in Fig. 4, all the Pt/LCO hybrids were patterned into Hall bar geometry and the electric current is applied along the $x$-axis. The $\theta_{xy}$, $\theta_{xz}$, and $\theta_{yz}$ are defined as angles between the applied magnetic field and the electric current. The $\theta_{xy}$ scan accesses the longitudinal ($\rho_\parallel$, $H \parallel$ $x$) and the transverse resistivity ($\rho_\textup{T}$, $H \parallel$ $y$), while the $\theta_{xz}$ and $\theta_{yz}$ scans can reach the perpendicular resistivity ($\rho_\perp$, $H \parallel$ $z$).

![(Color online) Planar Hall resistance under various magnetic fields at temperatures of 100 K (a) and 10 K (b) for Pt(2 nm)/LCO/LAO hybrid. The solids lines through the data are fits to R$_\textup{xy}$ = R$_1$sin$\theta$cos$\theta$. Angular dependence of the Hall resistance R$_\textup{xy}$ under various magnetic fields at temperatures of 100 K (c) and 10 K (d) for Pt(2 nm)/LCO/LAO hybrid; The magnetic field sweeps within $yz$-plane.[]{data-label="fig7"}](Fig7.eps){width="3.0in"}

In this section, we discuss the results of transverse Hall resistance R$_\textup{xy}$ of Pt/LCO hybrids with perpendicular magnetic field ranging from -70 KOe to 70 KOe and temperature ranging from 2 K to 300 K. In Pt thin film, the ordinary hall resistance (OHR) R$_\textup{OHR}$, which is proportional to the external field, is subtracted from the measured R$_\textup{xy}$, i.e., R$_\textup{EHR}$ = 