  Electric control of magnetic properties is an important challenge for modern
magnetism and spintronic development. In particular, an ability to write
magnetic state electrically would be highly beneficial. Among other methods,
the use of electric field induced deformation of piezoelectric elements is a
promising low-energy approach for magnetization control. We investigate the
system of piezoelectric substrate Pb[Zr$_x$Ti$_{1-x}$]O$_3$ with CoFe
overlayers, extending the known reversible bistable electro-magnetic coupling
to surface and multistate operations, adding the initial state reset
possibility. Increasing the CoFe thickness improves the magnetoresistive
sensitivity, but at the expenses of decreasing the strain-mediated coupling,
with optimum magnetic thin film thickness of the order of 100 nm. The simplest
resistance strain gauge structure is realized and discussed as a multistate
memory cell demonstrating both resistive memory (RRAM) and magnetoresistive
memory (MRAM) functionalities in a single structure.
