^{1,a)}

### Abstract

Supercurrent transport phenomena in -oriented epitaxialthin films of the the high- superconducting (HTS) cuprate (YBCO) with a high critical current density are investigated by four-probe transport measurements, low-frequency magnetic susceptibility studies, and SQUID magnetometry. The film samples are deposited on a single-crystal sapphire (-cut) substrates with a or buffer layer by off-axis dc magnetron sputtering or pulsed laser ablation. A model of the mechanisms of Abrikosov vortex pinning and supercurrent limitation is developed and discussed by comparing its predictions with the results of measurements of the critical current and its dependence on applied magnetic fields of different strength and orientation and also with nanostructure data obtained by high-resolution transmission electron microscopy and electron diffraction in a backscattering geometry. It is shown that the low-angle subboundaries (LABs) formed between domains with a slight azimuthal misorientation during the epitaxialgrowth of the film play a key role in the phenomena observed in the transport of supercurrent. The tilt LABs form equidistant ordered rows of edge dislocations with nonsuperconducting cores about in diameter. The dislocation lines in the LABs are parallel to each other and perpendicular to the film plane. The average density of dislocations over the area of the film depends on the real statistics of the random system of LABs and can reach . Since the diameter of the “normal” core of a dislocation is close to the diameter of the core of an Abrikosov vortex, the elementary pinning force of the vortex to the core of the dislocation is close to the maximum possible. The pinning on dislocation subboundaries has the following characteristics: 1) the achievement of high values and in epitaxialfilms and conductors; 2) the existence of a “plateau” on the curve, i.e., for ; 3) a logarithmic decline of for , i.e., at the transition from the single-particle pinning regime to the collective pinning of the vortex lattice on the statistical ensemble of randomly distributed dislocation subboundaries; 4) the existence of a threshold field that determines the limit up to which the vortices in a thin film remain rectilinear and perpendicular to the film even in a field inclined at a large angle; 5) the evolution of the angle dependence of with a change of field strength is in complete agreement with the model of dominant pinning on “threading” edge dislocations. A new “peak effect”—an increase of with increasing longitudinal field—is observed for the first time for , i.e, after the end of the “plateau” .

I. INTRODUCTION

II. PINNING OF ABRIKOSOV VORTICES IN EPITAXIALFILMS OF HTS CUPRATES

III. MATERIALS AND METHODS OF STUDY

A. Epitaxialfilms

B. Methods of measurement of the critical current density

IV. INFLUENCE OF MAGNETIC FIELD ON THE CRITICAL CURRENT DENSITY FOR DIFFERENT ORIENTATIONS OF THE FIELD VECTOR

A. Magnetic field vector directed along the axis of the film

1. Vortex pinning at low external applied fields

2. “Collective” pinning of the vortex lattice by dislocation walls

3. Real nanostructure and the results of electromagnetic measurements

B. Magnetic field vector directed along the film plane

C. Magnetic field vector directed at an arbitrary angle to the axis of a single-crystalYBCOfilm

V. ANGULAR DEPENDENCE OF THE CRITICAL CURRENT DENSITY

VI. DISCUSSION OF THE RESULTS

VII. CONCLUSIONS

### Key Topics

- Rotating flows
- 104.0
- Magnetic films
- 65.0
- Magnetic fields
- 61.0
- Critical currents
- 58.0
- Thin films
- 57.0

## Figures

Transmission electron-microscope images of transverse sections of films with a comparatively low magnification (approximately ). The films were deposited by pulsed laser ablation on a (100) substrate. a—substrate temperature , the subboundaries are of a diffuse, disordered character, and the size of the domains is ; b—substrate temperature , one can see domains separated from each other by well-formed ordered dislocation subboundaries; stacking faults with a domain size of can also be seen, (c) a schematic illustration of a typical nanostructure of domains in a film; also shown are threading edge dislocations in the subboundaries.

Transmission electron-microscope images of transverse sections of films with a comparatively low magnification (approximately ). The films were deposited by pulsed laser ablation on a (100) substrate. a—substrate temperature , the subboundaries are of a diffuse, disordered character, and the size of the domains is ; b—substrate temperature , one can see domains separated from each other by well-formed ordered dislocation subboundaries; stacking faults with a domain size of can also be seen, (c) a schematic illustration of a typical nanostructure of domains in a film; also shown are threading edge dislocations in the subboundaries.

Critical current density as a function of the applied perpendicular field, measured at different temperatures with the aid of a SQUID magnetometer for film sample K1509 (off-axis dc magnetron sputtering, thickness ). The data from measurements by the transport method at are shown for comparison.

Critical current density as a function of the applied perpendicular field, measured at different temperatures with the aid of a SQUID magnetometer for film sample K1509 (off-axis dc magnetron sputtering, thickness ). The data from measurements by the transport method at are shown for comparison.

