Magnetic field distribution and characteristic fields of the vortex lattice for a clean superconducting niobium sample in an external field applied along a three-fold axis

TL;DR

This study investigates the magnetic field distribution in the vortex lattice of a clean niobium superconductor using TF-$mu$SR, establishing the applicability of Delrieu's model across various temperature and field regimes.

Contribution

It demonstrates that Delrieu's analytical model, combined with phenomenological parameter formulas, reliably describes the vortex lattice in clean BCS superconductors over a wide range of conditions.

Findings

Experimental validation of Delrieu's model for vortex lattice fields.

Identification of temperature and field regions corresponding to different theoretical models.

Reasonable understanding of experimental results via numerical solutions of Eilenberger's equations.

Abstract

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 temperatures and fields. The experimental data have been analyzed with the Delrieu's 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 Delrieu's, Ginzburg-Landau's, and Klein's regions of the vortex lattice. Using the numerical solution of the quasiclassical Eilenberger's equation the experimental results have been reasonably understood. They should apply to all clean BCS superconductors. The analytical Delrieu's 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 Abrikosov's limit is contained in it.