We present a local probe study of the magnetic superconductor, ErNi$_2$B$_2$C, using magnetic force microscopy at sub-Kelvin temperatures. ErNi$_2$B$_2$C is an ideal system to explore the effects of concomitant superconductivity and ferromagnetism. At 500 mK, far below the transition to a weakly ferromagnetic state, we directly observe a structured magnetic background on the micrometer scale. We determine spatially resolved absolute values of the magnetic penetration depth $λ$ and study its temperature dependence as the system undergoes magnetic phase transitions from paramagnetic to antiferromagnetic, and to weak ferromagnetic, all within the superconducting regime. In addition, we estimate the absolute pinning force of Abrikosov vortices, which shows a position- and temperature dependence as well, and discuss the possibility of the purported spontaneous vortex formation.
Vortex penetration affects the stability of a superconducting system and limits the possible application of the system. However, the mathematical description to this phenomenon is currently unavailable. Here I present a mathematical model in which I consider the effects of bulk pinning and internal field repulsive force on vortex hopping. Thereafter, I proposed a series expansion to the activation energy and derived a general formula for describing the time dependence of the vortex penetration process. With these formulas, I can analyze the experimental data and calculate the activation energy…
The information about the current-carrying ability of a type-II superconductor can be obtained by studying the flux relaxation and vortex penetration phenomena in the superconductor. In early studies, the infinite series models of the flux relaxation and vortex penetration phenomena were constructed at a vanishing current density and vanishing internal field, respectively. However, this is not the only possibility. Here it is shown that one can reconstruct the theoretical models at the critical points. The new polynomial model of the flux relaxation (vortex penetration) phenomenon was construc…
The temperature and field dependence of the effective magnetic penetration depth in the vortex state of a d-wave superconductor, as measured by muon spin rotation experiments, is calculated using a nonlocal London model. We show that at temperatures below T^* \propto \sqrt{B}, the linear T-dependence of the effective penetration depth crosses over to a T^3-dependence. This could provide an explanation for the low temperature flattening of the effective penetration depth curves observed in a recent muon spin rotation experiment.
We use a magnetic force microscope (MFM) to investigate single vortex pinning and penetration depth in NdFeAsO$_{1-x}$F$_x$, one of the highest-$T_c$ iron-based superconductors. In fields up to 20 Gauss, we observe a disordered vortex arrangement, implying that the pinning forces are stronger than the vortex-vortex interactions. We measure the typical force to depin a single vortex, $F_{\mathrm{depin}} \simeq 4.5$ pN, corresponding to a critical current up to $J_c \simeq 7 \times 10^5$ A/cm$^2$. Furthermore, our MFM measurements allow the first local and absolute determination of the supercond…
A variational calculation for vortex penetration is presented. Variational trial functions for the Meissner state are combined with variational functions for a vortex near the surface. The latter is based on Clem's trial solutions for a vortex in bulk, which were adapted to include surface effects through consideration of an image vortex. Three variational parameters are considered, corresponding to the effective coherence length of the vortex, the effective penetration length for the Meissner currents, and the value of the order parameter at the surface. The results show that the last two var…
We report measurements of the magnetic penetration depth λ_m(T) in the presence of a DC magnetic field in optimally doped BSCCO-2212 single crystals. Warming, after magnetic field is applied to a zero-field cooled sample, results in a non-monotonic λ_m(T), which does not coincide with a curve obtained upon field cooling, thus exhibiting a hysteretic behaviour. We discuss the possible relation of our results to the vortex decoupling, unbinding, and dimensional crossover.
