Cross-Control of Magnetization and Polarization by Electric and Magnetic Fields with Competing Multiferroic and Weak-Ferromagnetic Phases

From our investigation of magnetoelectric properties of a multiferroic phase in ${\mathrm{Eu}}_{0.75}{\mathrm{Y}}_{0.25}{\mathrm{MnO}}_3$ competing with a weak-ferromagnetic phase in magnetic fields, we found intriguing hysteretic behaviors of physical properties with variation of temperature and magnetic field. These hysteretic behaviors arise from the kinetic arrest (dearrest) processes of the first-order multiferroic-weak-ferromagnetic transition, resulting in frozen (melted) magnetoelectric glass states with coexisting two phases. Tipping the delicate balance of two competing phases by applying electric and magnetic fields leads to a remarkable control of magnetization and electric polarization.

Figure 1

(a),(b) Crystallographic and low-$T$ Mn-spin structures of orthorhombic perovskite ${\mathrm{Eu}}_{1-x}{\mathrm{Y}}_x{\mathrm{MnO}}_3$. Magnetic ${\mathrm{Mn}}^{3+}$ ions locate at the center of octahedral ${\mathrm{O}}^{2-}$ cages. Also shown are the directions of $M$ and $P$ of canted A-type AFM (WFM) and cycloidal-spiral magnetic phases, respectively. (c) $T$ dependence of the $H_c$-induced WFM moment along the $c$ axis, $\Delta M_c$, in $H_c=5.5–7.0\mathrm{T}$ applied after zero-field cooling. (d) $T$ dependence of $P$ along the $a$ axis, $P_a$, in $H_c=5.9–7.0\mathrm{T}$. Reduction of $P_a$ in intermediate $T$ ranges correlates with the emergence of WFM moment in (c).

Figure 2

(a)–(c) $T$ dependence of $\Delta M_c$ in $H_c=5.9\mathrm{T}$, $P_a$ in $H_c=6.3\mathrm{T}$, and ${\epsilon }_a$ [$\tan \delta$ in the inset in (c)] in $H_c=6.3\mathrm{T}$, respectively. For the data in each figure, three different measurements were performed: upon warming after cooling in $H_c=0\mathrm{T}$ (ZFC-W, open circles), upon cooling in $H_c$ (FC-C, open squares), and upon warming after cooling in $H_c$ (FC-W, open triangles). $T_f$ denotes a freezing $T$. $T_c$ and $T_w$ correspond to the first-order transition $T$ between the MF and WFM phases for cooling and warming, respectively. (d)–(f) $H\mathrm{\text{−}}T$ phase diagrams for three different procedures (ZFC-W, FC-C, and FC-W), obtained from $T$-dependent $\Delta M_c$ data. Dark areas represent the coexistence regions of FE and WFM phases, depending on the $T\mathrm{\text{−}}H$ history.

Figure 3

(a) Comparison of $T$-dependent $\Delta M_c$ in $H_c=5.9\mathrm{T}$ measured in $E_a=0$ [the same with the data in Fig. 2a] and $E_a\approx +10\mathrm{kV}/\mathrm{cm}$ (solid curves) for ZFC-W, FC-C, and FC-W. $\Delta M_c$ is significantly reduced by the application of $E_a$ in the two-phase coexisting regions. (b) Comparison of $T$-dependent $P_a$ in $H_c=6.3\mathrm{T}$ in $E_a=0$ [the same with data in Fig. 2b] and $E_a\approx +10\mathrm{kV}/\mathrm{cm}$ (solid curves) for ZFC-W and FC-W. $P_a$ becomes enhanced with applied $E_a$ in the intermediate $T$ range, where $\Delta M_c$ is suppressed with $E_a$.

Figure 4

(a),(b) Repeated variation of $\Delta M_c$ ($\delta M_c$) at 15 K in $H_c=5.5\mathrm{T}$ by applying $E_a$, varied linearly with time between $+10$ and $-10\mathrm{kV}/\mathrm{cm}$. The inset in (a) shows time-dependent $\Delta M_c$ in $H_c=5.5\mathrm{T}$ at 15 K without $E_a$. $\delta M_c$ was obtained after subtracting the relaxation part shown in the inset in (a). $\delta M_c$ follows a linear fit well (solid line) and varies in a manner opposite to the $E_a$ variation, shown in (b). (c),(d) Linearly modulated $P_a$ ($\delta P_a$) with time at 5 K with a linear variation of $H_c$ between 6.1 and 7.0 T. The inset in (c) displays $H_c$-dependent $M_c$ at 5 K for $6.1\mathrm{T}<H_c<7.0\mathrm{T}$ after cooling in 6.1 T.