Ferroelectricity Induced by Spin-Dependent Metal-Ligand Hybridization in ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathbf{O}}_7$

We have investigated the variation of induced ferroelectric polarization under a magnetic field with various directions and magnitudes in a staggered antiferromagnet ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$. While the ferroelectric polarization cannot be explained by the well-accepted spin current model nor the exchange striction mechanism, we have shown that it is induced by the spin-dependent $p\mathrm{\text{−}}d$ hybridization between the transition metal (Co) and ligand (O) via the spin-orbit interaction. On the basis of the correspondence between the direction of electric polarization and the magnetic state, we have also demonstrated the electrical control of the magnetization direction.

Figure 1

(a) Schematic view of the crystal structure of ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$. (b) Coordination of the spin moment in a ${\mathrm{CoO}}_4$ tetrahedron. (c),(d) The temperature dependence of (c) $[001]$ and (d) $[100]$ components of the electric polarization $P$ in the magnetic field 5 T applied along various directions.

Figure 2

(a)–(c) Canted antiferromagnetic structures in magnetic fields with various in-plane directions. (d) The experimental configuration of the in-plane $H$-rotation measurement. (e),(f) The variations of (e) in-plane component of $M$ and (f) $P$ at 2 K under rotating $H$ around the $[001]$ direction. (g) The experimental setup under rotating $H$ around the $[100]$ direction. (h),(i) ${\theta }_H$ dependence of (h) $M$ and (i) $P$ at 2 K at 5 T. (j) The rotation hysteresis of $P_a$ in the vicinity of $H\parallel [001]$. (k),(l) Canted antiferromagnetic structures and the induced electric polarization under out-of-plane magnetic field.

Figure 3

(a) Illustration of the spin-structural change with increasing magnetic field along $[110]$. (b),(c) $H(\parallel [110])$ dependence of (b) $M$ (c) $P_c$ at various temperatures as well as the calculated curve of $P_c$ at 2 K based on the spin-dependent hybridization mechanism [see Eq. (1)]. The definition of the structural parameter $\kappa$ is shown in Fig. 1a.

Figure 4

$P\mathrm{\text{−}}E$ curve obtained in $H\parallel [001]$ of 5 T at 2 K. $P_a$ reversal is equivalent to the magnetization flop around $[001]$ as shown in the insets. Incidentally, the large $E$-linear term in $P_a$ comes from the paraelectric component ${ϵ}_r{ϵ}_{0}E$, where ${ϵ}_r\sim 10$ and ${ϵ}_0$ is the dielectric constant in vacuum.