Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

We review experimental studies of the time decay of the nonequilibrium magnetization in high-temperature superconductors, a phenomenon known as magnetic relaxation. This effect has its origin in motion of flux lines out of their pinning sites due to thermal activation or quantum tunneling. The combination of relatively weak flux pinning and high temperatures leads to rich properties that are unconventional in the context of low temperature superconductivity and that have been the subject to intense studies. The results are assessed from a purely experimental perspective and discussed in the context of present phenomenological theories. [S0034-6861(96)00403-5]

Magnetic relaxation in high-temperature superconductors

In the past few years magneto-optical flux imaging (MOI) has come to take an increasing role in the investigation and understanding of critical current densities in high-Tc superconductors (HTS). This has been related to the significant progress in quantitative high-resolution magneto-optical imaging of flux distributions together with the model-independent determination of the corresponding current distributions. We review in this article the magneto-optical imaging technique and experiments on thin films, single crystals, polycrystalline bulk ceramics, tapes and melt-textured HTS materials and analyse systematically the properties determining the spatial distribution and the magnitude of the supercurrents. First of all, the current distribution is determined by the sample geometry. Due to the boundary conditions at the sample borders, the current distribution in samples of arbitrary shape splits up into domains of nearly uniform parallel current flow which are separated by current domain boundaries, where the current streamlines are sharply bent. Qualitatively, the current pattern is described by the Bean model; however, changes due to a spatially dependent electric field distribution which is induced by flux creep or flux flow have to be taken into account. For small magnetic fields, the Meissner phase coexists with pinned vortex phases and the geometry-dependent Meissner screening currents contribute to the observed current patterns. The influence of additional factors on the current domain patterns are systematically analysed: local magnetic field dependence of jc(B), current anisotropy, inhomogeneities and local transport properties of grain boundaries. We then continue to an overview of the current distribution and current-limiting factors of materials, relevant to technical applications like melt-textured samples, coated conductors and tapes. Finally, a selection of magneto-optical experiments which give direct insight into vortex pinning and depinning mechanisms are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/65/5/202/pdf

Magneto-optical studies of current distributions in high-Tc superconductors

This protocol details how to design and conduct experiments to deliver nucleic acids to adherent and suspension cell cultures in vitro by magnetic force-assisted transfection using self-assembled complexes of nucleic acids and cationic lipids or polymers (nonviral gene vectors), which are associated with magnetic (nano) particles. These magnetic complexes are sedimented onto the surface of the cells to be transfected within minutes by the application of a magnetic gradient field. As the diffusion barrier to nucleic acid delivery is overcome, the full vector dose is targeted to the cell surface and transfection is synchronized. In this manner, the transfection process is accelerated and transfection efficiencies can be improved up to several 1,000-fold compared with transfections carried out with nonmagnetic gene vectors. This protocol describes how to accomplish the following stages: synthesis of magnetic nanoparticles for magnetofection; testing the association of DNA with the magnetic components of the transfection complex; preparation of magnetic lipoplexes and polyplexes; magnetofection; and data processing. The synthesis and characterization of magnetic nanoparticles can be accomplished within 3-5 d. Cell culture and transfection is then estimated to take 3 d. Transfected gene expression analysis, cell viability assays and calibration will probably take a few hours. This protocol can be used for cells that are difficult to transfect, such as primary cells, and may also be applied to viral nucleic acid delivery. With only minor alterations, this protocol can also be useful for magnetic cell labeling for cell tracking studies and, as it is, will be useful for screening vector compositions and novel magnetic nanoparticle preparations for optimized transfection efficiency in any cell type.

Generation of magnetic nonviral gene transfer agents and magnetofection in vitro

Local magnetic relaxation measurements in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} crystals show evidence for plastic vortex creep associated with the motion of dislocations in the vortex lattice. This creep mechanism governs the vortex dynamics in a wide range of temperatures and fields below the melting line and above the field corresponding to the peak in the {open_quote}{open_quote}fishtail{close_quote}{close_quote} magnetization. In this range the activation energy {ital U}{sub pl}, which decreases with field, drops below the elastic (collective) creep activation energy, {ital U}{sub el}, which increases with field. A crossover in flux dynamics from elastic to plastic creep is shown to be the origin of the fishtail in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}}. {copyright} {ital 1996 The American Physical Society.}

https://arxiv.org/pdf/supr-con/9606003.pdf

Plastic Vortex Creep in YBa2Cu3O7-x Crystals.

Nanophase formation of strontium hexaferrite fine powder by the sonochemical method using Fe(CO)5

Nanocrystalline perovskite-type LaFeO3 with particle size of about 30 nm was prepared by a sonochemical method using iron pentacarbonyl and lanthanum carbonate as starting materials. The overall process involves three steps: formation of lanthanum carbonate using lanthanum nitrate and urea; reaction of the so-formed lanthanum carbonate with iron pentacarbonyl resulting in the formation of a precursor; calcination of the precursor to obtain nanocrystalline particles of LaFeO3. Transmission electron microscopy revealed the particles to have a mean size of about 30 nm. Study of the magnetic properties of nanocrystalline LaFeO3 particles shows a coercivity of ∼250 Oe, while the saturation magnetization is ∼40 memu g−1.

Sonochemical synthesis of nanocrystalline LaFeO3

Measurements of the magnetic irreversibility line and time-logarithmic decay of the magnetization are described for three ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ samples composed of regular amorphous, acicular amorphous, and crystalline nanoparticles. The relaxation rate is the largest and the irreversibility temperature is the lowest for the regular amorphous nanoparticles. The crystalline material exhibits the lowest relaxation rate and the largest irreversibility temperature. We develop a phenomenological model to explain the details of the experimental results. The main new aspect of the model is the dependence of the barrier for magnetic relaxation on the instantaneous magnetization and therefore on time. The time-dependent barrier yields a natural explanation for the time-logarithmic decay of the magnetization. Interactions between particles as well as shape and crystalline magnetic anisotropies define an energy scale that controls the magnetic irreversibility. Introducing this energy scale yields a self-consistent explanation of the experimental data.

https://arxiv.org/pdf/cond-mat/9811206.pdf

Magnetic irreversibility and relaxation in assembly of ferromagnetic nanoparticles

We report the structural and magnetic properties of SmCo7−xCux, where x=0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.7. X-ray diffraction shows that these alloys from the disordered hexagonal TbCu7-type structure. For large values of x(x⩾0.8) the hexagonal TbCu7-type structure cannot be formed. X-ray diffraction on magnetically aligned samples show that these samples have uniaxial anisotropy. The lattice parameters (a and c) are dependent on the Cu concentration, and the unit cell volume is found to increase with x. The saturation magnetization decreases with x at both room temperature and 25 K. The Curie temperature increases with x for small values of x while it decreases with x for large values of x. A maximum value of TC=852 °C is found in these alloys.

/pdf/magnetic-and-structural-properties-of-smco7-xcux-alloys-4bq3i6w3d0.pdf

Y. Yeshurun

Papers

Plastic Vortex Creep in YBa2Cu3O7-x Crystals.

Nanophase formation of strontium hexaferrite fine powder by the sonochemical method using Fe(CO)5

Sonochemical synthesis of nanocrystalline LaFeO3

Magnetic irreversibility and relaxation in assembly of ferromagnetic nanoparticles

Magnetic and structural properties of SmCo7-xCux alloys