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We present a study of the upper critical field, H$_{c2}$, of pristine andproton-irradiated RbEuFe$_4$As$_4$ crystals in pulsed magnetic fields of up to65 T. The data for H$_{c2}$ reveal pronounced downwards curvature, particularlyfor the in-plane field orientation, and a superconducting anisotropy thatdecreases with decreasing temperature. These features are indicative of Pauliparamagnetic limiting. For the interpretation of these data, we use a model ofa clean single-band superconductor with an open Fermi surface in the shape of awarped cylinder, which includes strong paramagnetic limiting. Fits to the datareveal that the in-plane upper critical field is Pauli paramagnetic limited,while the out-of-plane upper critical field is orbitally limited and that theorbital and paramagnetic fields have opposite anisotropies. A consequence ofthis particular combination is the unusual inversion of the anisotropy,$H_{c2}^{ab} < H_{c2}^c$, of the irradiated sample at temperatures below 10 K.The fits also yield an in-plane Maki parameter, $\alpha_M^{110} \approx$ 2.6,exceeding the critical value for the formation of theFulde-Ferrell-Larkin-Ovchinnikov state. Nevertheless, the current measurementsdid not reveal direct evidence for the occurrence of this state.

Anisotropic upper critical field of pristine and proton-irradiated single crystals of the magnetically ordered superconductor RbEuFe$_4$As$_4$