We consider nonlinear dynamics of a single vortex in a superconductor in a strong rf magnetic field $B_0\sinωt$. Using the London theory, we calculate the dissipated power $Q(B_0,ω)$, and the transient time scales of vortex motion for the linear Bardeen-Stephen viscous drag force, which results in unphysically high vortex velocities during vortex penetration through the oscillating surface barrier. It is shown that penetration of a single vortex through the ac surface barrier always involves penetration of an antivortex and the subsequent annihilation of the vortex antivortex pairs. Using the …
We study the penetration field $H_{\rm P}$ for vortex nanocrystals nucleated in micron-sized samples with edges aligned along the nodal and anti-nodal directions of the d-wave superconducting parameter of Bi$_2$Sr$_2$CaCu$_2$O$_{8 - δ}$. Here we present evidence that the $H_{\rm P}$ for nanocrystals nucleated in samples with edges parallel to the nodal direction is larger than for the antinodal case, $\sim 72$\,\% at low temperatures. This finding supports the theoretical proposal that surface Andreev bound states appearing in a sample with edges parallel to the nodal direction would produce a…
Vortex penetration and flux relaxation phenomenon carry the information about the pinning ability, and consequently current-carrying ability, of a type-II superconductor. However, the theoretical descriptions to these phenomena are currently limited to the cases with special initial conditions. A generalization to the recently developed infinite series models is presented here. It is shown that one can convert a vortex penetration process with a non-zero initial internal field into a process with a zero initial internal field by introducing some time parameters. Similarly, one can also convert…
We investigate how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors using self-consistent Bogoliubov-de Gennes equations. We find that the entrance of the vortex happens when the current density at the hot spots reaches the depairing current density. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconduc…
The penetration depth l_j in superconducting junctions is identified within the Ginzburg-Landau theory as a function of the interfacial pair breaking, of the magnetic field and of the Josephson coupling strength. When the interfacial pair breaking goes up, l_j increases and an applicability of the local Josephson electrodynamics to junctions with a strong Josephson coupling is extended. In the junctions with strongly anharmonic current-phase relations, the magnetic field dependence of l_j is shown to lead to a significant difference between the weak-field penetration depth and the characterist…
Muon-spin rotation spectroscopy has been used to measure the internal magnetic field distribution in NbSe2 for Hc1 << H < 0.25 Hc2. The deduced profiles of the supercurrent density indicate that the vortex-core radius in the bulk decreases sharply with increasing magnetic field. This effect, which is attributed to increased vortex-vortex interactions, does not agree with the dirty-limit microscopic theory. A simple phenomenological equation in which the core radius depends on the intervortex spacing is used to model this behaviour. In addition, we find for the first time that the in-plane magn…
Analytical formula to evaluate the vortex-penetration field at a groove with a depth smaller than penetration depth is derived, which can be applied to surfaces of cavities or test pieces made from extreme type II superconductors such as nitrogen-doped Nb or alternative materials like Nb3Sn or NbN.
Applying the London theory we study curved vortices produced by an external current near and parallel to the surface of a type II superconductor. By minimizing the energy functional we find the contour describing the hard core of the flux line, and predict the threshold current for entrance of the first vortex. We assume that the vortex entrance is allowed due to surface defects, despite the Bean-Livingston barrier. Compared to the usual situation with a homogeneous magnetic field, the main effect of the present geometry is that larger magnetic fields can be applied locally before vortices ent…
The equations of viscous evolution of 3D arbitrarily shaped vortices in an isotropic type II superconductor and necessary boundary conditions are formulated in the frame of London approximation. The theory is applied to analyse characteristic scenaria of vortex penetration into current-carrying thick plate or bulk samples with another geometry. It is shown that regarding of the surface transport current value a vortex penetrates either as "flexible stick" or as "elastic thread". The latter regime is accompanied by giant stretching of the vortex core along the current-induced surface magnetic f…
We report on muon spin rotation measurements of the internal magnetic field distribution n(B) in the vortex solid phase of YBa2Cu3Oy (YBCO) single crystals, from which we have simultaneously determined the hole doping dependences of the in-plane Ginzburg-Landau (GL) length scales in the underdoped regime. We find that Tc has a sublinear dependence on 1/lambda_{ab}^2, where lambda_{ab} is the in-plane magnetic penetration depth in the extrapolated limits T -> 0 and H -> 0. The power coefficient of the sublinear dependence is close to that determined in severely underdoped YBCO thin films, indic…
The vortex penetration field of the multilayer coating model with a single superconductor layer and a single insulator layer formed on a bulk superconductor are derived. The same formula can be applied to a model with a superconductor layer formed on a bulk superconductor without an insulator layer.
