Superconductivity (SC) in the Ba-122 family of iron-based compounds can be controlled by aliovalent or isovalent substitutions, applied external pressure, and strain, the combined effects of which are sometimes studied within the same sample. Most often, the result is limited to a shift of the SC dome to different doping values. In a few cases, the maximum SC transition at optimal doping can also be enhanced. In this work, we study the combination of charge doping together with isovalent P substitution and strain by performing ionic gating experiments on BaFe$_2$(As$_{0.8}$P$_{0.2}$)$_2$ ultrathin films. We show that the polarization of the ionic gate induces modulations to the normal-state transport properties that can be mainly ascribed to surface charge doping. We demonstrate that ionic gating can only shift the system away from the optimal conditions, as the SC transition temperature is suppressed by both electron and hole doping. We also observe a broadening of the resistive transition, which suggests that the SC order parameter is modulated nonhomogeneously across the film thickness, in contrast with earlier reports on charge-doped standard BCS superconductors and cuprates.
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