Anomalous field evolution of the mixed-state linewidth in the second superconducting dome of LaFeAsO${}_{1-x}{M}_x$ ($M=\mathrm{F},\mathrm{H}$)

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${}_{1-x}{M}_x$ ($M=\mathrm{F},\mathrm{H}$) family, respectively. Below the superconducting transition temperature $T_{\mathrm{c}}$, the linewidth of the internal-field distribution increases in both samples, indicating the formation of a vortex lattice. Above $T_{\mathrm{c}}$, 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 ${\sigma }_{\mathrm{s}\mathrm{c}}$ exhibits qualitatively different field dependences in the two samples. At 4K, the SC1 ($x_{\mathrm{F}}=0.11$) sample shows the expected monotonic decrease with increasing field, whereas the SC2 ($x_{\mathrm{H}}=0.25$) sample develops a pronounced local maximum near 3T. A contour representation of ${\sigma }_{\mathrm{s}\mathrm{c}}(T,H)$ further reveals a ridge of local maxima whose field position, $H_{\sigma ,\max }(T)$, shifts to lower fields upon warming and disappears near $T_{\mathrm{c}}$. 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.