We report our results on vortex penetration in two realizations of heterogeneos magneto-superconducting systems (HMSS) based on London approach; semi-infinite ferromagnetic(FM)-superconducting(SC) bilayers and a FM dot on a semi-infinite SC film. In the first case, we study quantitatively the vortex entry in FM-SC bilayers which manifests Bean-Livingston-like vortex barrier, controlled by FM film's magnetization $m$ and SC film's Ginzburg parameter $κ$. In the second case, we investigate the conditions for sponteneous vortex creation and determine the position of vortex for various values of m…
A single vortex overcoming the surface barrier in a mesoscopic superconductor with lateral dimensions of several coherence lengths and thickness of several nanometers provides an ideal platform to study thermal activation of a single vortex. In the presence of thermal fluctuations, there is non-zero probability for vortex penetration into or exclusion from the superconductor even when the surface barrier does not vanish. We consider the thermal activation of a single vortex in a mesoscopic superconducting disk of circular shape. To obtain statistics for the penetration and exclusion magnetic f…
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…
In order to compare magnetic and non-magnetic pinning we have nanostructured two superconducting films with regular arrays of pinning centers: Cu (non-magnetic) dots in one case, and Py (magnetic) dots in the other. For low applied magnetic fields, when all the vortices are pinned in the artificial inclusions, magnetic dots prove to be better pinning centers, as has been generally accepted. Unexpectedly, when the magnetic field is increased and interstitial vortices appear, the results are very different: we show how the stray field generated by the magnetic dots can produce an effective reduc…
The dependence of the vortex penetration and expulsion on the geometry of mesoscopic superconductors is reported. Hall magnetometry measurements were performed on a superconducting Al square and triangle. The stability of the vortex patterns imposed by the sample geometry is discussed. The field-temperature $H-T$ diagram has been reconstructed showing the transitions between states with different vorticity. We have found that the vortex penetration is only weakly affected by the vortex configuration inside the sample while the expulsion is strongly controlled by the stability of the vortex pat…
We argue that odd-frequency triplet superconductivity can be conveniently realized in hybrid superconductor-ferromagnet (SF) structures with a ferromagnetic vortex. We demonstrate that due to proximity-induced long-range triplet pairing such SFS junctions can sustain appreciable supercurrent which can be directly measured in experiments.
As first pointed out by Bardeen and Ginzburg in the early sixties, the amount of magnetic flux carried by vortices depends on their distance to the sample edge and can be smaller than one flux quantum, f0 = h/2e. In bulk superconductors, this reduction of flux becomes negligible already at submicron distances from the edge but, in thin films, the effect may survive at much larger distances. In the absence of any experimental observation, such flux reduction is perceived to be an exotic or unimportant effect, and it is often assumed that magnetic field enters type-II superconductors in units of…
Using an expansion of the order parameter over the eigenfunctions of the linearized first Ginzburg-Landau (GL) equation, we obtain numerically the saddle points of the free energy separating the stable states with different number of vortices. In contrast to known surface and geometrical barrier models, we find that in a wide range of magnetic fields below the penetration field, the saddle point state for flux penetration into a disk does not correspond to a vortex located nearby the sample boundary, but to a region of suppressed superconductivity at the disk edge with no winding of the curren…
We report on a microscopic evaluation of electrodynamic response for the vortex lattice state of a model s-wave superconductor. Our calculation accounts self-consistently for both quasiparticle and order parameter response and establishes the collective nature of linear response in the clean limit. We discuss the effects of homogeneous and inhomogeneous pinning on the optical conductivity and the penetration depth, and comment on the relationship between macroscopic and local penetration depths. We find unexpected relationships between pinning arrangements and conductivity due to the strongly …
We have measured the surface impedance of thick superconductors in the mixed state over a broad 2 kHz - 20 MHz frequency range. The depinning cross-over is observed; but it is much broader than expected from classical theories of pinning. A striking result is the existence of size effects which invalidate the common interpretation of the low-frequency surface inductance in terms of a single penetration depth. Instead, a two-mode description of vortex dynamics, assuming free vortex flow in the bulk and surface pinning, accounts quantitatively for the spectrum of the complex apparent penetration…
By means of small magnetic field ac susceptibility measurement at 10 kHz we found that the real and imaginary parts of ceramic $YBa_2Cu_3O_ x$ susceptibility in presence of the external low frequency field close to 0.1 Hz exhibit frequency dependence. The wide maximum of hysteresis losses and {\color{black} the exponential dependence} of the {\color{black} effectiveness of flux penetration} with increasing of external field frequency were obtained. We observed a nonlinear dynamic magnetic response in presence dc field and we suggest that this behavior is due to the dynamic and static Josephson…
Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ defining a…
It is shown that attempts to accurately deduce the magnetic penetration depth of overdoped BaFe_{1.82}Co_{0.18}As2 single crystals by transverse-field muon spin rotation (TF-muSR) are thwarted by field-induced magnetic order and strong vortex-lattice disorder. We explain how substantial deviations from the magnetic field distribution of a nearly perfect vortex lattice by one or both of these factors is also significant for other iron-based superconductors, and this introduces considerable uncertainty in the values of the magnetic penetration depth obtained by TF-muSR.
