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.
In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (lambda_a), the penetration depth anisot
ropy (gamma=lambda_c/lambda_a) and the temperature dependence of 1/lambda_i^2 (i=a,c) were studied in single crystals. A strong decrease of lambda_a with pressure was observed, while gamma and lambda_i^2(0)/lambda_i^2(T) are pressure independent. A linear relationship between 1/lambda_a^2(270 mK) and Tc was also found. The large decrease of lambda_a with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.
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)$Pr(x)Ba2Cu3O7 systems, where R is a rare earth element.
The magneto-electric (ME) coupling on spin-wave resonances in single-crystal Cu2OSeO3 was studied by a novel technique using electron spin resonance combined with electric field modulation. An external electric field E induces a magnetic field compon
ent mu_0 H^i = gamma E along the applied magnetic field H with gamma=0.7(1) mu T/(V/mm) at 10 K. We found that ME coupling strength gamma is temperature dependent and highly anisotropic. gamma(T) nearly follows that of spin susceptibility J(T) and rapidly decreases above the Curie temperature Tc. The ratio gamma/J monotonically decreases with increasing temperature without an anomaly at Tc.
We report on muon spin rotation studies of the noncentrosymmetric heavy fermion antiferromagnet CeRhSi$_3$. A drastic and monotonic suppression of the internal fields, at the lowest measured temperature, was observed upon an increase of external pres
sure. Our data suggest that the ordered moments are gradually quenched with increasing pressure, in a manner different from the pressure dependence of the Neel temperature. At $unit{23.6}{kbar}$, the ordered magnetic moments are fully suppressed via a second-order phase transition, and $T_{rm{N}}$ is zero. Thus, we directly observed the quantum critical point at $unit{23.6}{kbar}$ hidden inside the superconducting phase of CeRhSi$_3$.
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.
