The quantitative understanding of converse magnetoelectric effects, i.e., the variation of the magnetization as a function of an applied electric field, in extrinsic multiferroic hybrids is a key prerequisite for the development of future spintronic
devices. We present a detailed study of the strain-mediated converse magnetoelectric effect in ferrimagnetic Fe3O4 thin films on ferroelectric BaTiO3 substrates at room temperature. The experimental results are in excellent agreement with numerical simulation based on a two-region model. This demonstrates that the electric field induced changes of the magnetic state in the Fe3O4 thin film can be well described by the presence of two different ferroelastic domains in the BaTiO3 substrate, resulting in two differently strained regions in the Fe3O4 film with different magnetic properties. The two-region model allows to predict the converse magnetoelectric effects in multiferroic hybrid structures consisting of ferromagnetic thin films on ferroelastic substrates.
TbMnO$_{3}$ films have been grown under compressive strain on (001)-oriented SrTiO$_{3}$ crystals. They have an orthorhombic structure and display the (001) orientation. With increasing thickness, the structure evolves from a more symmetric (tetragon
al) to a less symmetric (bulk-like orthorhombic) structure, while keeping constant the in-plane compression thereby leaving the out-of-plane lattice spacing unchanged. The domain microstructure of the films is also revealed, showing an increasing number of orthorhombic domains as the thickness is decreased: we directly observe ferroelastic domains as narrow as 4nm. The high density of domain walls may explain the induced ferromagnetism observed in the films, while both the decreased anisotropy and the small size of the domains could account for the absence of a ferroelectric spin spiral phase.
We report on an extensive investigation of the multiferroic compound TbMnO$_3$. Non-resonant x-ray magnetic scattering (NRXMS) revealed a dominant $A$-type domain. The temperature dependence of the intensity and wavevector associated with the incomme
nsurate magnetic order was found to be in good agreement with neutron scattering data. XRS experiments were performed in the vicinity of the Mn $K$ and Tb $L_3$ edges in the high-temperature collinear phase, the intermediate temperature cycloidal/ferroelectric phase, and the low-temperature phase. In the collinear phase resonant $E1-E1$ satellites were found at the Mn $K$ edge associated with $A$-type but also $F$-type peaks. The azimuthal dependence of the $F$-type satellites (and their absence in the NRXMS experiments) indicates that they are most likely non-magnetic in origin. We suggest instead that they may be associated with an induced charge multipole. At the Tb $L_3$ edge resonant $A$- and $F$-type satellites ($E1-E1$) were observed in the collinear phase. These we attribute to a polarisation of the Tb 5$d$ states by the ordering of the Mn sublattice. In the cycloidal/ferroelectric phase a new set of resonant satellites appear corresponding to $C$-type order. These appear at the Tb $L_3$ edge only. In addition to a dominant $E1-E1$ component in the $sigma-pi^prime$ channel, a weaker component is found in the pre-edge with $sigma-sigma^prime$ polarization. Calculations of the XRS were performed using the $FDMNES$ code showing that the unrotated $sigma-sigma^prime$ component of the Tb $L_3$ $C$-type peaks appearing in the ferroelectric phase contains a contribution from a multipole that is odd with respect to both space and time, known in various contexts as the anapole.
