Muon Spin Rotation in Heavy Electron Pauli Limited Superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli limited heavy electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to Muon Spin Rotation ($\mu$SR) experiment. On the basis of the Ginzburg-Landau expansion for the superconductor free energy we study the evolution with respect to external field of the static linewidth both in the limit of independent vortices (low magnetic field) and in the near $H_\mathrm{c2}^\mathrm{p}(T)$ regime by using an extension of the Abrikosov analysis to Pauli limited superconductors. We conclude that in the Ginzburg-Landau regime with Pauli limit, the electrodynamics of the vortex lattice predicts anomalous variations with applied field of the static linewidth which is a result of the spin response contribution to screening supercurrents that dominates the usual charge response. The model is proposed as a benchmark for comparison with possible other effects including vortex core localized states or interplay with magnetism.