Magnetoelectric properties of epitaxialFe3O4thin films on (011) PMN-PT piezosubstrates

We determine the magnetic and magnetotransport properties of 33 nm thick ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ films epitaxially deposited by rf-magnetron sputtering on unpoled (011) ${[{\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_{3}]}_{0.68}\ensuremath{-}{[{\mathrm{PbTiO}}_{3}]}_{0.32}$ (PMN-PT) substrates. The magnetoresistance (MR), as well as the magnetization reversal, strongly depend on the in-plane crystallographic direction of the epitaxial (011) ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ film and strain. When the magnetic field is applied along [100], the magnetization loops are slanted and the sign of the longitudinal MR changes from positive to negative around the Verwey transiti…