Perovskite manganites hosting versatile multiferroic phases with symmetric and antisymmetric exchange strictions

Complete magnetoelectric (ME) phase diagrams of orthorhombic $R{\text{MnO}}_3$ with and without magnetic moments on the $R$ ions have been established. Three kinds of multiferroic ground states, the $ab$-cycloidal, the $bc$-cycloidal, and the collinear $E$-type phases, have been identified by the distinct ME responses. The electric polarization of the $E$-type phase dominated by the symmetric spin exchange $\left({\mathit{S}}_i\cdot {\mathit{S}}_j\right)$ is more than ten times as large as that of the $bc$-cycloidal phase dominated by the antisymmetric one $\left({\mathit{S}}_i\times {\mathit{S}}_j\right)$ and the ME response is enhanced near the bicritical phase boundary between these multiferroic phases of different origins. These findings may provide generic features of the magnetically induced multiferroics.

Figure 1

(Color online) Phase diagrams of $o\text{−}R{\text{MnO}}_3$ with (a) magnetic $R=\text{Gd}$, Tb, Dy, Ho, Er, Tm, and Yb, and (b) nonmagnetic $R={\text{Eu}}_{1-x}{\text{Y}}_x$ and ${\text{Y}}_{1-y}{\text{Lu}}_y$ (PM, IC, and AF denote paramagnetic, incommensurate, and antiferromagnetic, respectively), (c) polarization $P$ value at 2 K for the compounds with nonmagnetic $R$ ions ($P^{\text{HP}}$, which is multiplied by a calibration factor $\left(=6\right)$ (Ref. 26), is for $P$ of the polycrystals, and $P_a$ is for $P$ along $a$ of the single crystals taken from Ref. 9, (d) $k$ in the magnetic propagation vector $\mathit{q}=\left(0,k,1\right)$ (taken from Refs. 5, 9, 14, 15, 16, 17, 24, 25), and (e) unit-cell volume as a function of the $R$-ion radius, of which coordination number is assumed to be 8 for an orthorhombically distorted perovskite lattice. $T_{\text{N}1}$ was determined by magnetic and dielectric measurements. $T_{\text{N}2}$ and $T_{\text{N}3}$ were determined from the measurements of $P$. $T_{\text{N}1}$ and $T_{\text{N}2}$ for $R{\text{MnO}}_3$ with $R=\text{Eu}$, Gd, and Tb were taken from Ref. 7. The shaded area in (b) represents a possible phase-coexisting region.

Figure 2

(Color) Temperature dependence of polarization $P$ of $o\text{−}R{\text{MnO}}_3$ with (a) nonmagnetic $R$ and (b) magnetic $R$ in the absence of external magnetic field $B$, and (c) $P$ of $o{\text{-Eu}}_{0.1}{\text{Y}}_{0.9}{\text{MnO}}_3$ (multiplied by 2) and (d) $P$ of $o{\text{-LuMnO}}_3$ measured in external $B$ perpendicular to the applied electric field, and $\chi$ measured in external $B$ of 0.1 T on increasing temperature. $B$ was applied during the poling procedure as well as the measuring process.

Figure 3

(Color) (a) Corrected magnitude of polarization $P$ displayed as a contour plot in the phase diagram of $o\text{−}R{\text{MnO}}_3$ with nonmagnetic $R$ (${\text{Eu}}_{1-x}{\text{Y}}_x$, ${\text{Y}}_{1-y}{\text{Lu}}_y$). Magnetic-field $B$ dependence of normalized $P$ at 2 K for (b) ${\text{Eu}}_{0.6}{\text{Y}}_{0.4}{\text{MnO}}_3$, (c) ${\text{Eu}}_{0.25}{\text{Y}}_{0.75}{\text{MnO}}_3$, (d) ${\text{Eu}}_{0.1}{\text{Y}}_{0.9}{\text{MnO}}_3$, and (e) ${\text{LuMnO}}_3$ ($P$ was normalized by the value at 2 K). Schematic of the spin rotation from the $bc$ cycloidal to the $ab$ cycloidal (f) under $\mathit{B}\parallel \mathit{c}$, (g) under $\mathit{B}\parallel {\mathit{P}}_m$ deviating from $c$ to $a$ by $\varphi$, and (h) under $\mathit{B}\perp {\mathit{P}}_m$ deviating from $c$ to $a$ by $\varphi$ $\left(\varphi <\pi /4\right)$. These illustrations depict the spin rotation in a single domain both for lattice and spin. The relational expressions between $P_m$ or $P_m^{\prime }$ and $\varphi$ are shown.