This Letter determined that EuTiO3, when appropriately strained, becomes a strong ferroelectric ferromagnet, in agreement with prediction. Strong ferroelectrics are proper ferroelectrics, having polarization as their order parameter, with high paraelectric-to-ferroelectric transition temperatures (Tc). Such ferroelectrics are manifested by a high Tc and a high peak at Tc in the dielectric constant versus temperature behaviour, signifying that ferroelectricity is driven by the soft mode, which is indicative of proper ferroelectricity. Our measurements of strained EuTiO3 demonstrate both of these characteristics (shown in Fig. 3 of our Letter), and led us to conclude that strained EuTiO3 is a strong ferroelectric. In contrast, all well-established prior single-phase ferroelectric ferromagnets are improper or pseudoproper ferroelectrics (that is, with weak ferroelectricity resulting in minuscule Ps). We did not present Ps values in our Letter. Second harmonic generation measurements do not provide quantitative values of Ps and attempts to determine Ps via pyroelectric measurements (Yan, L., Li, J. F. & Viehland, D., personal communication)1 resulted in unphysically high values, presumably owing to electrical leakage. Nonetheless, the magnitude of the Ps of our strained EuTiO3 films can be estimated as follows. In their classic work, Abrahams, Kurtz, and Jamieson1 established a correlation between Ps and Tc for displacive ferroelectrics. By studying numerous displacive ferroelectrics they found1
where Tc is the paraelectric-to-ferroelectric transition temperature in K, Δz is the atomic displacement of the ‘homopolar’ metal atom in Å, and Ps is the spontaneous polarization of the ferroelectric in μC cm−2. Combining these equations to eliminate Δz allows Ps to be estimated from Tc in displacive ferroelectrics. The huge anomaly of the soft optical phonon near Tc that we observe (Supplementary Fig. 1 of our Letter) shows that strained EuTiO3 is a displacive ferroelectric, making the aforementioned correlation applicable. Plugging in our measured value of Tc (Fig. 3 in our Letter) yields Ps = 29 ± 2 μC cm−2 for our strained EuTiO3 films from this established correlation. This rough estimate is consistent with our first-principles theoretical predictions—Ps = 21 μC cm−2 for EuTiO3 under +1.1% biaxial tension, corresponding to the strain of our commensurate EuTiO3 films grown on (110) DyScO3. Thus, the data in our Letter shows that appropriately strained EuTiO3 is a strong ferroelectric ferromagnet.