In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

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

Nanofabrication of magnetic storage media, where servo marks, discrete tracks or individual islands are defined, offer the prospect for improved performance and increased areal density. However, this increase in performance will require that new and additional processes be introduced into disk manufacturing. We review here the fundamental patterning and fabrication processes that have been proposed, along with their respective strengths and weaknesses and the potential advantages they may offer for magnetic recording. The increase in data density afforded by nanofabrication may have added significance as more conventional approaches to ever increasing density will encounter physical limitations set by the thermal stability of the recorded bits.

https://iopscience.iop.org/article/10.1088/0022-3727/38/12/R01/pdf

Nanofabricated and self-assembled magnetic structures as data storage media

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

The anomalous magnetization characteristic, intra-grain granularity and the magnitude of the flux pinning in single crystals of YBa2Cu307–δ are shown to be intimately linked. As the nominal oxygen deficiency δ decreases towards zero, the flux pinning declines and the crystals lose their explicitly granular signature. As δ is seldom specifically controlled at levels below ˜0.05 in even the most carefully made materials, small oxygen deficiencies may contribute significantly to both the flux pinning and the weak-link properties.

Oxygen-defect flux pinning, anomalous magnetization and intra-grain granularity in YBa 2 Cu 3 0 7–δ

Investigation of inter- and intragrain critical currents in high Tc ceramic superconductors☆

The current density $j$ in bulk ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ frequently shows a maximum at fields far above the self-field The responsible defect structure for this peak effect (PE) are small clusters of oxygen vacancies, impurity atoms, or dopants The current density caused by these defects is studied during the evolution of the PE Very pure, twin-free crystals without a $j(B)$ peak after high-pressure oxidation were subsequently oxygen reduced, which increases the pinning strength, ie, concentration and probable size of the vacancy clusters The peak that appears first very close below the melting line broadens, increases in height, and shifts to lower fields going from the overdoped into the optimally doped region Above the peak field ${B}_{p}$ the current becomes less sensitive to the growing strength of the defect structure in accordance with a plastic deformation of vortices In the field region below ${B}_{p}$ the very low current density is related to a collective interaction The transition of this elastic interaction below ${B}_{p}$ into a regime of plastic deformation above, initiated by the thermal softening of the shear modulus, results in the rise of the current density The shift of this transition to lower magnetic fields with increasing oxygen reduction as well as with decreasing temperature is related to the thermal influence on the distribution of pinning energies that result in a temperature-dependent effective concentration of pinning defects

Peak effect and its evolution from oxygen deficiency in YBa 2 Cu 3 O 7 − δ single crystals

Intragrain junctions in YBa2Cu3O7−x ceramics and single crystals

The influence of the oxygen stoichiometry on magnetization and relaxation of R${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (R=Y,Tm) single crystals was studied for 0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}0.55. The field dependences of the shielding currents ${\mathit{j}}_{\mathit{s}}$(H) and flux creep rates S(H) were analyzed. Three different kinds of ${\mathit{j}}_{\mathit{s}}$(H) and S(H) behavior can be seen in highly oxygenated samples (\ensuremath{\delta}0.1). (i) At high temperatures, ${\mathit{j}}_{\mathit{s}}$(H) shows a common fishtail peak, which is present for all oxygen contents. The field position and height of the ${\mathit{j}}_{\mathit{s}}$ peak increase rapidly with decreasing \ensuremath{\delta}. Approaching the stoichiometric state \ensuremath{\delta}=0, the value of the current starts to decrease with lower oxygen deficiency, in contrast to the still increasing irreversibility field ${\mathit{B}}_{\mathrm{irr}}$. This points to the importance of oxygen disorder for the pinning and stresses the melting nature of the irreversibility line. The peak position ${\mathit{B}}_{\mathrm{max}}$ is found to correlate with ${\mathit{B}}_{\mathrm{irr}}$. A possible relation of the fishtail with a synchronization effect and with the vanishing of ${\mathrm{C}}_{66}$ at the melting transition is proposed. (ii) In the intermediate-temperature region, some of the samples showed a new second peak with weak temperature and \ensuremath{\delta} dependence. The probable origin of this feature is matching with twin structure. This peak disappears for \ensuremath{\delta}g0.1, when the fishtail position shifts below the matching field. (iii) The low-temperature region is characterized by a monotonic decrease of ${\mathit{j}}_{\mathit{s}}$(B). This region becomes narrower with larger \ensuremath{\delta} and disappears for \ensuremath{\delta}g0.3. Thus in highly deoxygenated samples, the fishtail feature is observed for practically all temperatures. The possible connection of the low-temperature region with the pinning of the small vortex bundles or with the slipping of vortices along the twin planes is considered.

Influence of oxygen stoichiometry on the irreversible magnetization and flux creep in RBa2Cu3O7- delta (R=Y,Tm) single crystals.

NdBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} single crystals and melt-textured samples were prepared in reduced atmospheres starting from the Nd-poor side of the phase diagram in order to minimize the Nd/Ba substitution and the second phase content. Current density j and irreversibility field B{sub irr} were measured as a function of temperature and angle between the c axis and applied field direction in samples with different impurity and oxygen contents. Current density vs field shows a pronounced peak effect which results from small clusters of oxygen vacancies, whereas a second peak is related to the twin structure. The current density at 77 K is for fields up to 4 T above 4{times}10{sup 4}A/cm{sup 2} and reaches values of 1.2{times}10{sup 5}A/cm{sup 2} in the peak at 2.1 T. The irreversibility fields parallel to the c axis reach 13.4 and 11.8 T at 77 K in pure and homogeneous single crystals and melt-textured samples, respectively. These extremely high values, which are caused by the twin structure, decrease to 10 and 8 T, respectively, if the current is optimized. The correlation and interference between j and B{sub irr} in the presence of weakly and strongly interacting defects such as small clusters of oxygen vacancies andmore » Nd-422 precipitates, respectively, as well as the influence of the twin structure are analyzed and discussed. {copyright} {ital 1997} {ital The American Physical Society}« less

H. Küpfer

Papers

Investigation of inter- and intragrain critical currents in high Tc ceramic superconductors☆

Peak effect and its evolution from oxygen deficiency in YBa 2 Cu 3 O 7 − δ single crystals

Intragrain junctions in YBa2Cu3O7−x ceramics and single crystals

Influence of oxygen stoichiometry on the irreversible magnetization and flux creep in RBa2Cu3O7- delta (R=Y,Tm) single crystals.

High irreversibility fields and current densities in NdBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} single crystals and melt-textured samples