Direct visualization of the vortex distributions in a superconducting film with a Penrose array of magnetic pinning centers: Symmetry induced giant vortex state

Using scanning Hall probe microscopy a direct visualization of the flux distribution in a Pb film covering a fivefold Penrose array of Co dots is obtained. We demonstrate that stable vortex configurations can be found for fields H ∼ 0.8H₁, H₁ and 1.6H₁, where H₁ corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H₁ corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H₁ the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H = 1.6H₁ interstitial and pinned vortices arrange themselves in ring-like structures (“vortex corrals”) which favor the formation of a giant vortex state at their center.     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Effects of binder addition on the mechanical properties of bulk Y–Ba–Cu–O superconductors

We studied the effects of binder addition on the mechanical properties of bulk Y–Ba–Cu–O superconductors. We prepared YBa₂Cu₃O_y, Y₂BaCuO₅ powders and polyvinyl alcohol mixed with water as a binder. These raw materials were mixed, and the binder-added powders were pressed into pellets. The hardness of the green compacts with binder is higher than that without the binder. However, the hardness of green compacts with 8% binder is the same as that with 4% binder. The maximum compression strength of the precursor with binder is higher than that without binder. Equally, the maximum strength of the green compacts with 8% binder is higher than that with 4% binder. The differential thermal analysis measurements showed that the exothermic reaction due to the decomposition of the organic binder started at 550 °C and gradually proceeded with further heating. After de-binder treatment, BaCO₃ powders were produced on the green compacts. The green compacts were subjected to melt-processing. We also measured trapped magnetic fields of binder-added bulk Y–Ba–Cu–O superconductors with a Hall probe scanning device. Trapped magnetic field of the bulk added with 4% is higher than that of the binder-free bulk. Hence, Y–Ba–Cu–O bulk with suitable amount of binder shows good influence for mechanical strength and trapped magnetic field.     

Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids

The formation of vortex–antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg–Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex–antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex–antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex–antivortex molecules found in mesoscopic superconductors.     

Magnetoelectric coupling in multiferroic heterostructure of rf-sputtered Ni–Mn–Ga thin film on PMN–PT

In this paper, we report a preparation of multiferroic heterostructure from thin film of Ni–Mn–Ga (NMG) alloy and lead magnesium niobate–lead titanate (PMN–PT) with effective magnetoelectric (ME) coupling between the film as ferromagnetic material and PMN–PT as piezoelectric material. The heterostructure was prepared by relatively low temperature (400 °C) deposition of the film on single crystal of piezoelectric PMN–PT substrate using rf magnetron co-sputtering of Ni₅₀Mn₅₀ and Ni₅₀Ga₅₀ targets. Magnetic measurements by Superconducting Quantum Interference Design (SQIUD) Magnetometer and Vibrating Sample Magnetometer (VSM) on the film revealed that the film is in ferromagnetically ordered martensitic state at room temperature with saturation magnetization of ∼240 emu/cm³ and Curie temperature of ∼337 K. Piezoresponse force microscopy (PFM) measurement done at room temperature on the substrate showed the presence of expected hysteresis loop confirming the stability of the piezoelectric state of the substrate after deposition. Room temperature ME voltage coefficient (α_ME) of the heterostructure was measured as a function of applied bias dc magnetic field in Longitudinal–Transverse (L–T) ME coupling mode by lock-in technique. A maximum ME coefficient α_ME of 3.02 mV/cm Oe was measured for multiferroic NMG/PMN–PT heterostructure which demonstrates that there is ME coupling between the film as ferromagnetic material and PMN–PT as piezoelectric material.     

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.     

Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.     

Anomalous Hall effect in the mixed state of high-temperature superconductors

The Hall effect in the mixed state of high-T_c superconductors (HTSC) is of an anomalous nature: near the transition there is a range of temperatures and of magnetic fields where the sign of the Hall effect is opposite to that in the normal state. The universality of the phenomenon in question is indicative of its connection with some general properties of the mixed state of type-II superconductors, namely, with peculiarities of motion of magnetic flux vortex lines (vortices) in these superconductors. This work puts forward a model accounting for a number of vortex motion specific features and providing a possibility to obtain the characteristics of the anomalous Hall effect.

