The microstructure of YBa2Cu3O7−δ thin films grown on vicinal SrTiO3(001) has been studied as a function of the vicinal angle by x-ray diffraction using the two-dimensional q-scan technique. Our results reveal a strong correlation between the miscut of a SrTiO3(001) substrate and the anisotropic defect structure of the film. Furthermore, we observed an anisotropy of the corresponding critical current density up to 4.6 depending on the angle of miscut.

Magneto-optical investigation of flux penetration into type-II superconductors allows the determination of the local critical current density jc by inversion of the Biot–Savart law. Due to the required computational effort, in the past, this method was limited to low spatial resolution of the current density. In this paper, we present a fast inversion scheme using Fast-Fourier-Transformation, which allows high spatial resolution imaging of current distributions. Due to the nonlocal relation between magnetic field and current density, it is necessary to use a method that images field and current distribution of superconductors as a whole, and enables high resolution at the same time. To demonstrate the power of our method, the local current density in a YBa2Cu3O7−δ square and disk are imaged with high resolution and described in detail for increasing and decreasing external magnetic fields. At low fields, the dependencies of jc(B) on the local magnetic field B and of the average jc (magnetic moment) on the applied magnetic field show significant differences. Finally, we directly image the local current density near macroscopic defects in a square and a disk. The observed current distributions near defects significantly differ from the predictions of an extended Bean model.

The microscopic screening currents circulating in the grains of the ceramic high-Tc superconductor YBa2Cu3O72d in a magnetic field are visualized by computing the current density with high spatial resolution of more than 10 pixels from magneto-optic images taken at the specimen surface with the same high resolution. Having solved several technical and mathematical problems, we can visualize the supercurrent density distribution inside and between the grains of a macroscopic polycrystalline specimen and make quantitative statements. Our method may thus be used to optimize the current-carrying capability of superconducting ceramics. @S0163-1829~98!09817-8#

The growth of YBCO thin films on miscut SrTiO3 substrates with various tilt angles towards [010] allows the controlled generation of planar defects, which are aligned to the surface steps of the substrate in [100] (L)direction. Due to the anisotropic microstructure we observe a strong anisotropy of flux penetration and critical current density by means of magneto-optics. The critical current density in the (ab)-plane of these c-axis oriented thin films is determined by a new method of high resolution inversion of Biot-Savart's law. New features Like periodic streaky flux patterns in L-direction and a strongly different magnetic field dependence of the critical current density longitudinal to the defect planes, j(c,L), and transversal, j(c,T), are observed. This gives rise to a magnetic field dependence of the anisotropy ratio of the critical current densities.

Recent progress in tailoring periodic step structures in vicinal SrTiO3 single crystal substrate surfaces enable a systematic study of the interplay of growth mediated defect structures and transport properties in HTS thin films. UHV annealed (001) oriented SrTiO3 substrates with a 10° miscut towards the [010] direction show after a UHV annealing a regular nanoscale step structure which generates an almost periodic terrace-like surface structure of the YBa2Cu3O7 film. Cross-sectional as well as planar view TEM reveals an anisotropic defect structure arising from the nanoscale step structure of the substrate surface. Transport measurements and magneto-optical analysis of the flux penetration show a growth-induced in plane anisotropy and an anisotropic enhancement of the critical current up to values close to the depairing limit.

The temperature dependence of the magnetic domain structure of Fe14Nd2B single crystals is investigated from room temperature down to 4.2 K by means of the magneto-optical Kerr effect. The parallel stripe domain structure characteristic of high-anisotropy uniaxial ferromagnets is observed on the (h k 0) planes of the crystals at room temperature. This structure remains practically unchanged down to about 140 K. In the vicinity of the magnetic phase transition at TSR = 135 K the domain structure undergoes intense realignment. Below TSR a new type of domain structure occurs being characterized by a periodic modulation of the magnetization orientation inside the main domains together with a developed system of closure domains having different preferential orientations. For the particular sample studied the width of the main domains at 4.2 K is about 100 μm, while that of closure domains is about 2–5 μm.

In high quality Y1Ba2Cu3O7−x thin films with circular, triangular and quadratic shape, the magnetic flux density distribution (MFDD) and magnetization curve are measured. Comparison of calculated and measured MFDD shows good agreement and yields the critical current densities of the films. These jc-values agree with the jc-values calculated from the maximum magnetization which is reached at the external field μ0H′P. Within the Bean model the field μ0H′P should agree with the penetration field μ0HP necessary for full flux penetration. The measurements show that μ0H′P is smaller than μ0HP by a factor of about 2. This is understood by taking into account a field dependent critical current density. Furtheron a formula is presented for the magnetic stray-field in the center of a regular polygon with homogeneous thickness which gives also the penetration field μ0HP.

