Magnetic Fields in Superconductors and Ferromagnetic Materials

A comparison is made between the treatment of magnetic fields in superconductors and normal materials. First some history is given, showing how early workers anticipated vortices. Later treatments tried to build a macroscopic theory using forces and torques on magnets. This was extremely unsatisfactory. Maxwell??s equations for normal materials are derived using average fields. The differences between the applied field, the demagnetising field, the local field on an atom and H are made clear. The derivation in superconductors follows a different path and uses the theory of Evetts. Simple and rigorous derivations of the forces on bodies and magnetic energies are derived, with comments on less satisfactory treatments. This is extended to thermodynamic potentials including the Ginzburg-Landau free energy.     

Critical Currents of High-Temperature Superconductors in Homogeneous Magnetic Fields

In this paper we report on the measurements of the critical current of a tape-formed high-temperature superconductor in a magnetic field corresponding to the field at different positions in a (transformer, reactor or magnet) winding. An applied magnetic field reduced the perpendicular component of the self-field of the sample. The measurements were performed in liquid nitrogen on a silver-sheathed Bi-2223 conductor. The results show a significant increase of the critical current with reduction of the perpendicular component of the self-field.     

Vortex Interaction with Mesoscopic Surface Cavities in Superconductors

The conformal mapping method is used to study the problem of flux line interaction with surface cavities having cylindrical profile and characteristic size , i.e., within mesoscopic scale, where λ is the penetration length. It is shown that the metastable states are achieved when the dimensions of the surface irregularities do not exceed the coherence length ξ. Our study shows that the surface barrier may vanish at some weak point at which the surface irregularities have mesoscopic scales. On the other hand, a remarkable decrease in the surface barrier occurs when the surface defects size . Our results are compared with the available experimental data and theoretical results.     

Organic Superconductors as Stages for Exploration of Superconductivity in High Magnetic Fields

The low dimensionality of organic superconductors leads to pronounced anisotropy in the upper critical field. In the vicinity of the field direction parallel to the superconducting plane, the critical field shoots out due to the suppression of the orbital pair-breaking effect. Organic superconductors are suitable for the study of the high-field state related to the spin effect under an aligned field, since they are of a high crystalline quality. The reported experimental results covering the behavior at low temperatures are reviewed first, and the breakthrough of the BCS Pauli paramagnetic limit is discussed. The potential of the low-dimensional organic superconductor for study of the effect of electronic spectrum quantization is argued.     

Effect of Columnar Defects on Magnetization of Mesoscopic Superconductors

In this work we investigated magnetization and vortex configurations in mesoscopic superconducting samples in the presence of square columnar defects (CDs). We solved numerically the nonlinear TDGL equations for different samples to study magnetization as a function of the applied magnetic field. In calculations, we focused mainly on four samples with different numbers of CDs which have the same total surface area. In this way, the total superconducting area remained the same with increasing the number of CDs for a fixed sample size. We found that the superconducting regions still exist inside the sample at high applied magnetic fields with increasing the number of CDs but irreversible effects became increasingly prominent, when the field is returned to zero. The results are discussed in frame of surface and pinning effects in mesoscopic systems.     

Irreversibility Line Measurement and Vortex Dynamics in High Magnetic Fields in Ni- and Co-Doped Iron Pnictide Bulk Superconductors

The de-pinning or irreversibility lines were determined by ac susceptibility, magnetization, radio-frequency proximity detector oscillator (PDO), and resistivity methods in Ba(Fe_0.92Co_0.08)₂As₂ ( T _c = 23.2 K), Ba(Fe_0.95Ni_0.05)₂As₂ ( T _c = 20.4 K), and Ba(Fe_0.94Ni_0.06)₂As₂ ( T _c = 18.5 K) bulk superconductors in ac, dc, and pulsed magnetic fields up to 65 T. A new method of extracting the irreversibility fields from the radio-frequency proximity detector oscillator induction technique is described. Wide temperature broadening of the irreversibility lines, for any given combination of ac and dc fields, is dependent on the time frame of measurement. Increasing the magnetic field sweep rate (dH/dt) shifts the irreversibility lines to higher temperatures up to about dH/d t = 40,000 Oe/s; for higher dH/dt, there is little impact on the irreversibility line. There is an excellent data match between the irreversibility fields obtained from magnetization hysteresis loops, PDO, and ac susceptibility measurements, but not from resistivity measurements in these materials. Lower critical field vs. temperature phase diagrams are measured. Their very low values near 0 T indicate that these materials are in mixed state in nonzero magnetic fields, and yet the strength of the vortex pinning enables very high irreversibility fields, as high as 51 T at 1.5 K for the Ba(Fe_0.92Co_0.08)₂As₂ polycrystalline sample, showing a promise for liquid helium temperature applications.     

