that the UCMR in the form of Eq. (1) persists even after the magnetization is saturated [@Miao2014]. Such high field UCMR and unusual EHR data indicate that the transport properties in NM/FMI hybrids are far from understood.

Up to now, most of the UCMR has been reported in the Y$_3$Fe$_5$O$_{12}$ (YIG)-based NM/FMI hybrids [@Miao2014; @Althammer2013; @Isasa2014; @Lin2014; @Hahn2013]. The large difference of magnitude of UCMR observed in Pt/YIG indicates the importance of interface quality [@Althammer2013]. In order to clarify the nature of the UCMR and EHR, it is highly desirable to investigate other NM/FMI hybrids. Ferromagnetic (FM) transition below $T_\textup{C} \approx$ 85 K has been recently observed in a perovskite-type LaCoO$_3$ (LCO) epitaxial film [@Fuchs2007; @Fuchs2008; @Herklotz2009; @Mehta2015], and its FM insulating ground state has been theoretically proposed and experimentally observed [@Freeland2008; @Hsu2012]. In contrast to the YIG film, which exhibits extreme high Curie temperature ($T_\textup{C} \approx$ 540 K) [@Uchida2015], it is much easier to investigate the difference of spin transport properties between the paramagnetic and ferromagnetic states in LCO-based hybrids. Moreover, the LCO exhibits much simper crystal structure and can be deposited on various single crystalline substrates, and its Curie temperature can be tuned by epitaxial strain [@Fuchs2008]. We 