Triangular antidot array to honeycomb wire network – Role of interstitial vortices

We present results on interesting vortex matching effects that arise out of the interplay between the geometric shape of the vortex and the geometry of the underlying nano-engineered antidot lattice in Nb thin films. The antidots are in the shape of honeycomb with gradually increasing area such that one essentially goes over from a triangular antidot array to a honeycomb wire network. The fractional matching at 1/2 is absent in the antidot array limit hinting towards a possible role of the interstitial vortices.     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Vortices trapped in the damaged surroundings of antidots in Nb films – Depinning transition

The depinning transition of Vortex Matter in the presence of antidots in superconducting Nb films has been investigated. The antidots were fabricated using two different techniques, resulting in samples with arrays of diverse pinning efficiency. At low temperatures and fields, the spatial arrangement of Vortex Matter is governed by the presence of the antidots. Keeping the temperature fixed, an increase of the field induces a depinning transition. As the temperature approaches T_c, the depinning frontier exhibits a characteristic kink at the temperature T_k, above which the phase boundary exhibits a different regime. The lower-temperature regime is adequately described by a power-law expression, whose exponent n was observed to be inversely proportional to the pinning capability of the antidot, a feature that qualifies this parameter as a figure of merit to quantify the pinning strength of the defect.     

Bi2Sr2CaCu2O8 crystal with a region of periodic blind antidots – transition between bulk and interface vortex pinning

This work focuses on differential magneto-optical two-dimensional imaging of the current distribution in a high-T_c superconducting Bi₂Sr₂CaCu₂O₈ crystal having a region of 170 × 170 μm² patterned with periodic blind antidots. By measuring the self-induced field of an applied current, we can map the current flow distribution within and at the edges of the patterned region. We detected three separate types of current flow within the patterned region, which correspond to three different arrangements of pancake vortices within and at the edges of the patterned region. At high temperatures the vortices delocalize from the antidots, presumably due to thermal fluctuations. However, at lower temperatures vortex pinning mechanisms become prominent, lowering the vortex mobility in the patterned region. There are two contributing mechanisms: bulk pinning by the patterned antidots and interface pinning due to an entry barrier into the patterned region. Each mechanism is dominant at different temperatures. From our experiments we see that the T–H transition line from the bulk to the interface pinning and the vortex melting line in the pristine region coincide.     

Vortex lattice matching effects in a washboard pinning potential induced by Co nanostripe arrays

An advanced mask-less nanofabrication technique, focused electron beam-induced deposition (FEBID), has been employed on epitaxial Nb thin films to prepare ferromagnetic decorations in the form of an array of Co stripes. These substantially modify the non-patterned films’ superconducting properties, providing a washboard-like pinning potential landscape for the vortex motion. At small magnetic fields B ? 0.1 T, vortex lattice matching effects have been investigated by magneto-transport measurements. Step-like drops in the field dependencies of the films resistivity ρ(B) have been observed in particular for the vortex motion perpendicular to the Co stripes. The field values, corresponding to the middle points of these drops in ρ(B), meet the vortex lattice parameter matching the pinning structure’s period. These disagree with the results of Jaque et al. (2002) [11], who observed matching effects corresponding to the stripe width in Nb films grown on periodically distributed submicrometric lines of Ni.     

Fractional matching effect in single-crystal films of with antidot lattice

To study the vortex behavior in 2D periodic pinning potentials, we measured field dependence of the vortex-flow resistance and the critical current in single-crystal Bi₂Sr₂CaCu₂O_8+y (Bi2212) films with an equilateral triangular array of antidots. Fractional matching effect was observed in 1/4, 1/3, 1/2, 2/3, 3/4, and 6/7 of the first matching field H₁, and even above H₁. While the most of fractional numbers except 1/2 can be explained from commensurability between triangular lattices of antidots and vortices, the matching effect in 1/2H₁ suggests the existence of the interstitial vortices in comparison with the results of a reported numerical simulation. The fractional matching effect above H₁ can be explained as a matching effect by multi-quanta vortices.     