The Influence of Pinning Centers in the Magnetization of the Mesoscopic Superconductors

In this work, we study the mesoscopic superconducting samples with pinning centers using the time-dependent Ginzburg-Landau theory (TDGL). The pinning centers are introduced via the phenomenological function f(r) Sorensen et al. (Physica C 533, 40–43 2017). We calculated the magnetization curves M(H) for some distances d from the boundary of the sample to the position of the pinning center. From this investigation arises the relation between the first magnetic field H _p and the distance d. It shows that the pinning centers located close to the boundary of the sample decrease H _p , and also the existence of two regimes of the penetration of the vortices. The magnetization curves revel the existence of ruddle of jumps for low magnetic fields for small distances d, indicating a complex vortex penetration.     

Magnetic Flux Penetration in a Mesoscopic Superconductor with a Slit

In this work, the vortex nucleation process in a mesoscopic squared superconductor with a slit is numerically investigated in terms of time dependent Ginzburg–Landau theory. We have calculated, simultaneously, the Gibbs free energy and the vortex configuration in function of time, it allows to identify the correspondence between special points in the Gibbs free energy and the configuration of the vortex system.     

Layered Superconductors in an External Magnetic Field

Presence of localized magnetic moments and inhomogeneites leads to an unconventional behavior of the upper critical field for layered superconductors. In addition, one can observe a large diamagnetic moment at H H _c2 and in the normal resistive state.     

Probing Inhomogeneities in Type II Superconductors by Means of Thermal Fluctuations, Magnetic Fields, and Isotope Effects

Type II superconductors, consisting of superconducting domains embedded in a normal or insulating matrix, undergo a rounded phase transition. Indeed, the correlation length cannot grow beyond the spatial extent of the domains. Accordingly, the thermodynamic properties will exhibit a finite size effect. It is shown that the specific heat and penetration depth data of a variety of type II superconductors, including cuprates, exhibit the characteristic properties of a finite size effect, arising from domains with nanoscale extent. The finite size scaling analysis reveals essential features of the mechanism. Transition temperature and superfluidity increase with reduced domain size. The combined finite size and isotope effects uncover the relevance of local lattice distortions.     

Magnetic Susceptibility in Normal States of Quasi-One-Dimensional Superconductors

The longitudinal magnetoresistance of a two-dimensional superconductor, β’-Et₂Me₂P[Pd(dmit)₂]₂ (dmit=C₃S ₅ ²⁻ ) under hydrostatic pressure was measured at low temperatures with the field applied perpendicular to the conducting layers. At 0.58 GPa, the field-dependent isothermal interlayer resistanceR╧ (H) exhibited a peak below the superconducting transition temperature T _C . This peak effect can be explained by a model of resistively-shunted Josephson-Junctions. The peak is strongly suppressed at a higher pressure, 0.71 GPa.     

Magnetic Flux Penetration and Motion in Antiferromagnetic Superconductors

The paper reviews a concept of induced spin-flop domain inside vortices in an antiferromagnetic superconductor. Such phenomenon may occur when an external magnetic field is strong enough to flip over magnetic moments in the core of the vortex from their ground state configuration. The formation of the domain structure inside vortices modifies the surface energy barrier of the superconductor. During this process the entrance of the flux is stopped and a newly created state exhibits perfect shielding. Such behavior should be visible as a plateau on the dependence of flux density as a function of the external magnetic field. The end of the plateau determines the critical field, which has been called the second critical field for flux penetration. Moreover, it is predicted and described how this phenomenon modifies flux creep in layered superconductors. The various scenarios of changing the creep regime from thermal to quantum and vice versa at constant temperature are discussed.     

Observation of the Curved and Entangled Vortex Tubes in 3D Mesoscopic Cubic Superconductors

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the superconducting samples with a cubic shape in a uniform external magnetic field. We obtain the different vortex patterns as a function of the magnetic field perpendicular to its surface. The vortex tubes must reach the surface perpendicularly in order to avoid a supercurrent component pointing outwards the surface. At the same time, we observed the arrangement of spiral vortices in the cubic superconductor. These results show that our approach is an effective and useful to interpret experimental data on vortex states in the mesoscopic superconductors.     

Thermometers in Low Magnetic Fields

In this article the effect of low amplitude DC magnetic fields on different types of thermometers is discussed. By means of a precision water-cooled electromagnet, the effect of a magnetic field on platinum resistance thermometers, thermistors, and type T, J, and K thermocouples was investigated, while thermometers were thermally stabilized in thermostatic baths. Four different baths were used for temperatures from 77 K (?196 °C) to 353 K (80 °C): liquid nitrogen bath (nitrogen boiling point at atmospheric pressure), ice-point bath, room-temperature air bath, and hot-water bath. The generated DC magnetic field of high relative precision (2 × 10^?4 at 1 T, 4 × 10^?5 short-term stability) and high relative uniformity (2 × 10^?5 over 1 cm², 10 mm gap) had a magnetic flux density of 1 T in the center of the gap between the magnet pole caps. The results indicate a magnetic effect of up to 100 mK due to a 1 T magnetic field for the types of thermocouples composed of ferromagnetic materials (Fe, Cr, Ni). For platinum resistance thermometers, thermistors, and non-magnetic type T thermocouples, the detected magnetic effect was weaker, i.e., under 10 mK.     

