'S. Zhang'
- 'Run-Wei Li'
title: 'Extraordinary Hall resistance and unconventional magnetoresistance in Pt/LaCoO$_3$ hybrids'
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\[sec:level1\]INTRODUCTION
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The interplay between spin and charge transport in nonmagnetic metal/ferromagnetic insulator (NM/FMI) hybrids gives rise to various interesting phenomena, such as spin injection [@Ohno1999; @Jedema2001], spin pumping [@Heinrich2011; @Rezende2012; @Kajiwara2010], and spin Seebeck [@Uchida2008; @Uchida2010]. The previous investigations on NM/FMI hybrids, e.g., Pt/Y$_3$Fe$_5$O$_{12}$, Pt/CoFe$_2$O$_4$, Pd/Y$_3$Fe$_5$O$_{12}$, and Ta/Y$_3$Fe$_5$O$_{12}$, demonstrated a new-type of magnetoresistance (MR) [@Miao2014; @Althammer2013; @Isasa2014; @Lin2014; @Hahn2013] in which the resistivity of the film, $\rho$, has an unconventional angular dependence, namely, $$\rho = \rho_0 - \Delta \rho \left[\hat{\bf m} \cdot (\hat{\bf z}\times \hat{\bf j}) \right]^2$$ where $\hat{\bf m}$ and $\hat{\bf j}$ are unit vectors in the directions of the magnetization and the current, respectively, and $\hat{\bf z}$ represents the normal vector perpendicular to the plane of the layers. The above unusual angular dependent resistivity differs from the conventional magnetoresistance (CMR) in which $\rho = \rho_0 + \Delta \rho (\hat{\bf m} \cdot \hat{\bf j})^2$, and thus several theoretical models have been developed to explain the effect. One of the most successful models is spin Hall magnetoresistance (SMR) which is built on the spin Hall and inverse spin Hall effects [@Hirsch1999; @Wunderlich2005; @Kato2004; 