Electric-Field Switching of a Magnetic Propagation Vector in a Helimagnet

We report novel magnetoelectric properties of a quantum-spin helimagnet ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$ with a noncentrosymmetric (but nonpolar) crystal structure. It was found that the spin helicity of the cycloidal spin order is always fixed to the lattice, therefore the magnetic propagation vector $k$ determines the sign of electric polarization in ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$. Consequently, not only the magnetic-field drive of the ferroelectric domain but also the electric-field switching of magnetic $k$ vector can be achieved.

Figure 1

(a) The schematic view of the (001) plane of ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$. The arrows and circles at the middle of the nearest neighboring Cu sites indicate the in-plane and out-of-plane components of the Dzyaloshinskii-Moriya (DM) vector, respectively. (b),(c) Corner shared ${\mathrm{CuO}}_4$ and ${\mathrm{GeO}}_4$ tetrahedrons along [110] (b) and $[1\overline{1}0]$ (c). (d) The transverse helical spin structure induced by the DM interaction. (e) Two types of the $k$ domains in ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$. Each $k$ domain is concurrent with the ferroelectric domain and connected by the symmetry operations of $\overline{4}$ or $2_1$.

Figure 2

(a) The $H$ dependence of the [001] component of $P$ under $H\parallel [110]$, $[1\overline{1}0]$, and [100] at 2 K. (b) Magnified scale of (a) around $H=0$. (c) Schematic diagrams of the $k$-domain control under $H\parallel [110]$ and $[1\overline{1}0]$. (d) The experimental setup under rotating $H$ around the [001] direction. $\theta$ is defined as the angle between [100] and the $H$ direction within the (001) plane. (e),(f) The $\theta$ dependences of the in-plane component of $M$ (e) and the [001] component of $P$ (f) at 2 K.

Figure 3

(a) Schematic diagrams of the $k$-domain control by the $E$-cooling procedure. (b),(c) $H$ dependence of $P$ (b) and $T$ dependence of $M$ (c) after the cooling under $E=\pm 1\mathrm{MV}/\mathrm{m}$ ($E+$, $E-$) and $0\mathrm{V}/\mathrm{m}$ at $H=0$. During these measurements, $E$ was turned off. $M$ was measured under $H=0.01\mathrm{T}$ applied along [110].

Figure 4

(a) $H$ dependence of $P$ at 2 K under $H\parallel [1\overline{1}0]$ after the application of various $E$ at $H=0$. The decrease of the $P$ around 0.1 T corresponds to the polarization changed by the $E$. (b) $E$ dependence of $P$ at $H=0\mathrm{T}$ at $T=2\mathrm{K}$. The ferroelectric $k$ domains can be controlled by the $E(>5\mathrm{MV}/\mathrm{m})$.