We have observed anisotropic flux pinning and resistivity in the substrate plane of YBa2Cu3O7-delta (YBCO) thin films grown on vicinal SrTiO3(001) with the c axis oriented along the SrTiO3[001] direction. Using UHV scanning tunneling microscopy and transmission electron microscopy we demonstrate the influence of a periodic nanoscale step structure of the clean substrate surface on the morphology and defect microstructure of subsequently deposited YBCO films. A linear array of dislocations generated via self-organization of the YBCO leads to an exceptionally large critical current density up to 8 X 10(11)A/m(2) at 4.2 K. The findings indicate that the critical current density of high-temperature superconductors can be enhanced in a controlled way growing thin films on tailored substrate surfaces.

We have generated an almost periodic step structure of c-axis-oriented YBa2Cu3O7−δ films grown on 10° miscut SrTiO3(001) substrates. Combined scanning tunneling microscopy and cross-sectional transmission electron microscopy studies reveal that this growth morphology is linked to an anisotropic defect microstructure. We present evidence that translational boundaries contribute to strong flux pinning in our films. The resistivity and critical current density in the miscut-grown YBa2Cu3O7−δ films have been found to be anisotropic.

As a result of the island growth mode all epitactic YBa2Cu3O7−δ thin films show surface roughness. To investigate a possible surface pinning mechanism, combined magneto-optical and atomic force microscopy studies were carried out. Measurement of the spatial distribution of magnetic flux density on the surface of thin YBa2Cu3O7−δ films by means of the magneto-optical Faraday effect (MOFE) under application of external magnetic fields allows an accurate determination of critical current densities jc. In order to have a quantitative comparison between the Bean model for thin films and experiment, a new nonlinear calibration technique for the flux densities was developed. For determining the thickness and roughness dependence of jc, samples with YBaCuO-strips of different thickness and roughness were patterned from one film. With the roughness determined experimentally by afm measurements, a satisfactory agreement between the measured and calculated thickness dependence of jc is achieved. Surface pinning is found to cause between 10%–30% of the critical current densities of epitactic YBa2Cu3O7−δ thin films. Additionally microscopic deviations of the flux profiles from the Bean model are detected. Evidence for matching effects of the vortex line distribution with the density of surface pins is given.

By means of the magneto-optical Kerr effect the domain structure of NdFe11Ti and NdFe11TiNx is investigated. From the mean domain width the domain wail energy gamma' and the critical diameter of the single domain particle D-c are calculated to be gamma' = 6.37 x 10(-7) J/cm(2), D-c = 0.12 mu m for NdFe11Ti and gamma' = 19.8 x 10(-7) J/cm(2), D-c = 0.255 mu m for NdFe11TiN.

All epitactic YBa2Cu3O7−δ thin films show an island mediated growth mode, which results in a chracteristic surface roughness. The thickness modulations influence the self energy of a vortex line and therefore can act as effective pinning centers and contribute to the high critical current densities. An exact calculation of the pinning energy must take into account the structural changes in the structure of a vortex line due to the complex surface morphology and accordingly represents a rather difficult problem. For a first approach, we have approximately calculated the surface pinning energy of vortex lines in thickness-modulated YBaCuO thin films within the framework of Ginzburg-Landau theory. The dependence of pinning energy, single vortex pinning force and critical current density jc on the roughness parameters of the surface are determined quantitatively assuming that the vortex lines remain rigid. In this model the surface roughness is approximated with a periodic thickness modulation of the superconducting film with wavelength lr and amplitude Δd of thickness modulation. The average film thickness is d-. Additionally the effect of vortex-line widening, which increases the magnetic extension of a vortex line in thin films with d-<2 λab, is considered. The calculated jc values with realistic surface roughnesses, observed in YBa2Cu3O7−δ thin films, have values of some 1010 A/m2, which is between 10% and 30% of the total jc in high quality epitactic thin films. The highest jc from surface pinning is yielded at film thickness d-≈ 2λab, large thickness variations Δd and roughness wavelenths of lr ≈λab.

The magneto-optical Faradayeffect [MOFE] is known to be an excellent tool for the spatially resolved analysis of the flux distribution in superconductors. We use three examples to demonstrate the power of this technique for device oriented investigations. It is shown that homogeneous Yba2Cu3O7 thin films with different shape show a flux pattern strongly depending on the geometry of the sample; model calculations for the flux distribution are in excellent agreement with the experimental results. Furthermore, we show, that crystallographic defects as well as imperfections due to pattern delineation are affecting the flux pattern on macroscopic scale. In a third example we use the MOFE to demonstrate that pulsed laser irradiation of Yba2Cu3O7 thin films with UV photons of moderate flux causes an enhancement of the critical current.

