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Large magnetic penetration depth and thermal fluctuations in a Ca$_{10}$(Pt$_{3}$As$_{8}$)[(Fe$_{1-x}$Pt$_{x}$)$_{2}$As$_{2}$]$_{5}$ (x=0.097) single crystal

We have measured the temperature dependence of the absolute value of the magnetic penetration depth $λ(T)$ in a Ca$_{10}$(Pt$_{3}$As$_{8}$)[(Fe$_{1-x}$Pt$_{x}$)$_{2}$As$_{2}$]$_{5}$ (x=0.097) single crystal using a low-temperature magnetic force microscope (MFM). We obtain $λ_{ab}$(0)$\approx$1000 nm via extrapolating the data to $T = 0$. This large $λ$ and pronounced anisotropy in this system are responsible for large thermal fluctuations and the presence of a liquid vortex phase in this low-temperature superconductor with critical temperature of 11 K, consistent with the interpretation of the electrical transport data. The superconducting parameters obtained from $λ$ and coherence length $ξ$ place this compound in the extreme type \MakeUppercase{\romannumeral 2} regime. Meissner responses (via MFM) at different locations across the sample are similar to each other, indicating good homogeneity of the superconducting state on a sub-micron scale.