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The upper critical field of multiband superconductors is an importantquantity that can reveal the details about the nature of the superconductingpairing. Here we experimentally map out the complete upper critical field phasediagram of a stoichiometric superconductor, CaKFe$_4$As$_4$, up to 90T fordifferent orientations of the magnetic field and at temperatures down to 4.2K.The upper critical fields are extremely large, reaching values close to ~3$T_c$at the lowest temperature, and the anisotropy decreases dramatically withtemperature leading to essentially isotropic superconductivity at 4.2K. We findthat the temperature dependence of the upper critical field can be welldescribed by a two-band model in the clean limit with band coupling parametersfavouring intraband over interband interactions. The large Pauli paramagneticeffects together with the presence of the shallow bands is consistent with thestabilization of an FFLO state at low temperatures in this cleansuperconductor.

Competing pairing interactions responsible for the large upper critical field in a stoichiometric iron-based superconductor, CaKFe$_4$As$_4$