SQUID-Detected Magnetic Resonance Imaging in Microtesla Magnetic Fields

We describe studies of nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) of liquid samples at room temperature in microtesla magnetic fields. The nuclear spins are prepolarized in a strong transient field. The magnetic signals generated by the precessing spins, which range in frequency from tens of Hz to several kHz, are detected by a low-transition temperature dc SQUID (Superconducting QUantum Interference Device) coupled to an untuned, superconducting flux transformer configured as an axial gradiometer. The combination of prepolarization and frequency-independent detector sensitivity results in a high signal-to-noise ratio and high spectral resolution (～1 Hz) even in grossly inhomogeneous magnetic fields. In the NMR experiments, the high spectral resolution enables us to detect the 10-Hz splitting of the spectrum of protons due to their scalar coupling to a ³¹P nucleus. Furthermore, the broadband detection scheme combined with a non-resonant field-reversal spin echo allows the simultaneous observation of signals from protons and ³¹P nuclei, even though their NMR resonance frequencies differ by a factor of 2.5. We extend our methodology to MRI in microtesla fields, where the high spectral resolution translates into high spatial resolution. We demonstrate two-dimensional images of a mineral oil phantom and slices of peppers, with a spatial resolution of about 1 mm. We also image an intact pepper using slice selection, again with 1-mm resolution. In further experiments we demonstrate T₁-contrast imaging of a water phantom, some parts of which were doped with a paramagnetic salt to reduce the longitudinal relaxation time T₁. Possible applications of this MRI technique include screening for tumors and integration with existing multichannel SQUID systems for brain imaging.     

Theoretical Study of Magnetic Behavior in Ru-based Ferromagnetic Superconductors

A microscopic theory of interplay of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr₂RECu₂O₈ (Ru-1212) (RE=Gd, Eu) is developed from first principles considering s–f model. Self-consistent equations for superconducting order parameter Δ and ferromagnetic order parameter 〈S ^Z 〉 are obtained using Green’s function technique and equation of motion method. The theory is applied to explain the experimental results for RuSr₂RECu₂O₈ system. This model clearly predicts the coexistence of superconductivity and spatially uniform ferromagnetism in RuSr₂RECu₂O₈. The theory shows that it is possible to become superconducting if the system is already ferromagnetic. Study of specific heat, density of states, free energy, critical field, and ac spin susceptibility is also presented. Agreement between experimental results and theory is quite convincing.     

Charge Variations in Cuprate Superconductors from Nuclear Magnetic Resonance

Charge inhomogeneities in the cuprates were reported early on and have been in the focus of much research recently. Nuclear magnetic resonance (NMR) is very sensitive to local charge symmetry through the electric quadrupole interaction that must detect any static charge density variation. Recent experiments in high magnetic fields that seem to induce charge density waves in some systems have rekindled the interest in static inhomogeneities. It has long been known that excessive NMR linewidths can be observed in all cuprates, but with the exception of a few materials. However, the relation of the quadrupolar linewidths with respect to variations of the charge density in the cuprates is not understood. Here, we investigate YBa₂Cu₃O₇ and we find even in a moderate magnetic field that below about 200 K, i.e., well above T _c, a temperature dependent NMR linewidth appears that must be related to incipient static charge density variations. We argue that this establishes field induced charge density variation as a more general phenomenon in the cuprates. In view of the very recent understanding of the relation between the hole distribution in the CuO₂ plane and T _c, it is argued that charge density variations are ubiquitous, but appear not related to the maximum T _c.     

Thermocapillary Convection in Floating Zone with Axial Magnetic Fields

Numerical simulations on the effects of axial magnetic fields on the thermocapillary convection in a liquid bridge of silicone-oil-based ferrofluid under zero gravity have been conducted. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the mass conserving level set approach is used to capture the free surface deformation of the liquid bridge. The obvious effects of the magnetic fields on the flow pattern as well as the velocity and temperature distributions in the liquid bridge can be detected. The axial magnetic fields suppress the thermocapillary convection and a stagnant flow zone is formed between the circulating flow and the symmetric axis as the magnetic fields increase. The axial magnetic fields affect not only the velocity level inside the liquid bridge but also the velocity level on the free surface. The temperature contours near the free surface illustrates conduction-type temperature profiles at moderate strength fields.