field was applied parallel (perpendicular) to the film surface.[]{data-label="fig2"}](Fig2.eps){width="3.4in"}

EXPERIMENTAL DETAILS
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The Pt/LCO hybrids were prepared in a combined ultra-high vacuum (10$^{-9}$ Torr) pulse laser deposition (PLD) and magnetron sputter system. The high quality LCO films with a thickness of approximately 50 nm were epitaxially grown on various (001)-orientated single crystalline substrates via PLD technique, i.e., LaAlO$_3$ (LAO), (La,Sr)(Al,Ta)O$_3$ (LSAT), and SrTiO$_3$ (STO). The stoichiometric sinter LCO target was used for epitaxial deposition. The deposition temperature and the oxygen background pressure were kept at 750 $^\circ$C and 50 mTorr, respectively. After deposition, the films were annealed at this deposition condition for one hour to ensure a complete and homogeneous oxygenation. The polycrystalline Pt films were sputtered at room temperature in 4 mTorr argon atmosphere in an in situ process with the Pt thickness in a range of 2 nm $\leq$ t$_\textup{Pt}$ $\leq$ 15 nm. All films were patterned into Hall bar geometry (central area: 0.3 mm $\times$ 10 mm and electrode: 0.3 mm $\times$ 1 mm). The thickness and crystal structure of films were characterized by using Bruker D8 Discover high-resolution x-ray diffractometer (HRXRD). The thickness was estimated by using the software package LEPTOS (Bruker AXS). The surface topography 