Influence of artificial pinning on vortex lattice instability in superconducting films (original) (raw)
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Vortex Dynamics in Superconducting Films: Comensurability and Surface Effects
physica status solidi (a), 2001
The penetration and further evolution of stiff vortex lines in a superconducting film under a parallel magnetic field is numerically simulated. A square array of in-plane columnar defects is considered as a periodic pinning potential. It is shown that the strong surface effects play an important role in the commensurability between the vortex lattice and the pinning potential. The matching peaks of the magnetization curve are associated to a stable composite vortex lattice in which two distinc vortex lattices are commensurate with the pinning potential.
Pinning effects on the vortex critical velocity in type-II superconducting thin films
Physica C: Superconductivity, 2010
We study the influence of artificial pinning centers on the vortex critical velocity in Al thin films deposited on top of a periodic array of Permalloy (FeNi) square rings. We demonstrate that the field dependence of the flux flow velocity strongly depends on the particular magnetic state of the rings. In particular, we find that, even when the rings are in a flux closure state, i.e. with little stray field, the vortex critical velocity shows a non-monotonic magnetic field dependence. This behaviour is in sharp contrast with the results obtained in a reference plain film, with no rings underneath. A comparison with the intrinsic strong pinning Nb films previously studied, suggests an interpretation in terms of a channel-like motion of vortices, here induced by the artificial pinning structure.
We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the absence of an applied magnetic field. The resulting zero-temperature resistance derives from two equally possible mechanisms: 1) quantum tunneling of vortices from the edges of the sample; and 2) homogeneous quantum nucleation of vortex-antivortex pairs in the bulk of the sample, arising from the instability of the Magnus field's "vacuum". We study both situations in the case where quantum dissipation dominates over the inertia of the vortices. We find that the vortex tunneling and nucleation rates have a very rapid dependence on the current density driven through the sample. Accordingly, whilst normally the superconductor is essentially resistancefree, for the high current densities that can be reached in high-T c films a measurable resistance might develop. We show that edge-tunneling appears favoured, but the presence of pinning centres and of thermal fluctuations leads to an enhancement of the nucleation rates. In the case where a periodic pinning potential is artificially introduced in the sample, we show that current-oscillations will develop indicating an effect specific to the nucleation mechanism where the vortex pair-production rate, thus the resistance, becomes sensitive to the corrugation of the pinning substrate. In all situations, we give estimates for the observability of the studied phenomena.
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).
Non-linear Flux Flow Resistance of Type-II Superconducting Films
Journal of Superconductivity and Novel Magnetism, 2011
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Superconductor Science and Technology, 2014
Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current I c (H), magnetization M(H) and ac-susceptibility ac (H) in a broad temperature range. Due to the coherence length divergence at T c , a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to T c , wire network behaviour is only present in a very narrow temperature window close to T c. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.
Physical Review B, 2010
We measure current-voltage characteristics as function of magnetic field and temperature in Nb strips of different thickness and width. The instability voltage of the flux flow state related to the vortex critical velocity v * is studied and compared with the Larkin-Ovchinnikov theory. Beside the usual power-law dependence v * ≈ B −1/2 , in the low field range a new cross-over field, Bcr1, is observed below which v * decreases by further lowering the external magnetic field B. We ascribe this unexpected cross-over to vortex channeling due to a fan-like penetration of the applied magnetic field as confirmed by magneto-optic imaging. The observation of Bcr1 becomes a direct evidence of a general feature in type-II superconducting films at low fields, that is a channel-like vortex motion induced by the inhomogeneous magnetic state caused by the relatively strong pinning.
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.
Superconducting film with weak pinning centers: Incommensurate vortex lattices
Physical Review B, 2007
Vortex configurations in a superconducting film with a square array of small antidots are studied within the Ginzburg-Landau ͑GL͒ theory. We find that in addition to the conventional vortex structures at the matching fields, a variety of vortex states can be stabilized by decreasing the pinning strength of the antidots, including ͑i͒ the triangular vortex lattice where some vortices are pinned by the antidots and others are located between them, ͑ii͒ vortex line structures, and ͑iii͒ a lattice of vortex cluster structures around the empty pinning centers. Although these partially pinned vortex structures are obtained more frequently in field cooled experiments than the square pinned vortex lattice, they are not the lowest energy states, i.e., the ground state, contrary to the results from a London approach. This result can be understood as due to the presence of a broad local minimum in the GL free energy which keeps the vortices away from the pinning centers. Our results can also be related to recent experiments on macroscopic metallic particles that move in a plane in the presence of a weak electrostatic pinning potential.