Upper critical fields in Ba2Ti2Fe2As4O single crystals: Evidence for dominant Pauli paramagnetic effect

Abstract

We report on magneto-optical imaging and the temperature dependency of the upper critical fields ${H}_{c2}^{c}(T)$ parallel to the $c$ axis and ${H}_{c2}^{ab}(T)$ parallel to the $ab$ plane in ${\mathrm{Ba}}_{2}{\mathrm{Ti}}_{2}{\mathrm{Fe}}_{2}{\mathrm{As}}_{4}\mathrm{O}$ single crystals. These data were inferred from the measurements of the temperature-dependent resistance in static magnetic fields up to 14 T and magnetoresistance in pulsed fields up to 60 T. ${H}_{c2}$ values are found to be 52 and 50 T for $H\ensuremath{\parallel}ab$ and $H\ensuremath{\parallel}c$, respectively. These values are 1.2--1.35 times larger than the weak-coupling Pauli paramagnetic limit $({H}_{p}\ensuremath{\sim}1.84{T}_{c})$, indicating that enhanced paramagnetic limiting is essential and this superconductor is unconventional. Our observations of strong bending in the ${H}_{c2}^{ab}(T)$ curves and a nearly isotropic maximum upper critical field ${H}_{c2}^{ab}(0)\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}{H}_{c2}^{c}(0)$ support the presence of a strong Pauli paramagnetic effect. We show that the Werthamer-Helfand-Hohenberg (WHH) formula that includes the spin-orbit scattering can effectively describe the ${H}_{c2}^{ab}(T)$ curve, whereas ${H}_{c2}$ deviates from the conventional WHH theoretical model without considering the spin paramagnetic effect for the $H\ensuremath{\parallel}c$ and $H\ensuremath{\parallel}ab$ directions. For $H\ensuremath{\parallel}c$, a two-band model is required to fully reproduce the behavior of ${H}_{c2}$, while for $H\ensuremath{\parallel}ab$ the spin paramagnetic effect is responsible for the behavior of ${H}_{c2}$. The anisotropy of ${H}_{c2}$ is close to 3 near ${T}_{c}$ and decreases rapidly at lower temperatures.