Anomalous field evolution of the mixed-state linewidth in the second superconducting dome of LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$)
We report a transverse-field muon-spin rotation/relaxation ($\mu$SR) study of the internal-field distribution in the mixed state of LaFeAsO$_{0.89}$F$_{0.11}$ and LaFeAsO$_{0.75}$H$_{0.25}$, representative of the first (SC1) and second (SC2) superconducting domes of the LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$) family, respectively. Below the superconducting transition temperature $T_{\rm c}$, the linewidth of the internal-field distribution increases in both samples, indicating the formation of a vortex lattice. Above $T_{\rm c}$, the linewidth remains field dependent and increases approximately linearly with field, consistent with broadening of the powder spectrum caused by an anisotropic Knight shift. After subtraction of this normal-state contribution, the superconducting linewidth $\sigma_{\rm sc}$ exhibits qualitatively different field dependences in the two samples. At 4K, the SC1 ($x_{\rm F}=0.11$) sample shows the expected monotonic decrease with increasing field, whereas the SC2 ($x_{\rm H}=0.25$) sample develops a pronounced local maximum near 3T. A contour representation of $\sigma_{\rm sc}(T,H)$ further reveals a ridge of local maxima whose field position, $H_{\sigma,\max}(T)$, shifts to lower fields upon warming and disappears near $T_{\rm c}$. The anomalous field evolution observed in the SC2 sample is consistent with an additional field-induced contribution associated with enhanced Pauli-paramagnetic effects, highlighting the distinct electronic character of the two superconducting domes.