The influence of a submicrometre antidot array on the vortex topology and the pinning mechanism in layered superconductors (original) (raw)
Related papers
Evidence of vortex kink formation in antidotted layered superconductors
Physical Review B, 2002
The angular dependence of the critical current density J c in external magnetic field has been measured in Nb/CuMn multilayers with and without a regular array of antidots. The multilayers without antidots behave coherently to what has already been reported in the literature, showing, for sufficiently high anisotropy, dissipation related only to the magnetic-field component perpendicular to the layers, H Ќ . This behavior is generally explained in terms of the presence of kinked vortices. The kink formation has been directly detected in the antidotted samples, where low angle modulation of J c , related to single vortex kinks entering the system, has been found. The presence of kinks explains also the unusual scaling of J c vs H Ќ found at low anisotropy in the antidotted case up to a value of the angle related to the geometrical structure of the system.
Superconducting films with antidot arrays—Novel behavior of the critical current
Europhysics Letters (EPL), 2006
Novel behavior of the critical current density jc of a regularly perforated superconducting film is found, as a function of applied magnetic field H. Previously pronounced peaks of jc at matching fields were always found to decrease with increasing H. Here we found a reversal of this behavior for particular geometrical parameters of the antidot lattice and/or temperature. This new phenomenon is due to a strong "caging" of interstitial vortices between the pinned ones. We show that this vortex-vortex interaction can be further tailored by an appropriate choice of the superconducting material, described by the Ginzburg-Landau parameter κ. In effective type-I samples we predict that the peaks in jc(H) at the matching fields are transformed into a step-like behavior.
Superconducting heterostructures: from antipinning to pinning potentials
Superconductor Science and Technology, 2014
We study vortex lattice dynamics in a heterostructure that combines two type-II superconductors: a niobium film and a dense triangular array of submicrometric vanadium (V) pillars. Magnetic ac susceptibility measurements reveal a sudden increase in ac penetration, related to an increase in vortex mobility above a magnetic field, * H T (), that decreases linearly with temperature. Additionally, temperature independent matching effects that occur when the number of vortices in the sample is an integer of the number of V pillars, strongly reduce vortex mobility, and were observed for the first and second matching fields, H 1 and H 2. The angular dependence of H 1 , H 2 and * H T () shows that matching is determined by the normal applied field component, while * H T () is independent of the applied field orientation. This important result identifies * H T () with the critical field boundary for the normal to superconducting transition of V pillars. Below * H T (), superconducting V pillars repel vortices, and the array becomes an 'antipinning' landscape that is more effective in reducing vortex mobility than the 'pinning' landscape of the normal V sites above * H T (). Matching effects are observed both below and above * H T (), implying the presence of ordered vortex configurations for 'antipinning' or 'pinning' arrays.
Vortex-Antivortex Lattices in Superconducting Films with Magnetic Pinning Arrays
Journal of Low Temperature Physics, 2005
Novel vortex structures are found when a thin superconducting film (SC) is covered with a lattice of out-of-plane magnetized magnetic dots (MDs). The stray magnetic field of the dots confines the vortices to the MD regions, surrounded by antivortices which "crystallize" into regular lattices. First and second order transitions are found as magnetic array is made sparser or MD-magnetization larger. For sparse MD-arrays fractional vortex-antivortex states are formed, where the crystalsymmetry is combined with a non-uniform "charge" distribution. We demonstrate that due to the (anti)vortices and the supercurrents induced by the MDs, the critical current of the sample actually increases if exposed to a homogeneous external magnetic field, contrary to conventional SC behavior. PACS numbers: 74.78.-w, 74.25.Op, 74.25.Qt, 74.25.Dw.
