Competition between the modification of intrinsic superconducting properties and the pinning landscape under external pressure in CaKFe$_4$As$_4$ single crystals

Measurements of low field magnetization, trapped flux magnetization and 5 K flux creep in single crystal of CaKFe$_4$As$_4$ under pressure up to 7.5 GPa in a diamond pressure cell are presented. The observed evolution of the temperature dependence of the self-field critical current and slowing down of the base temperature flux creep rate are explained within the two sources of pinning hypothesis involving presence of CaKFe$_4$As$_4$ intergrowths suggested in the literature. Above the half collapsed tetragonal structural transition under pressure, where superconductivity is non-bulk or absent, critically diminished or no diamagnetism and flux trapped magnetization were observed.