Flux confinement by regular arrays and clusters of antidots in Pb/Cu bilayers

We have studied the magnetoresistance and superconducting–normal phase boundary of superconducting films with an antidot array and mesoscopic antidot clusters of 2 × 2 μm²with only four antidots. For both systems characteristic minima have been observed in the magnetoresistance which are caused by the formation of certain vortex configurations minimizing the free energy. By comparing experimental data with calculations carried out in the London limit of the Ginzburg Landau theory, these vortex configurations have been identified.     

Vortices in superconducting nano-networks with anti-dots array

Vortices (magnetic flux quanta) in the superconducting networks perforated with anti-dots (holes) arrays behave as electrons in atomic lattice of crystals. Repulsive and attractive interaction among vortices and anti-dots resemble to those among electrons and atoms in crystals. To confirm the variety of the vortex physics similar to the solid state physics, we have fabricated such superconducting networks with antidots array in metallic, inter-metallic and high-T _c superconductors (HTSCs), and have measured magneto-resistance of vortex-flow. In these materials, we have observed integer-matching at the matching fields and fractional-matching effect between them. Most of them are well explained by commensurability between Abrikosov vortex lattice and anti-dots array. Furthermore, the effect of the anti-dots array in HTSCs appears as another kind of phase transitions instead of to the first-order melting transition of vortex lattice in pristine samples.     

Vortex motion in high-Tc films and a micropattern-induced phase transition

A micropattern-induced transition in the mechanism of vortex motion and vortex mobility is observed in high-T_c thin films. The competition between the anomalous Hall effect and the guidance of vortices by rows of microholes (antidots) lead to a sudden change in the direction of vortex motion that is accompanied by a change in the critical current density and microwave losses. The latter effect demonstrates the difference in vortex mobility in different phases of vortex motion in between and within the rows of antidots.     

Correlation length of quasiperiodic vortex lattices

We investigated vortex-lattice dynamics in superconducting Nb thin films with different quasiperiodic arrays of magnetic pinning centers. The mixed-state magnetoresistance exhibits minima for well-defined applied fields, related to matching effects between the vortex lattice and those arrays. The results show that critical matching can originate at a local scale. For fractal arrays, the vortex-lattice correlation length is longer and the minima are deeper, close to those of periodic arrays.     

Antidot diameter dependence of matching effect in Bi2Sr2CaCu2O8+y with antidot array

To explore vortex states and their dynamics in superconductors with large thermal fluctuation and artificial pinning potentials, we have studied the influence of periodic arrays of antidots in high-T_c superconductor Bi₂Sr₂CaCu₂O_8+y (Bi2212). The diameter dependence of the matching effect in Bi2212 without a change of the thickness and oxygen doping level was investigated using one Bi2212 single-crystal film of homogeneous thickness in which several different-diameter antidot arrays were introduced. The matching effect observed by vortex-flow resistance measurements changed systematically depending on the diameter. The antidot-diameter dependence of the irreversibility lines was examined.     

Commensurability effects in superconducting Nb films with quasiperiodic pinning arrays

We study experimentally the critical depinning current I(c) versus applied magnetic field B in Nb thin films which contain 2D arrays of circular antidots placed on the nodes of quasiperiodic (QP) fivefold Penrose lattices. Close to the transition temperature T(c) we observe matching of the vortex lattice with the QP pinning array, confirming essential features in the I(c)(B) patterns as predicted by Misko et al. [Phys. Rev. Lett. 95, 177007 (2005)]. We find a significant enhancement in I(c)(B) for QP pinning arrays in comparison to I(c) in samples with randomly distributed antidots or no antidots.     

Rectified vortex motion in an Nb film with a spacing-graded array of holes

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.     