2007
Isolated vortex line 1.5.3 Interaction between vortex lines 1.5.4 Vortex lattices 1.6 Flux pinning 1.6.1 Pinning mechanism 1.6.2 Artificial pinning centers 1.7 Thin superconducting films 1.8 Mesoscopic superconductors 1.9 Details of the numerical approach ii Contents Surface barrier for flux penetration and expulsion in thin mesoscopic superconductors 37 2.1 Introduction 2.2 Theoretical formalism 2.2.1 Ginzburg-Landau theory 2.2.2 London approach and phase of the order parameter 2.3 Superconducting disk 2.3.1 A single vortex: estimation of the H c1 2.3.2 Comparison with London theory 2.3.3 The L = 2 state in the disk 2.3.4 Temperature dependence of the energy barrier 2.4 Superconducting ring 2.5 Superconducting square 2.6 Conclusions 3 A superconducting square with antidots 57 3.1 Introduction 3.2 Theoretical formalism 3.3 Free energy and magnetization 3.4 Stability of different vortex states 3.5 Superconducting/Normal phase transition 3.6 Conclusions 4 Superconducting thin films with an antidot lattice 71 4.1 Introduction 4.2 Theoretical formalism 4.3 Vortex structure in perforated superconducting films 4.3.1 Equilibrium vortex configurations 4.3.2 Influence of temperature on the stability of the vortex-antivortex pairs 4.3.3 The hole occupation number n o 4.4 Vortex structure in effective type-I superconducting film with an antidot array 4.5 Weak pining centers: stability of pinned square and partially pinned vortex structures 4.6 The critical current of patterned superconducting films 4.6.1 Influence of the geometrical parameters 4.6.2 Temperature dependence of the critical current Contents iii 4.7 H − T phase diagram 97 4.8 Conclusions 99 5 Vortex-cavity interaction Summary 153 List of important realizations 157 Outlook 159 iv Contents Samenvatting 161 References 167 Curriculum Vitae 179 List of publications 181 1950s the materials that were developed for use as superconductors include: solid solutions of NbN and NbC with T c = 17.8 K; V 3 Si with T c = 17 K; Nb 3 Sn with T c =18 K; NbTi with T c =9 K. Later (1973) Nb 3 Ge was added to this list with the highest T c of all, at 23.2 K, a record that lasted until 1986. The history of the development of T c is shown in Fig. 1.1 [4]. MgB 2 superconductor. Superconductivity in MgB 2 was discovered as late as 2001 [5], with T c at 39 K, a record by far in ordinary metallic compounds. This value of T c is close to what has been considered the maximum possible by pairing caused by electron-phonon interaction. The main disadvantage of early MgB 2 samples is their low critical magnetic field H c2. But H c2 can be increased up to more than 40 T in bulk and up to near 60 T in oriented thin films by Carbon doping. Due to its enhanced mechanical properties, as compared to high-T c superconductors this material is expected to be very promising for applications. Organic superconductors. Superconductivity in a polymer material was first found in (Sn) x in 1975. This was followed by the discovery in 1979 of superconductivity in a molecular salt, (TMTSF) 2 FF 6 under 1.2 Gpa pressure, and with a T c of 0.9 K [6]. Since then, a long list of organic superconductors have been synthesized. T c of those materials remains low, although it has which leads to a temperature dependence of the GL parameter κ = κ(0)/(1+t 2) with t = T /T c0 and κ(0) = λ(0)/ξ(0), agrees better with experiment. 4πλ 2 c ∇ × j + h = zΦ 0 δ(r), (1.31) where z is a unit vector along the vortex and δ(r) a δ-function at the location of the core. Combining Eq. (1.31) with the Maxwell equation ∇ × h = 4π/cj The next configuration very close in energy consists of a square array of vortices (see Fig. 1.8). Here the nearest neighbor distance is given by a = (Φ 0 /H) 1/2. (1.41) Thus, for a given flux density in a homogeneous superconductor, a > a. Taking into account the repulsion of the vortices, it is reasonable that the vortex Consequently, the better the pinning the higher the critical current density J c. The upper limit for the critical current density is the depairing current density H c2 (T) = H c2 (0) |1 − T /T c0 | , (1.54) where H c2 (0) = c /2eξ(0) 2 and T c0 is the critical temperature at zero magnetic field. y +(1 − T) |Ψ j | 2 − 1 Ψ j +f j (t).
