Tunable Magnetoresistance and Charge Carrier Density in Cr:In2O3/PbMg1/3Nb2/3O3−PbTiO3 Ferroelectric Field-Effect Devices

We report the epitaxial growth of the $\mathrm{Cr}$-doped ${\mathrm{In}}_{2\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{O}}_{3}$ (x = 0.05) ($\mathrm{Cr}$:${\mathrm{In}}_{2}{\mathrm{O}}_{3}$) semiconducting thin films on perovskite-type (111)-oriented $0.7\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$\ensuremath{-}$0.3{\mathrm{Pb}\mathrm{Ti}\mathrm{O}}_{3}$ (PMN-PT) ferroelectric single-crystal substrates in the form of ferroelectric field-effect devices that allow us to obtain an in situ tuning of the electron carrier density and magnetoresistance (MR) as well as the resistance in a reversible and nonvolatile manner, thereby stringently disclosing the relationship between the MR and the electron carrier density. Specifically, for the thinnest 25-nm $\mathrm{Cr}$:${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ film the polarization switching of the PMN-PT from the positively polarized ${P}_{r}^{+}$ state to the negatively polarized ${P}_{r}^{\ensuremath{-}}$ state results in a large increase in the resistance and MR. Particularly, at T = 10 K, the polarization switching induces reversible and nonvolatile changes in the magnitude and sign of MR, demonstrating strong coupling between the MR and the electron carrier density. Moreover, regardless of the polarization states of PMN-PT, MR for films with different thicknesses can be quite well described by a combination of the two-band model and the semiempirical model proposed by Khosla and Fischer based on which the positive MR (PMR) and negative MR (NMR) could be disentangled into positive component [MR(+)] and negative component [MR(\ensuremath{-})], respectively. We find that the polarization-switching-induced large decrease in the PMR and the change in the sign of MR from positive to negative is mainly due to the rapid decrease in the MR(+), demonstrating that the coupling between MR(+) and electron carrier density plays a dominant role in controlling the magnitude and sign of MR.