The work is based on the phenomenologically generalized results of Bardeen-Stephen and Nozieres-Vinen, supplemented with an allowance for a new mechanism of vortex “friction” associated with Andreev electron reflection on the interface between the normal core and the superconducting periphery of a vortex. Within the framework of the model suggested, magnetic field (and temperature) dependences of the longitudinal and Hall resistances of a mixed state superconductor have been calculated at temperatures nearing T_c. At certain quite realistic parameters which define the forces acting on the vortices, there is a range of magnetic fields and temperatures where the sign of the Hall effect is opposite to that in the normal state. The lower limit of this range is the irreversibility line and the upper critical field.     

Doping dependence of Meissner effect in cuprate superconductors

Within the t–t′–J model, the doping dependence of the Meissner effect in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. Following the linear response theory, it is shown that the electromagnetic response consists of two parts, the diamagnetic current and the paramagnetic current, which exactly cancels the diamagnetic term in the normal state, and then the Meissner effect is obtained for all the temperature T ? T_c throughout the superconducting dome. By considering the two-dimensional geometry of cuprate superconductors within the specular reflection model, the main features of the doping and temperature dependence of the local magnetic field profile, the magnetic field penetration depth, and the superfluid density observed on cuprate superconductors are well reproduced. In particular, it is shown that in analogy to the domelike shape of the doping dependent superconducting transition temperature, the maximal superfluid density occurs around the critical doping δ ≈ 0.195, and then decreases in both lower doped and higher doped regimes.     

Physical processes in high-temperature superconductors at the interface between the vortex-filled and meissner regions

A technique has been proposed for investigating the magnetic microstate of high-temperature superconductors with a simultaneous analysis of the crystalline microstate of the sample with the aim of elucidating the specific features of the interaction between the crystalline and magnetic microstructures of polycrystalline high-temperature superconductors. Qualitatively new results have been obtained for samples with different microstructures. In particular, it has been found that the magnetic field dependences of the trapped magnetic flux density B _tr(H ₀) of polycrystalline and epitaxial films of high-temperature superconductors exhibit regular steps for both increasing and decreasing magnetic fields. The obtained results have demonstrated that, in strong magnetic fields, the studied epitaxial films, as well as bulk and thin-film polycrystalline high-temperature superconductors, “break down” into single domains, crystallites, and subcrystallites with different demagnetization factors. It has been revealed that the dependences B _tr(H ₀) also exhibit steps due to the simultaneous penetration of vortices into crystallites of approximately the same sizes and into more regularly arranged subcrystallites. As the quality of the samples increases, these steps become more pronounced because of the increase in the short-range order. The absence of steps in the dependence B _tr(H ₀) of the polycrystalline bulk samples clearly demonstrates the absence of long-range order in these samples. It is the vitreousness of the crystallographic microstructure of high-temperature superconductors which is responsible for the observed transformations in the vortex system. The similarity of the results obtained for samples with different microstructures indicates that the penetration (escape), distribution, and trapping of the magnetic flux in these samples occur through a universal mechanism. It has been found that the polycrystalline high-temperature superconductors are actually multi-step rather than two-step systems. It has been shown that the vitreousness of the microstructure of high-temperature superconductors and the presence of close-packed twin boundaries in samples lead to the penetration of a magnetic flux in the form of hypervortices into the sample and cause the formation of a superconducting glass state on a different physical basis as compared to the Ebner-Stroud model of a granulated glass.     

Electron magnetic chiral dichroism in CrO2 thin films using monochromatic probe illumination in a transmission electron microscope

Electron magnetic chiral dichroism (EMCD) has been studied in CrO₂ thin films (with (100) and (110) growth orientations on TiO₂ substrates) using a gun monochromator in an aberration corrected transmission electron microscope operating at 300 kV. Excellent signal-to-noise ratio is obtained at spatial resolution ∼10 nm using a monochromatic probe as compared to conventional parallel illumination, large area convergent beam electron diffraction and scanning transmission electron microscopy techniques of EMCD. Relatively rapid exposure using mono probe illumination enables collection of EMCD spectra in total of 8–9 min in energy filtered imaging mode for a given Cr L_2,3 energy scan (energy range ∼35 eV). We compared the EMCD signal obtained by extracting the Cr L_2,3 spectra under three beam diffraction geometry of two different reciprocal vectors (namely g=110 and 200) and found that the g=200 vector enables acquisition of excellent EMCD signal from relatively thicker specimen area due to the associated larger extinction distance. Orbital to spin moment ratio has been calculated using EMCD sum rules for 3d elements and dichroic spectral features associated with CrO₂ are compared and discussed with XMCD theoretical spectra.     