Multi-vortex versus interstitial vortices scenario in superconducting antidot arrays
Physica C: Superconductivity, 2010
In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing a 0 , antidot diameter d, lattice symmetry, orientation, etc) along with the characteristic length scales of the superconducting thin films, viz., the coherence length (ξ) and the penetration depth (λ). There are at least two competing scenarios: (i) multiple vortices sit on each of the antidots at a higher matching period, and, (ii) there is nucleation of vortices at the interstitial sites at higher matching periods. Furthermore it is also possible for the nucleated interstitial vortices to reorder under suitable conditions. We present our experimental results on NbN antidot arrays in the light of the above scenarios.
Journal of Applied Physics, 2010
Nb thin films containing a regular square array of antidots with 17 nm diameter and 50 nm spacing have been fabricated using a relatively simple lithographic process. The critical current density j c ͑H͒ curves, obtained here by electric transport measurements, exhibit commensurability effects with pronounced maxima just above the expected 0 H 1 = 0.830 T and 0 H 1/2 = 0.415 T matching fields, down to temperatures as low as 2.3 K. The behavior of j c ͑H͒ as well as the position of the maxima are consistent with the ones calculated in the framework of the time dependent Ginzburg-Landau model.
Vortex properties in superconducting Nb/Pd multilayers
Physical Review B, 1998
We have investigated the upper critical magnetic field H c2 , the critical current density J c , and the pinning force F p in sputtered Nb/Pd multilayers, varying the temperatures T, the Pd thicknesses d Pd and the magnetic field H orientation ͑parallel and perpendicular to the plane of the sample͒. In perpendicular fields, the vortex dynamics was strongly influenced by grain-boundary pinning. In parallel fields, a peak was observed in the J c (H) curves for samples with Pd thicknesses d Pd Ͼ100 Å. After comparing the experimental results with the existing theories, we have related the presence of this peak effect to the matching of vortex kinks with the layered artificial structure.
Flux pinning force in Nb thin films with periodic vortex pinning arrays
Journal of Applied Physics, 2002
Flux pinning force has been investigated in superconducting Nb thin films with square arrays of artificial flux pinning centers. These pinning centers due to the structural corrugation in the Nb thin film were created. In the mixed state, the magnetoresistance minima and critical current density maxima to be separated at constant field intervals corresponding to the matching fields were found. The temperature dependence of critical current density can be fitted to an expression (1 ϪT/T C 0) n near superconducting transition temperature. The n values at applied field equal matching fields (HϭH 1 ,H 2 ,H 3 ...) are 5/2, in contrast to 3/2 at half integer matching fields. It indicates that the dynamics of interstitial vortices at higher matching fields is similar to those at the first matching field. It can be believed that the collective flux pinning force stabilized by the vortices on pinning centers indirectly prevents interstitial vortices from flowing.
Physical Review B, 2006
Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter κ *. Giant-vortex states, combination of giant-and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antidot occupation number no is calculated as a function of related parameters and comparison with existing expressions for the saturation number ns and with experimental results is given. For a small radius of antidots a triangular vortex lattice is obtained, where some of the vortices are pinned by the antidots and some of them are located between them. Transition between the square pinned and triangular vortex lattices is given for different values of the applied field. The enhanced critical current at integer and rational matching fields is found, where the level of enhancement at given magnetic field directly depends on the vortex-occupation number of the antidots. For certain parameters of the antidot lattice and/or temperature the critical current is found to be larger for higher magnetic fields. Superconducting/normal H − T phase boundary exhibits different regimes as antidots are made larger, and we transit from a plain superconducting film to a thin-wire superconducting network. Presented results are in good agreement with available experiments and suggest possible new experiments.