Multiferroic phase diagram of E -type RMnO3 films studied by neutron and x-ray diffraction

We present a generalized multiferroic phase diagram for orthorhombic $R{\mathrm{MnO}}₃\phantom{\rule{4pt}{0ex}}(R=\mathrm{Gd}--\mathrm{Lu})$ based on coherently grown thin films. The magnetic order was identified by neutron-diffraction and resonant soft x-ray scattering experiments. For large $R$-ions $(R=\mathrm{Gd}--\mathrm{Dy})$, the transition temperature to a long-range ordered antiferromagnetic phase is only weakly dependent on the $R$-ion radius, but decreases monotonically with decreasing $R$-ion radius for films with $R=\mathrm{Ho}--\mathrm{Lu}$. The antiferromagnetic phase is characterized by an incommensurate order of the ${\mathrm{Mn}}³⁺$ spins, which successively locks into a commensurate $E$-type state. These findings confirm a uniform multiferroic ground state independent of the $R$ ion and are in excellent agreement with predicted properties of strain-induced multiferroicity in these materials. In particular, strong variation of multiferroic properties in these epitaxial films compared to bulk highlights the tuning ability of strain.