I–V characteristics and critical currents in superconducting/ferromagnetic bilayers

Current–voltage (I–V) characteristics and critical current density, J_c, for the onset of vortex motion were measured at different magnetic fields, H, and temperatures, T, in a superconducting (S)/ferromagnetic (F) bilayer and in a single Nb film. We choose Nb as a superconductor and a weak ferromagnetic alloy, Pd_1−xNi_x with x = 16, as F. We found that J_c was smaller for the S/F bilayer with respect to the single Nb film. The result was related to the reduced value of the superconducting order parameter in the bilayer.     

B and Pt NMR study of the superconductors Li2(Pd1−xPtx)3B without inversion symmetry

We report the ¹¹B and ¹⁹⁵Pt NMR measurements in non-centrosymmetric superconductors Li₂(Pd_1−xPt_x)₃B (x = 0.0, 0.2, 0.5, 1.0). From the measurements of spin–lattice relaxation time (T₁), we found that there was a coherence peak (CP) just below superconducting transition temperature (T_c) for x = 0–0.5 but no CP in x = 1. We demonstrated that the system for x = 0–0.5 were BCS superconductors but there existed line node in the superconducting gap for x = 1.0. The ¹⁹⁵Pt Knight Shift in x = 0.2 decreased below T_c, indicating spin-singlet state. The results showed that BCS superconducting state evolves into an exotic state with line-nodes in the gap function when x is increased, as the spin–orbit coupling is enhanced.     

Behavior of the irreversibility line in the new superconductor La1.5+xBa1.5+x−yCayCu3Oz

The irreversibility properties of high-T_c superconductors are of major importance for technological applications. For example, a high irreversibility magnetic field is a more desirable quality for a superconductor [1]. The irreversibility line in the H–T plane is constituted by experimental points, which divides the irreversible and reversible behavior of the magnetization. The irreversibility lines for series of La_1.5+xBa_1.5+x−yCa_yCu₃O_z polycrystalline samples with different doping were investigated. The samples were synthesized using the usual solid estate reaction method. Rietveld-type refinement of x-ray diffraction patterns permitted to determine the crystallization of material in a tetragonal structure. Curves of magnetization ZFC–FC for the system La_1.5+xBa_1.5+x−yCa_yCu₃O_z, were measured in magnetic fields of the 10–20,000 Oe, and allowed to obtain the values for the irreversibility and critical temperatures. The data of irreversibility temperature allowed demarcating the irreversibility line, T_irr(H). Two main lines are used for the interpretation of the irreversibility line: one of those which suppose that the vortexes are activated thermally and the other proposes that associated to T_irr a phase transition occurs. The irreversibility line is described by a power law. The obtained results allow concluding that in the system La_1.5+xBa_1.5+x−yCa_yCu₃O_z a characteristic bend of the Almeida–Thouless (AT) tendency is dominant for low fields and a bend Gabay–Toulouse (GT) behavior for high magnetic fields. This feature of the irreversibility line has been reported as a characteristic of granular superconductors and it corroborates the topological effects of vortexes mentioned by several authors 1 and 2.     