The internal field distribution in the vortex state of YBa2Cu3O6.60 is shown to be a sensitive measure of both the magnetic penetration depth and the vortex-core radius. The temperature dependence of the vortex core radius is found to be weaker than in the conventional superconductor NbSe2 and much weaker than theoretical predictions for an isolated vortex. The effective vortex-core radius decreases sharply with increasing H, whereas the penetration depth is found to be much stronger than in NbSe2.
I apply the recently developed formalism of generalized quasiclassical theory to show that using hybrid superconducting systems with non-collinear strong ferromagnets one can realize the Josephson junction between Berezinskii-type superconductors. The reported calculation reproduces main features observed in the recent experiment, namely the the slightly asymmetric double-slit Fraunhofer interference pattern of the Josephson current through the ferromagnetic vortex. The double-slit structure results from the spatially inhomogeneous Berezinskii state with the amplitude controlled by the local a…
We have developed the quasi-classical formalism for a self-induced vortex state in ferromagnetic superconductors. By combining the spatially averaged approximation of the superconductivity with the phenomenological form of the ferromagnetism, we demonstrate the thermodynamic properties of the p-wave triplet equal-spin-pairing state with the spontaneous vortex lattice. The occurrence condition for the self-induced vortex state is discussed within this formalism. The comparison of the calculated quantities with the observed ones indicates that the self-induced vortex state indeed occurs in UCoGe…
We report transverse field and zero field muon spin rotation studies of the superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse field measurements (H=0.007 T) show line broadening below Tc, which is characteristic of a vortex state, demonstrating conclusively the type-II nature of this superconductor. The penetration depth is seen to level off below about 400 mK (T/Tc~0.4), with a rather large value of lambda (T=0)~7500A. The temperature independent behavior below ~ 400 mK is consistent with a nodeless superconducting energy gap. Zero-field measurements indicate no static magnetic f…
The current distribution and the AC loss in a composite superconducting tape containing a layer from magnetic material is calculated and compared with experiments, showing a very good agreement. The situations of an alternating uniform applied field or a transport current are studied. The newly developed numerical model is an approximation to the critical state model, adapted for the applicability to commercial finite elements codes that solve the vector potential. Substantial feature of this procedure is that it can be carried out in the case when the critical current density in superconducto…
Using differential magneto-optical imaging, we address the question of mesoscopic inhomogeneity in underdoped Bi-2212 single crystals. Among other features, it is shown that an anomalous temperature dependence of the penetration field and of the first order transition (FOT) field of the vortex lattice in such crystals can be understood as arising from inhomogeneity. The effect of chemical inhomogeneity and pinning on flux penetration and the FOT is discussed.
