Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

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

Most large-scale applications of the high-temperature copper oxide superconductors (HTSCs) require high critical current densities (Jc9s) at temperatures near the boiling point of liquid nitrogen to be technologically useful, although thermally activated flux flow reduces Jc dramatically at these temperatures. This intrinsic limitation can be overcome by introducing nanometer-sized columnar defects into an HTSC. Nanorods of magnesium oxide were grown and incorporated into HTSCs to form nanorod-HTSC composites. In this way, a high density of nanorod columnar defects can be created with orientations perpendicular and parallel to the copper oxide planes. The Jc9s of the nanorod-HTSC composites are enhanced dramatically at high temperatures and magnetic fields as compared with reference samples; these composites may thus represent a technologically viable strategy for overcoming thermally activated flux flow in large-scale applications.

https://science.sciencemag.org/content/sci/273/5283/1836.full.pdf

Nanorod-superconductor composites : A pathway to materials with high critical current densities

We report a dramatic change in the irreversibility line of Y-Ba-Cu-O crystals after irradiation with Pb ions. Near the transition temperature, following irradiation, the irreversibility temperature increases and the curvature of the irreversibility line changes sign. These changes are accompanied by a strong enhancement of critical current density and a decrease in flux creep rate. Pb irradiation induces damage in the form of amorphous tracks which penetrate throughout the thickness of the sample. We maintain that these defects are most efficient in terms of flux trapping and are responsible for the observed changes in irreversible magnetic features in the irradiated sample.

Effect of 5.3-GeV Pb-ion irradiation on irreversible magnetization in Y-Ba-Cu-O crystals.

We measured the peak effect in the magnetic hysteresis loop of an untwinned ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ crystal in the vicinity of the critical temperature and studied its temperature, time, and angular dependence. The location of the peak is determined by the component of the field along the c direction. The pinning force density ${\mathit{F}}_{\mathit{p}}$(B) is scaled into a single curve for all measured isotherms (75--87 K) and time scales (4--1500 sec), and its functional form reflects the observed peak effect. The scaling field is related to the irreversibility field of oxygen-deficient regimes. The results indicate that pinning in this system is due to inhomogeneity of the oxygen deficiency and that the peak is related to the formation of a percolationlike network of reversible regimes.

Peak effect and scaling of irreversible properties in untwinned Y-Ba-Cu-O crystals.

The system Y{sub 1{minus}{ital x}}Pr{sub {ital x}}Ba{sub 2}Cu{sub 3{minus}{ital y}}Fe{sub {ital y}}O{sub {ital z}}, with {ital x}=0 to 1, {ital y}=0 and 0.3, and {ital z}=6 and 7, has been studied by ac and dc magnetometry to determine the superconducting phase transition temperature, {ital T}{sub {ital c}}, by {sup 57}Fe Moessbauer spectroscopy to determine the antiferromagnetic phase transition temperature of the Cu(2) site, {ital T}{sub {ital N}}, and by specific-heat measurements to determine {gamma} and the antiferromagnetic ordering temperature of the Pr site, {ital T}{sub {ital n}}. {ital T}{sub {ital c}} ({ital x},{ital z}=7), {ital T}{sub {ital N}} ({ital x},{ital z}=6,7), and {ital T}{sub {ital n}} ({ital x},{ital z}=7) were obtained for {ital x} values of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. For {ital z}=6, {ital T}{sub {ital N}} changes very little with {ital x} ({ital T}{sub {ital N}}(0,6)=415 K and {ital T}{sub {ital N}}(1,6)=350 K), but for {ital z}=7, {ital T}{sub {ital N}} changes sharply with {ital x} ({ital T}{sub {ital N}}(1,7)=325 K, {ital T}{sub {ital N}}(0.6,7)=230 K, and {ital T}{sub {ital N}}(0.4,7){le}35 K). There is no conclusive evidence for overlap of superconductivity and antiferromagnetism. {ital T}{sub {ital n}} also decreases strongly with decreasing {ital x}, {ital T}{submore » {ital n}}(1,7)=17 K, while {ital T}{sub {ital n}}(0.4,7){le}2.5 K. The specific-heat measurements show large linear temperature terms. The slope {gamma} increases strongly with {ital x} and with the introduction of the Fe probe.« less

Magnetic order and superconductivity in Y1-xPrxBa2Cu3O7.

Bi 2 Sr 2 CaCu 2 O 8 (BSCCO) crystals were irradiated with 58-GeV Pb ions to produce columnar defects either along the c direction or at 45 o with respect to it Magnetization curves of the irradiated BSCCO crystals were measured with the applied field at different directions relative to the defects The width of the magnetization curves, which reflects the pinning strength, is found to be the largest for fields along the defects This unidirectional enhancement clearly indicates the line nature of the vortices in BSCCO

Evidence for line vortices in Bi2Sr2CaCu2O8.

We investigated ${\mathrm{Pr}}_{2}$${\mathrm{BaO}}_{4}$ and ${\mathrm{PrBaO}}_{3}$ by several complementary experimental techniques. ${\mathrm{PrBaO}}_{3}$ crystallize in an orthorhombic structure. dc and ac susceptibility measurements exhibit irreversibility phenomena below ${\mathit{T}}_{\mathit{N}}$=11.7 K and reveal the magnetic structure of ${\mathrm{PrBaO}}_{3}$, which consists of an antiferromagnetic ordering together with a small canting of the spins which produces the ferromagnetic component. Both magnetic and specific-heat studies show that ${\mathit{T}}_{\mathit{N}}$ is not affected by the applied magnetic field up to 9 T. ${\mathrm{Pr}}_{2}$${\mathrm{BaO}}_{4}$ crystallizes in an orthorhombic structure where a=10.56 \AA{}, b=12.43 \AA{}, and c=3.617 \AA{} belongs to Pnam space group. dc and ac susceptibility and specific-heat measurements show that ${\mathrm{Pr}}_{2}$${\mathrm{BaO}}_{4}$ is paramagnetic down to 2 K, with a vanishing electronic specific-heat coefficient \ensuremath{\gamma}. X-ray photoemission spectroscopy shows that Pr is mainly trivalent in ${\mathrm{Pr}}_{2}$${\mathrm{BaO}}_{4}$ and close to being tetravalent in ${\mathrm{PrBaO}}_{3}$. The pronounced ferromagnetic-like behavior found below 11.7 K in the ${\mathrm{Pr}}_{\mathit{x}}$${\mathit{R}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{z}}$ system is due to the impurity of ${\mathrm{PrBaO}}_{3}$.

E. R. Yacoby

Papers

Effect of 5.3-GeV Pb-ion irradiation on irreversible magnetization in Y-Ba-Cu-O crystals.

Peak effect and scaling of irreversible properties in untwinned Y-Ba-Cu-O crystals.

Magnetic order and superconductivity in Y1-xPrxBa2Cu3O7.

Evidence for line vortices in Bi2Sr2CaCu2O8.

Crystal structure, magnetic properties, x-ray-photoemission-spectroscopy, and specific-heat measurements on Pr2BaO4 and PrBaO3.