Influence of flat milling on vortex matching effect in Bi2Sr2CaCu2O8+y with antidot array

Significant enlargements of antidot diameter by Ar-ion milling were observed in Bi₂Sr₂CaCu₂O_8+y single-crystal films with antidot arrays as well as the thinning of the films. In an original sample with triangular array of antidots, whose diameter is about 200 nm, a few dip structures by the matching effect were observed in the vortex-flow resistance as a function of magnetic field. With increasing the milling time, the number of the dips increases and the appearance of the flow resistance becomes periodic oscillations. These features can be explained mainly by the increase of the antidot diameter.     

Vortex pinning in superconducting Nb thin films deposited on nanoporous alumina templates

We present a study of magnetization and transport properties of superconducting Nb thin films deposited on nanoporous aluminium oxide templates. Periodic oscillations in the critical temperature vs. field, matching effects in fields up to 700 mT and strongly enhanced critical currents were observed. These fields are considerably higher than those typical for periodic pinning arrays made by lithographic techniques, which reflects the benefits of nanostructuring superconductors by using self-organized growth. This method provides a periodic pinning potential with sub-100 nm spacing between the pinning centers, which enhances vortex pinning in broad field and temperature ranges.     

Vortex lattice ordering in the flux flow state of Nb thin films

We measure current–voltage characteristics at high driving currents for different magnetic fields and temperatures in Nb thin films of rather strong pinning. In a definite range of the B–T phase diagram we find that a current induced transition occurs in the flux flow motion of the vortex lattice, namely a dynamic ordering (DO). Contrary to the case of weaker pinning materials, DO is observed only at low fields, due to the stronger intrinsic disorder that can deform plastically the moving vortex lattice even for small applied fields.     

Vortex configurations in regular arrays of pinning sites

The vortex states interacting with a triangular lattice of pinning sites in a two-dimensional (2D) superconducting sample have been investigated by using a molecular dynamics approach. The Nordborg–Vinokur potential is used to model the interaction between the vortices and the pinning sites. We have found several ordered vortex configurations, such as pentagons, hexagons, and shells depending on two critical parameters of the system, namely pinning radius and vorticity. Our results are in good agreement with the results of Bitter decoration experiments performed on type-II superconductors with blind hole and pillar arrays.     

Shifting and pinning of a magnetic vortex core in a permalloy dot by a magnetic field

Magnetic pinning in thin films seems to be a major research subject in the near future, as it is involved in all switching processes which include a movement of a domain wall or a magnetic vortex. We used Lorentz transmission electron microscopy and vortex pinning at artificial pinning sites to investigate the pinning behavior of magnetic vortices for the first time with high spatial resolution.     

Commensurability effects in the critical forces of a superconducting film with Kagomé pinning array at submatching fields

Using molecular dynamics simulations, we find the commensurability force peaks in a two-dimensional superconducting thin-film with a Kagomé pinning array. A transport force is applied in two mutually perpendicular directions, and the magnetic field is increased up to the first matching field. Usually the condition to have pronounced force peaks in systems with periodic pinning is associated to the rate between the applied magnetic field and the first matching field, it must be an integer or a rational fraction. Here, we show that another condition must be satisfied, the vortex ground state must be ordered. Our calculations show that the pinning size and strength may dramatically change the vortex ground state. Small pinning radius and high values of pinning strength may lead to disordered vortex configurations, which fade the critical force peaks. The critical forces show anisotropic behavior, but the same dependence on pinning strength and radius is observed for both driven force directions. Different to cases where the applied magnetic field is higher than the first matching field, here the depinning process begins with vortices weakly trapped on top of a pinning site and not with interstitial vortices. Our results are in good agreement with recent experimental results.     

Preferential diagonal penetration of vortices into square superconducting networks

We have observed vortex penetration into Nb thin films with square arrays of square holes with variable sizes and lattice constants. We find that when the lattice spacing is large and the width of superconducting line is narrow, vortices penetrate diagonally rather than parallel to the nearest neighbor direction. This phenomenon is also confirmed in NbTiN samples with the same geometry. We also confirm that the direction of edge relative to that of hole array is not relevant. Possible origin of such a preferential penetration is proposed.