The vortex contribution to the dc field (H) dependent microwave surface impedance Z_s = R_s+iX_s of YBa_2Cu_3O_{7-x} thin films was measured using suspended patterned resonators. Z_s(H) is shown to be a direct measure of the flux density B(H) enabling a very precise test of models of flux penetration. Three regimes of field-dependent behavior were observed: (1) Initial flux penetration occurs on very low field scales H_i(4.2K) 100Oe, (2) At moderate fields the flux penetration into the virgin state is in excellent agreement with calculations based upon the field-induced Bean critical state for…
We investigate numerically the local density of states (LDOS) in the vicinity of a vortex core in a ferromagnetic superconductor. Specifically, we investigate how the LDOS is affected by the relative weight of the spin bands in terms of the superconducting pairing, and we also examine the effect of different pairing symmetries for the superconducting order parameter. Our findings are directly related to scanning tunneling microscopy measurements and may thus be highly useful to clarify details of the superconducting pairing in recently discovered ferromagnetic superconductors.
Observation of individual vortex penetration in a coplanar superconducting resonator
The University of Tokyo（东京大学）；University of Connecticut（康涅狄格大学）；University of Arizona（亚利桑那大学）；Institute of Science Tokyo（东京科学大学）；National Institute for Materials Science（物质材料研究机构）
We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner state, with boundary conditions appropriate for this geometry. Using the Monte Carlo Simulated Annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed state provides express…
A multilayered structure with a single superconductor layer and a single insulator layer formed on a bulk superconductor is studied. General formulae for the vortex-penetration field of the superconductor layer and the magnetic field on the bulk superconductor, which is shielded by the superconductor and insulator layers, are derived with a rigorous calculation of the magnetic field attenuation in the multilayered structure. The achievable peak surface field depends on the thickness and its material of the superconductor layer, the thickness of the insulator layer and material of the bulk supe…
A spontaneous vortex state (SVS) between 30 K and 56 K was observed for the weak-ferromagnetic superconductor RuSr2GdCu2O8 with ferromagnetic Curie temperature TC = 131 K and superconducting transition temperature Tc = 56 K. The low field (20 G) Superconducting hysteresis loop indicates a narrow Meissner state region within average lower critical field Bc1(T)= Bc1(0)[1 - (T/T0)2], with average Bave c1 (0) = 12 G and T0 = 30 K. Full Meissner shielding signal in very low applied field indicates an ab-plane Bab c1(0) ~ 4 G with an estimated anisotropic parameter g ~ 7 for this layered system. The…
The coexistence of weak ferromagnetism and superconductivity in ErNi$_{2}$B$% _{2}$C suggests the possibility of a spontaneous vortex phase (SVP) in which vortices appear in the absence of an external field. We report evidence for the long-sought SVP from the in-plane magnetic penetration depth $Δλ(T)$ of high-quality single crystals of ErNi$_{2}$B$_{2}$C. In addition to expected features at the Néel temperature $T_{N}$ = 6.0 K and weak ferromagnetic onset at $T_{WFM}=2.3 $K, $Δλ(T)$ rises to a maximum at $T_{m}=0.45$ K before dropping sharply down to $\sim $0.1 K. We assign the 0.45 K-maximum…
Measurements of the rf penetration depth λ(T,H,θ) are used to study the superconducting order parameter, vortex dynamics in the mixed state and delineate critical fields in the borocarbide superconductor YNi_2B_2C. The lower critical field has an anomalous T dependence, H_{c1}(T)=1.12[1-(T/T_c)] kOe, which is however consistent with independent superfluid density measurements at microwave frequencies. The vortex response is dominated by viscous flux flow, indicative of extremely weak pinning, and is parametrized by a field scale H_{c2,eff}. The angular dependence of the vortex contribution λ(θ…
The conformal mapping method is used to study the problem of flux line interaction with surface cavities having cylindrical profile and characteristic size much less than the penetration length, i.e, within mesoscopic scale. It is shown that the metastable states are achieved when the dimensions of the surface irregularities do not exceed the coherence length. Our study shows that the surface barrier may vanished at some weak point at which the surface irregularities have mesoscopic scales. On the other hand, the surface barrier is completely disappeared when the surface defects size is more g…
Application of a tunnel-diode resonator (TDR) technique for studies of the vortex response in magnetic superconductors is described. Operating at very small excitation fields and sufficiently high frequency, TDR was used to probe small-amplitude linear AC response in several types of single crystals where long-range magnetic order coexists with bulk superconductivity. Full local - moment ferromagnetism destroys superconductivity and can coexist with it only in a narrow temperature range ($\sim 0.3$ K). In contrast, weak ferromagnetic as well as antiferromagnetic orders can coexist with bulk su…
