Ferroelectric field effect tuning of planar Hall effect in epitaxial La$_{\mathrm{0.8}}$Sr$_{\mathrm{0.2}}$MnO$_{\mathrm{3\thinspace }}$thin films

We report the ferroelectric field effect modulation of planar Hall effect in ultra-thin La$_{\mathrm{0.8}}$Sr$_{\mathrm{0.2}}$MnO$_{\mathrm{3\thinspace }}$(LSMO) films. We fabricated LSMO thin filmsand Pb(Zr,Ti)O$_{\mathrm{3}}$ (PZT)/LSMO heterostructures on (001) SrTiO$_{\mathrm{3}}$ substrates via off-axis RF magnetron sputtering, with high crystallinity and smooth surfaces. We worked with LSMO thin films with thickness close to the electric dead layer thickness (\textasciitilde 4 nm). The resistivity-peak temperature (T$_{\mathrm{p}})$ is \textasciitilde 170 K, significantly lower than the bulk value, with magnetoresistance (MR) ratio of 8.6 observed at 150K. We employed planar Hall effect (PHE) to study the in-plane magnetocrystalline anisotropy (MCA). The PHE resistance of LSMO films exhibits sinusoidal angular dependence in an in-plane magnetic field and shows four-fold resistance switching below a critical magnetic field of 500 Oe. This yields a biaxial magnetic anisotropy energy density of \textasciitilde 1.09 x 10$^{\mathrm{5}}$ erg/cm$^{\mathrm{3}}$, with the easy axis along \textless 110\textgreater directions. We then modulate the carrier density in the PZT/LSMO heterostructure via ferroelectric polarization switching. We will discuss the effect of electric field doping on the magnetotransport properties such as T$_{\mathrm{p}}$, MR, and MCA of the LSMO thin films.