Vortex configurations on a thin superconducting spherical shell in the presence of a magnetic dipole

In this work we study vortex configurations on a thin superconducting spherical shell of radius R and thickness d  (R?d?ξ)$(R?d?\xi )$ with a magnetic dipole inside it. The point magnetic dipole (with magnetic moment, m_z$m_z$) is oriented along one of the sphere main axis. It is placed a distance z₀$z_0$ from the center of the sphere. Due to the symmetry of the sample, there are vortices and antivortices pancakes on the shell resulting in zero total vorticity. The vortex interactions with the shielding currents produced by the external fields – as well as with other vortices – are calculated within the London limit. The vortex configurations are obtained by solving numerically the Bardeen–Stephen equation of motion for the vortices. For z₀≈0$z_0\approx 0$ the most frequent vortex configurations present equal arrangements of vortices and antivortices on the north and south hemispheres. For z₀≈0.5R$z_0\approx 0.5R$, the diversity of vortex configurations increases, with a higher number of configurations (in comparison to smaller z₀$z_0$) having different vortices and antivortices distributions on each shell hemisphere. We also study the equilibrium states dependence on the magnetic dipole strength and position.     

Hard disk magnetic domain nano-spatial resolution imaging by using a near-field scanning microwave microscope with an AFM probe tip

A near-field scanning microwave microscope (NSMM) incorporating an atomic force microscope (AFM) probe tip was used for the direct imaging of magnetic domains of a hard disk under an external magnetic field. We directly imaged the magnetic domain changes by measuring the change of reflection coefficient S₁₁ of the NSMM at an operating frequency near 4.4 GHz. Comparison was made to the magnetic force microscope (MFM) image. Using the AFM probe tip coupled to the tuning fork distance control system enabled nano-spatial resolution. The NSMM incorporating an AFM tip offers a reliable means for quantitative measurement of magnetic domains with nano-scale resolution and high sensitivity.     

Vortex oscillations in TFA-grown YBCO thin-films with BZO nanoparticles

An ac susceptibility methodology has been applied to investigate the vortex dynamics of YBa₂Cu₃O_7−x–BaZrO₃ nanocomposites grown by the chemical solution deposition TFA route, close to the irreversibility line. By analysing the linear, non-dissipative Campbell regime at low ac fields, we determined the temperature and field dependence of the restoring pinning constant, α_L(H_dc, T), characterising the harmonic oscillation of vortices inside their potential wells. Different than standard TFA–YBCO films, BZO nanocomposites displayed increasing α_L(H_dc) curves in the whole studied (H_dc, T) phase diagram, a behavior not predicted by the standard collective theory. We suggest results may be explained by the softening of the vortex-lattice, owed to the microstrain induced by the nanoparticles in the YBCO matrix.     

Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density j_c at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution j_c^coll. The latter allows one to estimate quasiparticle scattering rates.     

Experimental determination of ultra-sharp stray field distribution from a magnetic vortex core structure

The fine magnetic stray field from a vortex structure of micron-sized permalloy (Ni₈₀Fe₂₀) elements has been studied by high-resolution magnetic force microscopy. By systematically studying the width of the stray field gradient distribution at different tip-to-sample distances, we show that the half-width at half-maximum (HWHM) of the signal from vortex core can be as narrow as ∼21 nm at a closest tip-to-sample distance of 23 nm, even including the convolution effect of the finite size of the magnetic tip. a weak circular reverse component is found around the center of the magnetic vortex in the measured magnetic force microscope (MFM) signals, which can be attributed to the reverse magnetization around the vortex core. Successive micromagnetic and MFM imaging simulations show good agreements with our experimental results on the width of the stray field distribution.     

Magnetic relaxation near a fishtail peak of isothermal magnetization in B1 NbCy encapsulated in multiwall carbon nanocages

Isothermal magnetization near a fishtail peak in nanocrystalline B1 NbC_y encapsulated in multiwall carbon nanocages is studied within the time window of 100 < t < 4000 s. The current density J exhibits a linear logarithmic time decay. The effective activation energy U_eff increases linearly with temperature T and is independent of applied magnetic field H. The results of J(t) and U_eff (T, H) are consistent with the Anderson–Kim flux–creep model for thermally activated motion of uncorrelated vortices or vortex bundles over a net potential barrier U_eff. U_eff at a fishtail peak field H_fp evolves quickly above a fishtail peak temperature T_fp, but slowly below that temperature. The result suggests that a decrease of flux viscosity coefficient above T_fp at H_fp is the origin of the fishtail peak in nanocrystalline B1 NbC_y encapsulated in multiwall carbon nanocages.