A true critical current density, $j_{c}$, as opposite to commonly measured relaxed persistent (Bean) current, $j_{B}$, was extracted from the Campbell penetration depth, $λ_{C}(T,H)$ measured in single crystals of LiFeAs. The effective pinning potential is non-parabolic, which follows from the magnetic field - dependent Labusch parameter $α$. At the equilibrium (upon field - cooling), $α(H)$ is non-monotonic, but it is monotonic at a finite gradient of the vortex density. This behavior leads to a faster magnetic relaxation at the lower fields and provides a natural \emph{dynamic} explanation f…
Strong pinning of superconducting flux quanta by a square array of 1 $μ$m-sized ferromagnetic dots in a magnetic-vortex state was visualized by low-temperature magnetic force microscopy (LT-MFM). A direct correlation of the superconducting flux lines with the positions of the dots was derived. The force that the MFM tip exerts on the individual vortex in the depinning process was used to estimate the spatial modulation of the pinning potential. It was found, that the superconducting vortices which are preferably located on top of the Py dots experience about 15 times stronger pinning forces as…
The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness and different geometries of the magnetic structures: disk, annulus(ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex positi…
We study the proximity effect in a ferromagnetic nanoparticle having a vortex magnetization pattern. We show that for axisymmetric system consisting of a circular particle and a magnetic vortex situated at the center of it no long range superconducting correlations are induced. It means that induced superconductivity is localized in the small area near the superconducting electrode. However, in the real systems axial symmetry can be broken by either a shift of the magnetic vortex from the origin or geometrical anisotropy of the ferromagnetic particle. In this case a long range proximity effect…
We demonstrate that there is a long-range vortex-vortex attraction in ferromagnetic superconductors due to polarization of the magnetic moments. Vortex clusters are then stabilized in the ground state for low vortex densities. The motion of vortex clusters driven by the Lorentz force excites magnons. This regime becomes unstable at a threshold velocity above which domain walls are generated for slow relaxation of the magnetic moments and the vortex configuration becomes modulated. This dynamics of vortices and magnetic moments can be probed by transport measurements.
Magnetic penetration depth, $λ_{m}$, was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, $λ_{L}\left(T\right)$, but in the applied field the signal includes the Campbell penetration depth, $λ_{C}\left(T\right)$, which is the characteristic length of the attenuation of small excitation field, $H_{ac}$, into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent $λ_C$ exhibit …
The experimental study of magnetic flux penetration under crossed magnetic fields in Bi2212:Pb single crystal performed by magnetooptic technique (MO) reveals remarkable field penetration pattern alteration (flux configuration change) and superconducting current anisotropy enhancement by the in-plane field. The anisotropy increases with the temperature rise up to $T_m = 54 \pm 2 K$. At $T = T_m$ an abrupt change in the flux behavior is found; the correlation between the in-plane magnetic field and the out-of-plane magnetic flux penetration disappears. No correlation is observed for $T > T_m$. …
Measurements of the first-flux-penetration field in surface-treated and coated Nb: Distinguishing between surface pinning and an interface energy barrier
Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.
We study the effect of the superconducting gap nodes on the vortex lattice properties of high temperature superconductors at very low temperatures. The nonlinear, nonlocal and nonanalytic nature of this effect is shown to have measurable consequences for the vortex lattice geometry and the effective penetration depth in the mixed state as measured by muon-spin-rotation experiments.
Using low-temperature Magnetic Force Microscopy (MFM) we provide direct experimental evidence for spontaneous vortex phase (SVP) formation in EuFe$_2$(As$_{0.79}$P$_{0.21}$)$_2$ single crystal with the superconducting $T^{\rm 0}_{\rm SC}=23.6$~K and ferromagnetic $T_{\rm FM}\sim17.7$~K transition temperatures. Spontaneous vortex-antivortex (V-AV) pairs are imaged in the vicinity of $T_{\rm FM}$. Also, upon cooling cycle near $T_{\rm FM}$ we observe the first-order transition from the short period domain structure, which appears in the Meissner state, into the long period domain structure with …