The penetration and exit of magnetic flux in type-II superconductors is investigated for the realistic situation where a transverse magnetic field is applied to a square or rectangular plate or film. In rectangular specimens the pattern of the sheet current and of the density of the perpendicular flux has some common features with the one-dimensional distributions in circular disks or long strips. Other features, however, are characteristic for the rectangular shape, e.g., the starlike pattern of the penetrating flux and, in the fully penetrated critical state, the discontinuity Lines at which the current stream lines perform sharp bends and at which the perpendicular magnetic field H-z(x,y) exhibits sharp ridges. These typical features have to be calculated from a genuine two-dimensional theory. Such a theory based on a highly nonlinear current-voltage law is outlined. The field patterns obtained by this general theory are compared with patterns observed magnetooptically at the surface of square and rectangular single crystals or films of high-T-c superconductors with homogeneous and inhomogeneous critical-current distribution. It is shown that the analysis of the current-discontinuity lines is essential to understand the flux dynamics in superconductors. In samples with inhomogeneous critical current density j(c)(r), a strong concentration of flux motion and electric field can occur along the lines where j(c) changes abruptly. This may trigger flux jumps.

The geometry of penetration of a magnetic field oriented perpendicular to the surface of a superconductor is changed by the presence of a longitudinal field. This is studied directly by means of the magneto-optical technique in different high-Tc materials. In YBa2Cu3O7 single crystals Brandt's mode of magnetization is observed, namely, penetration of an AC field only along the longitudinal field even if the corresponding dimension of the sample is much longer than the other two. This anisotropy is the evidence that the force-free configuration of current and vortices cannot be destroyed by cutting and reconnection of the vortices in this 3D superconductor. On the contrary, the absence of the induced anisotropy in Bi2Sr2CaCu2O8 single crystals reveals the independence of pancake vortices in CuO layers from longitudinal field which makes a realization of the force-free configuration impossible in the layered 2D superconductor. An intermediate effect in thin films indicates that vortices are almost normal to the film surface even if the applied field is nearly parallel to it. The described experiment can be used as a new tool to study the internal vortex structure in superconductors.

The magnetization curve of a two-phase two-sublattice model is calculated analytically. In one phase a ferromagnetic coupling is assumed which contributes to the total magnetization whereas in the other phase a ferrimagnetic interaction takes place. Within the framework of a molecular field theory the magnetization curve of this ferrimagnetic phase is calculated assuming a certain distribution of the molecular field interactions. The law of approach to magnetic saturation yields for the leading term a H−1-dependence in contrast to fluctuations of the local magnetic anisotropy which in general yield a H−built12-law. The calculations of the two-phase two-sublattice model agree well with measurements of the high-field magnetization curve of amorphous Fe1−xZrx-alloys with 0.076 ≤ x ≤ 0.11 showing that with decreasing Zr-content an increase of the ferrimagnetic phase exists.

Analytical expressions are given for the spatial distribution of the magnetic flux density B(r) of a sample with rectangular cross-section (xy-plane) elongated in the z direction in which a given electric current density j(z)(x, y) = SIGMA(n=0.1),...a(n)(x-x0)n exists. Application of these formulae to magneto-optical Faraday effect measurements of the B(y) field obtained at the surface of a type-II superconductor in the mixed state allows one to calculate the current-density distribution in the samples. The analysis of the magneto-optical measurements performed on thick Nb bars and thin stripe-structured YBa2Cu3O7-x films show that after full flux penetration the current density is spatially constant in the sample. The characteristic features of the magnetic flux-density distribution of a homogeneous current (n = 0), e.g., the spatial field-line distribution, inverse flux zones and the influence of external magnetic fields, are described as functions of the sample thickness. The analysis of the Faraday measurements of the thin stripes show that for partly penetrated flux an additional current distribution in the flux-free region has to be taken into account. Analytical expressions are given to calculate the critical current density of a sample with width W and thickness D from measurements of the B(y) field in the center or at the sample edge. Furthermore simple expressions are given for the external applied field necessary for full flux penetration.

Direct observation and measurement of the spatial flux density distribution on the surface of Y1Ba2Cu3O7-x, superconducting thin films under application of an external magnetic field are performed using magneto-optical EUS/EuF2 and iron-garnet indicators. A new, very accurate method to determine the critical current density of stripe-structured thin films is presented, based on a recent theory for flux penetration in superconducting thin films.