Ferroelectric ferromagnets are exceedingly rare, fundamentally interesting multiferroic materials that could give rise to new technologies in which the low power and high speed of field-effect electronics are combined with the permanence and routability of voltage-controlled ferromagnetism1, 2. Furthermore, the properties of the few compounds that simultaneously exhibit these phenomena1, 2, 3, 4, 5 are insignificant in comparison with those of useful ferroelectrics or ferromagnets: their spontaneous polarizations or magnetizations are smaller by a factor of 1,000 or more. The same holds for magnetic- or electric-field-induced multiferroics6, 7, 8. Owing to the weak properties of single-phase multiferroics, composite and multilayer approaches involving strain-coupled piezoelectric and magnetostrictive components are the closest to application today1, 2. Recently, however, a new route to ferroelectric ferromagnets was proposed9 by which magnetically ordered insulators that are neither ferroelectric nor ferromagnetic are transformed into ferroelectric ferromagnets using a single control parameter, strain. The system targeted, EuTiO3, was predicted to exhibit strong ferromagnetism (spontaneous magnetization, ~7 Bohr magnetons per Eu) and strong ferroelectricity (spontaneous polarization, ~10 µC cm−2) simultaneously under large biaxial compressive strain9. These values are orders of magnitude higher than those of any known ferroelectric ferromagnet and rival the best materials that are solely ferroelectric or ferromagnetic. Hindered by the absence of an appropriate substrate to provide the desired compression we turned to tensile strain. Here we show both experimentally and theoretically the emergence of a multiferroic state under biaxial tension with the unexpected benefit that even lower strains are required, thereby allowing thicker high-quality crystalline films. This realization of a strong ferromagnetic ferroelectric points the way to high-temperature manifestations of this spin–lattice coupling mechanism10. Our work demonstrates that a single experimental parameter, strain, simultaneously controls multiple order parameters and is a viable alternative tuning parameter to composition11 for creating multiferroics.
Figures at a glance
Figure 1: Predicted effect of biaxial strain on EuTiO3 and our approach to imparting such strain in EuTiO3 films using epitaxy. 
a, First-principles epitaxial phase diagram of EuTiO3 strained from −2% (biaxial compression) to +2% (biaxial tension), calculated in 0.1% steps. Regions with paraelectric (PE), ferroelectric (FE), antiferromagnetic (AFM) and ferromagnetic (FM) behaviour are shown. b, c, Schematic of unstrained bulk EuTiO3 (b) and epitaxially strained thin-film EuTiO3 on the DyScO3 substrate (c), showing the in-plane expansion due to biaxial tension.
Figure 2: Structural characterization by X-ray diffraction and STEM of 22-nm-thick commensurate epitaxial EuTiO3 films. 
a, θ–2θ X-ray diffraction scans of EuTiO3 on DyScO3 (red), EuTiO3 on SrTiO3 (blue) and EuTiO3 on LSAT (green) in the vicinity of the out-of-plane 001p EuTiO3 reflection, where the subscript refers to pseudocubic indices. Clear thickness fringes are seen. The substrate peaks are denoted with asterisks. b, Annular dark-field and spectroscopic imaging of the EuTiO3-on-DyScO3 heterostructure characterized in a. Top: annular dark-field/STEM images of the structure showing a coherent interface and a low density of defects in the EuTiO3 film. Bottom: A-site and B-site elemental maps of the interface obtained by combining the Eu-M4,5 (green) and Dy-M4,5 (red) electron energy-loss spectroscopy edges, and the Ti-L2,3 (yellow) and Sc-L2,3(blue) edges extracted from two separate 256 × 256-pixel spectrum image acquisitions (one for the Eu/Dy edges, the other for the Sc/Ti edges). Intermixing is limited to one to two atomic layers at the interface.
Figure 3: Commensurate EuTiO3 strained in biaxial tension at +1.1% on DyScO3 is ferroelectric below Tc ≈ 250 K. 
a, Temperature dependence of the SHG signal of EuTiO3 on DyScO3 (red), EuTiO3 on SrTiO3 (blue) and EuTiO3 on LSAT (green). b, Experimental polar plots (points) and mm2 fit (line) with analyser along
100
p directions for EuTiO3 on DyScO3 at 5 K. The P and S polarizations are in and perpendicular to the incidence plane, respectively, where the incidence plane is formed by the sample normal and the direction of propagation of the incident light field. c, SHG hysteresis loop (top) and corresponding polarization loop (bottom) for EuTiO3 on DyScO3 at 5 K. d, Dielectric constant versus temperature for a nearly commensurate (εs = +1.1%) 100-nm-thick EuTiO3-on-DyScO3 film, determined by far-infrared reflectance spectroscopy.
Figure 4: Magnetization and capacitance measurements showing that EuTiO3 on DyScO3 is ferromagnetic below TC = 4.24 ± 0.02 K and that these two quantities are coupled. 
- ftp://mail.ihim.uran.ru/localfiles/nature09331.pdf
