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

## TL;DR

This study investigates the upper critical magnetic field of pristine and proton-irradiated RbEuFe$_4$As$_4$ superconductors, revealing anisotropic effects, Pauli limiting, and potential for exotic superconducting states.

## Contribution

It introduces a model combining orbital and paramagnetic effects to explain the anisotropic upper critical field behavior in RbEuFe$_4$As$_4$, including effects of proton irradiation.

## Key findings

- In-plane Hc2 is Pauli limited, out-of-plane Hc2 is orbitally limited.
- Superconducting anisotropy decreases with temperature, showing inversion at low T.
- The in-plane Maki parameter exceeds the threshold for FFLO state formation.

## Abstract

We present a study of the upper critical field, H$_{c2}$, of pristine and proton-irradiated RbEuFe$_4$As$_4$ crystals in pulsed magnetic fields of up to 65 T. The data for H$_{c2}$ reveal pronounced downwards curvature, particularly for the in-plane field orientation, and a superconducting anisotropy that decreases with decreasing temperature. These features are indicative of Pauli paramagnetic limiting. For the interpretation of these data, we use a model of a clean single-band superconductor with an open Fermi surface in the shape of a warped cylinder, which includes strong paramagnetic limiting. Fits to the data reveal that the in-plane upper critical field is Pauli paramagnetic limited, while the out-of-plane upper critical field is orbitally limited and that the orbital and paramagnetic fields have opposite anisotropies. A consequence of this 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 the Fulde-Ferrell-Larkin-Ovchinnikov state. Nevertheless, the current measurements did not reveal direct evidence for the occurrence of this state.