We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $gamma_lambda(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superc
onductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $Delta(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $Delta(T)/Delta(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {bf 131}, 1 (2003), which simplifies considerably the evaluation of $gamma_lambda(T)$. Of particular interest is mixed order parameters of two symmetries for which $gamma_lambda(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $Delta_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $Delta$.
The anisotropic London equations taking into account the normal currents are derived and applied to the problem of the surface impedance in the Meisner state of anisotropic materials. It is shown that the complex susceptibility of anisotropic slab de
pends on the orientation of the applied microwave field relative to the crystal axes. In particular, the anisotropic sample in the microwave field is subject to a torque, unless the field is directed along with one of the crystal principle axes.
We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies $gamma_H$ of the upper critical field and $gamma_lambda$ of the London penetration depth depend on temperature, the feat
ure commonly attributed to multi-band superconductors. The parameters $gamma_H$ and $gamma_lambda$ may have opposite temperature dependencies or may change in the same direction depending on Fermi surface shape and on character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.
Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating total magnet
ic moment by integrating the magnetic induction obtained from a full three dimensional solution of the Maxwell equations using adaptive mesh. The results are relevant for superconductors (and conductors in AC fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse field as well as infinite rectangular and elliptical cross-section strips.
A two-band model with repulsive interband coupling and interband {it transport} (potential) scattering is considered to elucidate their effects on material properties. In agreement with previous work, we find that the bands order parameters $Delta_{1
,2}$ differ and the large is at the band with a smaller normal density of states (DOS), $N_{n2}<N_{n1}$. However, the bands energy gaps, as determined by the energy dependence of the DOS, are equal due to scattering. For each temperature, the gaps turn zero at a certain critical interband scattering rate, i.e. for strong enough scattering the model material becomes gappless. In the gapless state, the DOS at the band 2 is close to the normal state value, whereas at the band 1 it has a V-shape with non-zero minimum. When the normal bands DOS are mismatched, $N_{n1} e N_{n2}$, the critical temperature $T_c$ is suppressed even in the absence of interband scattering, $T_c(N_{n1})$ has a dome-like shape. With increasing interband scattering, the London penetration depth at low temperatures evolves from being exponentially flat to the power-law and even to near linear behavior in the gapless state, the latter being easily misinterpreted as caused by order parameter nodes.
By evaluating the upper and thermodynamic critical fields, $H_{c2}$ and $H_c$, and their ratio $H_{c2}/H_c $ at arbitrary temperatures, we argue that situations are possible when a type-II material is transformed to type-I by adding magnetic impurities.
A single crystal of isovalently substituted Ba(Fe$_{1-x}$Ru$_{x}$)$_2$As$_2$ ($x=0.24$) was sequentially irradiated with 2.5 MeV electrons up to a maximum dose of $2.1 times 10^{19}$ electrons/cm^2. The electrical resistivity was measured textit{in -
situ} at $T=$22 K during the irradiation and textit{ex - situ} as a function of temperature between subsequent irradiation runs. Upon irradiation, the superconducting transition temperature, $T_c$, decreases and the residual resistivity, $rho_0$, increases. We find that electron irradiation leads to the fastest suppression of $T_c$ compared to other types of artificially introduced disorder, probably due to the strong short-range potential of the point-like irradiation defects. A more detailed analysis within a multiband scenario with variable scattering potential strength shows that the observed $T_c$ vs. $rho_0$ is fully compatible with $s_pm$ pairing, in contrast to earlier claims that this model leads to a too rapid a suppression of $T_c$ with scattering.
In- and out-of-plane magnetic penetration depths were measured in three iron-based pnictide superconducting systems. All studied samples of both 122 systems show a robust power-law behavior, $lambda (T) T^n$, with the sample-dependent exponent n=2-2.
5, which is indicative of unconventional pairing. This scenario could be possible either through scattering in a $s_{pm }$ state or due to nodes in the superconducting gap. In the Nd-1111 system, the interpretation of data may be obscured by the magnetism of rare-earth ions. The overall anisotropy of the pnictide superconductors is small. The 1111 system is about two times more anisotropic than the 122 system. Our data and analysis suggest that the iron-based pnictides are complex superconductors in which a multiband three-dimensional electronic structure and strong magnetic fluctuations play important roles.
Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions d
own to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.
Tunnel-diode resonator technique was used to study crystals of ferromagnetic re-entrant superconductor, ErRh$_{4}$B$_{4}$. At the boundary between ferromagnetism (FM) and superconductivity (SC), dynamic magnetic susceptibility, $chi(T,H)$, exhibits h
ighly asymmetric behavior upon warming and cooling as well as enhanced diamagnetism on the SC side. SC phase nucleates upon warming in a cascade of discontinuous jumps in magnetic susceptibility $chi(T,H)$, whereas FM phase develops gradually as reported in detail in cite{prozorov2008}. Here we further investigate enhanced diamagnetism. We find that when a magnetic field is applied along the magnetic easy axes, a region of enhanced diamagnetic screening is smaller than in the perpendicular orientation. A discussion of possible causes of this effect is provided.
