved collectively, and maintained triangular lattices due to strong vortex-vortex interactions during the motion. Howev…
