Displacement-Type Ferroelectricity with Off-Center Magnetic Ions in Perovskite ${\mathrm{Sr}}_{1\mathbf{-}\mathit{x}}{\mathrm{Ba}}_x{\mathrm{MnO}}_3$

We report a ferroelectric transition driven by the off-centering of magnetic ${\mathrm{Mn}}^{4+}$ ions in antiferromagnetic Mott insulators ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{MnO}}_3$ with a perovskite structure. As $x$ increases, the perovskite lattice shows the typical soft-mode dynamics, as revealed by the momentum-resolved inelastic x-ray scattering and far-infrared spectroscopy, and the ferroelectricity shows up for $x\ge 0.45$. The observed polarization is comparable to that for a prototypical ferroelectric ${\mathrm{BaTiO}}_3$. We further demonstrate that the magnetic order suppresses the ferroelectric lattice dilation by $\sim 70\%$ and increases the soft-phonon energy by $\sim 50\%$, indicating the largest magnetoelectric effects yet attained.

Figure 1

(a) Phase diagram for ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{MnO}}_3$ as a function of $x$. $G$-AFM, FE, and MF denote $G$-type antiferromagnetic, ferroelectric, and multiferroic phases, respectively. $T_{\mathrm{N}}$ was deduced from the temperature profiles of magnetization [21]. (b) Variation in the lattice constant at 300 K. (c) Variation in the soft-mode energy (${\omega }_{\mathrm{TO}1}$) at 300 K at the wave vector of $q=0$ and 0.11, determined from the optical spectra and inelastic x-ray scattering, respectively. The linewidth (${\gamma }_{\mathrm{TO}1}$) at $q=0.11$ is also plotted. (d) Variation in dielectric constant ${\epsilon }_1$ (left axis) and loss $\tan \delta$ (right axis) at 4 K. For $x=0.2$, 0.3, and 0.4 with a relatively large leakage current (larger $\tan \delta$), the values at 1 GHz are plotted to minimize the carrier hopping contribution [21], while those at 1 MHz are plotted for other well-insulating compounds.

Figure 2

(a) Imaginary part of dielectric permittivity ${\epsilon }_2$ as a function of photon energy $\omega$ for $x=0–0.3$, deduced from the reflectivity measurements ($q=0$). Plots of the inelastic-x-ray-scattering intensity at 300 K in the energy-wave-vector ($\omega \mathrm{\text{−}}q$) plane in the [110] ($\Gamma \mathrm{\text{−}}M$) direction for (b) $x=0$, (c) 0.2, (d) 0.3, and (e) 0.4, measured around 005 reflection. The closed symbols denote the phonon frequency ${\omega }_q$, obtained by the fitting based on the damped harmonic oscillators [21]. The points at $q=0$ were determined from the optical spectra.

Figure 3

(a) Remnant $P\mathrm{\text{−}}E$ hysteresis curve (2 K, 1 kHz, 0 T) along [001] in the pseudocubic setting for $x=0.5$, where the specimen was heavily twinned. The nonswitching components arising from leakage current and field-induced polarization are subtracted [21]. Temperature profiles of (b) magnetization $M$ at 0.5 T and (c) tetragonality $c/a$ for $x=0.5$. The values of $c/a$ were estimated from the split of the 002/200 peaks in powder x-ray diffraction. Schematic diagrams for the crystal structure at (d) 50 and (e) 225 K, deduced from the single-crystal x-ray diffraction. Each atomic displacement is shown on the basis of the Mn-centered unit cell.

Figure 4

(a) Optical conductivity $\sigma$ as a function of photon energy $\omega$ at various temperatures for $x=0.3$. (b) Temperature dependence of soft-mode (TO1) energy ${\omega }_{\mathrm{TO}1}$ and linewidth ${\gamma }_{\mathrm{TO}1}$ for $x=0.3$, obtained by fitting the reflectivity spectra to the Lorentz oscillator model [21].