Schematic illustration of a 1° low-angle subboundary. The “windows” for the flow of supercurrent between the normal cores are shown. A distance between dislocations of corresponds to a misorientation angle of 1°.

Schematic illustration of a 1° low-angle subboundary. The “windows” for the flow of supercurrent between the normal cores are shown. A distance between dislocations of corresponds to a misorientation angle of 1°.

Schematic picture of rectangular domains and the triangular Abrikosov vortex lattice. Shown are the characteristic sizes that are important for the model of limitation of on account of depinning of vortices from conditions in low-angle domain subboundaries.

Schematic picture of rectangular domains and the triangular Abrikosov vortex lattice. Shown are the characteristic sizes that are important for the model of limitation of on account of depinning of vortices from conditions in low-angle domain subboundaries.

Calculated dependence of on the dimensionless parameter at different values of , i.e., upon a change of the accomodation function . The straight lines correspond to the approximation .

Calculated dependence of on the dimensionless parameter at different values of , i.e., upon a change of the accomodation function . The straight lines correspond to the approximation .

Reduced field dependence of the critical current for a film obtained by off-axis magnetron sputtering on a sapphire∕ substrate. The solid line is a combined fit of the experimental data for 10, 30, and . The dashed lines are the calculated curves for a broad distribution and for “solid” (continuous) boundaries ; is the reduced distance between dislocations.

Reduced field dependence of the critical current for a film obtained by off-axis magnetron sputtering on a sapphire∕ substrate. The solid line is a combined fit of the experimental data for 10, 30, and . The dashed lines are the calculated curves for a broad distribution and for “solid” (continuous) boundaries ; is the reduced distance between dislocations.

Model size distribution functions of the domains (the integral is normalized to unity). The value corresponds to the position of the peak. The experimental results correspond to .

Model size distribution functions of the domains (the integral is normalized to unity). The value corresponds to the position of the peak. The experimental results correspond to .

Fourier transform of the diffraction function for the reflections (1 0 6) and (2 0 12) for a YBCO film grown by magnetron sputtering on a sapphire∕ substrate; is the parameter of the Fourier transformation.

Fourier transform of the diffraction function for the reflections (1 0 6) and (2 0 12) for a YBCO film grown by magnetron sputtering on a sapphire∕ substrate; is the parameter of the Fourier transformation.

Plots of (squares) and (triangles) for the film sample K2 ( thick, obtained by magnetron sputtering) at , measured by the magnetic susceptibility method immediately after cooling (filled symbols) and after thermocycling between 77 and (unfilled symbols).

Plots of (squares) and (triangles) for the film sample K2 ( thick, obtained by magnetron sputtering) at , measured by the magnetic susceptibility method immediately after cooling (filled symbols) and after thermocycling between 77 and (unfilled symbols).

Plots of (filled symbols) and (unfilled symbols) for film sample K6300 ( thick, obtained by magnetron sputtering) at , measured by the four-probe transport method.

Plots of (filled symbols) and (unfilled symbols) for film sample K6300 ( thick, obtained by magnetron sputtering) at , measured by the four-probe transport method.

Plots of for the film sample K34-2 ( thick, grown by magnetron sputtering) for different orientations of the magnetic field: the symbols are experimental, the curves, calculated.

Plots of for the film sample K34-2 ( thick, grown by magnetron sputtering) for different orientations of the magnetic field: the symbols are experimental, the curves, calculated.

Bending of vortices partially pinned on edge dislocations. Left: completely pinned vortex; for a parallel field does not penetrate into the film. Right: a vortex with partially depinned ends at .

Bending of vortices partially pinned on edge dislocations. Left: completely pinned vortex; for a parallel field does not penetrate into the film. Right: a vortex with partially depinned ends at .

Angle dependence of for film sample K2 for three values of the applied magnetic field. Angular hysteresis at a field of : the filled and unfilled symbols are the ascending and descending branches, respectively, and is the angle between and the axis.

Angle dependence of for film sample K2 for three values of the applied magnetic field. Angular hysteresis at a field of : the filled and unfilled symbols are the ascending and descending branches, respectively, and is the angle between and the axis.

Angular hysteresis of the critical current at an intermediate value of the applied magnetic field for the film sample K2.

Angular hysteresis of the critical current at an intermediate value of the applied magnetic field for the film sample K2.

Calculated evolution of the angle dependence with increasing applied magnetic field from . Some of the curves were obtained from measurements of under direct variation of the orientation of the film with respect to the field vector, while others are data interpolated with the use of the curves measured for the same film at various fixed values of .

Calculated evolution of the angle dependence with increasing applied magnetic field from . Some of the curves were obtained from measurements of under direct variation of the orientation of the film with respect to the field vector, while others are data interpolated with the use of the curves measured for the same film at various fixed values of .

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