The field distribution in the vortex lattice of a pure niobium single crystal with an external field applied along a three-fold axis has been investigated by the transverse-field muon-spin-rotation (TF-$mu$SR) technique over a wide range of temperatu
res and fields. The experimental data have been analyzed with the Delrieus solution for the form factor supplemented by phenomenological formulas for the parameters. This has enabled us to experimentally establish the temperatures and fields for the Delrieus, Ginzburg-Landaus, and Kleins regions of the vortex lattice. Using the numerical solution of the quasiclassical Eilenbergers equation the experimental results have been reasonably understood. They should apply to all clean BCS superconductors. The analytical Delrieus model supplemented by phenomenological formulas for its parameters is found to be reliable for analyzing TF-$mu$SR experimental data for a substantial part of the mixed phase. The Abrikosovs limit is contained in it.
We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (mu SR) technique. Analysis of the mu SR data in the framework of the BCS-Gorkov theory allowed us to determine microscopic parameters and
the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
We review the magnetic form factor deduced by Delrieu from the Gorkovs equation for a Bardeen-Cooper-Schrieffer (BCS) type-II superconductor near its Bc2 phase boundary, i.e. when its magnetization is small. A numerical study of the form factor, fiel
d map, and field distribution follows. The characteristics of the transition from the low-temperature BCS to the high-temperature Ginzburg-Landau vortex lattices is studied. The exotic shape of the component field distribution and the form factor at low temperature and as a function of the external field intensity are discussed. Our numerical work should be helpful for the analysing of small angle neutron scattering and muon spin rotation vortex-lattice data recorded for BCS superconductors and maybe other superconductors in the clean limit.
We report on a study of the superconducting properties for a series of polycrystalline BaPt(4-x)Au(x)Ge12 filled skutterudite compounds for x = 0, 0.5, 0.75, and 1. Muon spin rotation (muSR) spectroscopy as well as magnetization, specific heat, and e
lectrical resistivity measurements were performed. The magnetic penetration depth lambda, the coherence length xi, and the Ginzburg-Landau parameter kappa are evaluated. The temperature dependence of the superfluid density is well described by an s-wave superconducting gap and this classical scenario is supported by the field-independent lambda. The gap-to-Tc ratio Delta/kTc increases with the Au content from 1.70 for x = 0 to 2.1(1) for x = 1. By combining muSR, magnetization, and specific heat data, we find that BaPt(4-x)Au(x)Ge12 compounds are in between the dirty and clean limits with mean free paths of the carriers l ~ xi. Interestingly, resistivity data for BaPt4Ge12 indicate a much higher upper critical field, which is probably due to defects or impurities close to the surface of the crystallites.
The effect of pressure on the copper and praseodymium magnetic order in the system Nd(1-x)$Pr(x)Ba2Cu3$O7 with x=0.3, 0.5, 0.7, and 1 was investigated by means of the muon spin rotation (muSR) technique. It was found that the effect of pressure on th
e Neel temperatures of both copper and praseodymium is positive for the whole range of Pr concentrations (0.3<x<1) studied. These findings are in contrast with a number of previous reports and clarify some of the puzzles related to the effect of pressure on superconductivity and magnetism in the praseodymium-substituted R}(1-x)$Pr(x)Ba2Cu3O7 systems, where R is a rare earth element.
The magneto-electric (ME) coupling on spin-wave resonances in single-crystal Cu2OSeO3 was studied by a novel technique using electron spin resonance combined with electric field modulation. An external electric field E induces a magnetic field compon
ent mu_0 H^i = gamma E along the applied magnetic field H with gamma=0.7(1) mu T/(V/mm) at 10 K. We found that ME coupling strength gamma is temperature dependent and highly anisotropic. gamma(T) nearly follows that of spin susceptibility J(T) and rapidly decreases above the Curie temperature Tc. The ratio gamma/J monotonically decreases with increasing temperature without an anomaly at Tc.
The pressure dependence of the magnetic penetration depth in polycrystalline samples of YBa2Cu3Ox with different oxygen concentrations x = 6.45, 6.6, 6.8, and 6.98 was studied by muon spin rotation (muSR). The pressure dependence of the superfluid de
nsity (p_s) as a function of the superconducting transition temperature Tc is found to deviate from the usual Uemura line. The ratio (dTc/dP)/(dp_s/dP) is factor of 2 smaller than that of the Uemura relation. In underdoped samples, the zero temperature superconducting gap and the BCS ratio both increase with increasing external hydrostatic pressure, implying an increase of the coupling strength with pressure. The relation between the pressure effect and the oxygen isotope effect on the magnetic penetration depth is also discussed. In order to analyze reliably the muSR spectra of samples with strong magnetic moments in a pressure cell, a special model was developed and applied.
A detailed zero and transverse field (ZF&TF) muon spin rotation (muSR) investigation of magnetism and the magneto-electric coupling in Cu2OSeO3 is reported. An internal magnetic field B_int(T=0) = 85.37(25) mT was found, in agreement with a ferrimagn
etic state below Tc = 57.0(1) K. The temperature dependence of the magnetic order parameter is well described by the relation B_int = B(0)(1-(T/Tc)^2)^b with an effective exponent b = 0.39(1) which is close to the critical exponent B ~ 1/3 for a three dimensional (3D) magnetic system. Just above Tc the muon relaxation rate follows the power low lambda (T)propto (T/Tc - 1)^omega with omega = 1.06(9), which is characteristic for 3D ferromagnets. Measurements of B_int(T) with and without an applied electrostatic field E = 1.66 x 10^5 V/m suggest a possible electric field effect of magnitude Delta Bv = Bv(0 V)-Bv(500 V) = - 0.4(4) mT.
Zero and longitudinal field muon spin rotation (muSR) experiments were performed on the superconductors PrPt4Ge12 and LaPt4Ge12. In PrPt4Ge12 below Tc a spontaneous magnetization with a temperature variation resembling that of the superfluid density
appears. This observation implies time-reversal symmetry (TRS) breaking in PrPt4Ge12 below Tc = 7.9 K. This remarkably high Tc for an anomalous superconductor and the weak and gradual change of Tc and of the related specific heat anomaly upon La substitution in La_(1-x)Pr_xPt_4Ge_(12) suggests that the TRS breaking is due to orbital degrees of freedom of the Cooper pairs.
A detailed analysis of muon-spin rotation ($mu$SR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact so
lution of the GL model were used. The limits of the validity of these models and the reliability to extract parameters such as the magnetic penetration depth $lambda$ and the coherence length $xi$ from the experimental $mu$SR spectra were investigated. The analysis of the simulated $mu$SR spectra showed that at high magnetic fields there is a strong correlation between obtained $lambda$ and $xi$ for any value of the Ginzburg-Landau parameter $kappa = lambda/xi$. The smaller the applied magnetic field is, the smaller is the possibility to find the correct value of $xi$. A simultaneous determination of $lambda$ and $xi$ without any restrictions is very problematic, independent of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of $lambda$ is practically independent of $xi$. The second-moment method frequently used to analyze $mu$SR spectra by means of a multi-component Gaussian fit, generally yields reliable values of $lambda$ in the whole range of applied fields $ H_{c1} ll H lesssim H_{c2}$ ($H_{c1}$ and $H_{c2}$ are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering (SANS) experiments of the vortex state in type-II superconductors.
