High spin-polarization in the low Curie temperature complex itinerant ferromagnet EuTi$_{1-x}$Nb$_x$O$_3$

The physical systems with ferromagnetism and "bad" metallicity hosting unusual transport properties are playgrounds of novel quantum phenomena. Recently EuTi$_{1-x}$Nb$_x$O$_3$ emerged as a ferromagnetic system where non-trivial temperature dependent transport properties are observed due to coexistence and competition of various magnetic and non-magnetic scattering processes. In the ferromagnetic state, the resistivity shows a $T^2$ temperature dependence possibly due to electron-magnon scattering and above the Curie temperature $T_c$, the dependence changes to $T^{3/2}$ behaviour indicating a correlation between transport and magnetic properties. In this paper, we show that the transport spin-polarization in EuTi$_{1-x}$Nb$_x$O$_3$, a low Curie temperature ferromagnet, is as high ($\sim 40\%$) as that in some of the metallic ferromagnets with high Curie temperatures. In addition, owing to the low Curie temperature of EuTi$_{1-x}$Nb$_x$O$_3$, the temperature ($T$) dependence of $P_t$ could be measured systematically up to $T_c$ which revealed a proportionate relationship with magnetization $M_s$ vs. $T$. This indicates that such proportionality is far more universally valid than the ferromagnets with ideal parabolic bands. Furthermore, our band structure calculations not only helped understand the origin of such high spin polarization in EuTi$_{1-x}$Nb$_x$O$_3$ but also provided a route to estimate the Hubbard $U$ parameter in complex metallic ferromagnets in general using experimental inputs.