Interplay between morphology and magnetoelectric coupling in Fe/PMN-PT multiferroic heterostructures studied by microscopy techniques

A ferromagnetic (FM) thin film deposited on a substrate of $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\text{\ensuremath{-}}{\mathrm{PbTiO}}_{3}$ (PMN-PT) is an appealing heterostructure for the electrical control of magnetism, which would enable nonvolatile memories with ultralow-power consumption. Reversible and electrically controlled morphological changes at the surface of PMN-PT suggest that the magnetoelectric effects are more complex than the commonly used ``strain-mediated'' description. Here we show that changes in substrate morphology intervene in magnetoelectric coupling as a key parameter interplaying with strain. Magnetic-sensitive microscopy techniques are used to study magnetoelectric coupling in Fe/PMN-PT at different length scales, and compare different substrate cuts. The observed rotation of the magnetic anisotropy is connected to the changes in morphology, and mapped in the crack pattern at the mesoscopic scale. Ferroelectric polarization switching induces a magnetic field-free rotation of the magnetic domains at micrometer scale, with a wide distribution of rotation angles. Our results show that the relationship between the rotation of the magnetic easy axis and the rotation of the in-plane component of the electric polarization is not straightforward, as well as the relationship between ferroelectric domains and crack pattern. The understanding and control of this phenomenon is crucial to develop functional devices based on FM/PMN-PT heterostructures.