Magnetic Reversal of the Ferroelectric Polarization in a Multiferroic Spinel Oxide

Ferroelectric transition has been detected in a ferrimagnetic spinel oxide of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ upon the transition to the conical spin order below 25 K. The direction $[\overline{1}10]$ of the spontaneous polarization is normal to both the magnetization easy axis $[001]$ and to the propagation axis $[110]$ of the transverse spiral component, in accord with the prediction based on the spin-current model. The reversal of the spontaneous magnetization by a small magnetic field ($\sim 0.1\mathrm{T}$) induces the reversal of the spontaneous polarization, indicating the clamping of the ferromagnetic and ferroelectric domain walls.

Figure 1

(a) Schematic structure of spinel ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ and the electronic configurations of constituent ${\mathrm{Co}}^{2+}$ and ${\mathrm{Cr}}^{3+}$ ions. (b) The structure viewed along the conical spin modulation direction $[110]$ (denoted as the $x$ axis). The circles with slanted arrows indicate the spiral plane of the respective spins with conical structure [22]. (c) The spin (${\mathit{S}}_i$ and ${\mathit{S}}_j$) canting between the two sites ($i$ and $j$) and the direction of induced polarization $\mathit{P}$. The spiral spin modulation as shown in the lower panel produces the homogeneous (macroscopic) polarization. (d) The relation among the net magnetization $\mathit{M}$, the spiral spin modulation vector $\mathit{q}$, and the induced polarization $\mathit{P}$, as represented for the case of the B2-site chain in ${\mathrm{CoCr}}_2{\mathrm{O}}_4$.

Figure 2

The temperature dependence of (a) magnetization $\mathit{M}$ and specific heat divided by temperature ($C/T$), and (b) dielectric constant $ϵ$ measured in the $y$ direction at 10 kHz and the induced polarization along the $y$ axis ($\parallel [\overline{1}10]$). $T_C$, $T_S$, and $T_{\mathrm{lock}\mathrm{\text{−}}\mathrm{in}}$ in (a) stand for the critical temperatures of ferrimagnetic transition, incommensurate conical spin transition, and its lock-in transition, respectively. The electric polarization $\mathit{P}$ in (b) was measured after the ME field cooling procedure, with the cooling magnetic field $H_c\parallel z(=0.01\mathrm{T})$ and electric field $E_c\parallel y(=400\mathrm{kV}/\mathrm{m}$).

Figure 3

Magnetic-field dependence of (a) magnetization and (b) electric polarization at temperatures above (27 K) and below (18 K) the ferroelectric transition temperature ($T_S=25\mathrm{K}$). For measurements of the polarization (b), the magnetic field was scanned between $+H_c$ and $-H_c$, for each ME cooled state prepared with ($+E_c,+H_c$) and ($+E_c,-H_c$), as represented by solid and open circles. Here, $E_c(=400\mathrm{kV}/\mathrm{m}$) and $H_c(=0.5\mathrm{T})$ stand for the cooling electric and magnetic fields, respectively. The inset shows the temperature dependence of the polarization ($\mathit{P}$) in the warming runs starting from the magnetic-field scan points (2) and (3) shown in (b).

Figure 4

The synchronized reversal of the polarization ($\mathit{P}\parallel y$, solid circles) at 18 K with change of the external magnetic field ($\mathit{H}\parallel z$) which periodically reverses the magnetization direction ($\mathit{M}\parallel z$). Upper panel depicts the plausible clamping process of the ferromagnetic and polarization domain walls. Note that every toroidal moment, defined as $\mathit{T}\propto \mathit{P}\times \mathit{M}$, is kept intact across the domain wall.