Cupric chloride ${\text{CuCl}}_2$ as an $S=\frac{1}{2}$ chain multiferroic

Magnetoelectric properties were investigated for an $S=1/2$ chain antiferromagnet ${\text{CuCl}}_2$, which turns out to be the first example of nonchalcogen based spiral-spin induced multiferroics. Upon the onset of helimagnetic order propagating along the $b$ axis under zero magnetic field $\left(H\right)$, we found emergence of ferroelectric polarization along the $c$ axis. Application of $H$ along the $b$ axis leads to spin-flop transition coupled with drastic suppression of ferroelectricity and rotation of $H$ around the $b$ axis induces the rotation of spin-spiral plane and associated polarization direction. These behaviors are explained well within the framework of the inverse Dzyaloshinskii-Moriya model, suggesting the robustness of this magnetoelectric coupling mechanism even under the strong quantum fluctuation.

Figure 1

(Color online) [(a)–(c)] Crystal structure of ${\text{CuCl}}_2$, and $P$ direction observed at the ground state. The $bc$-cycloidal spin order suggested by Banks et al. (Ref. 27) is illustrated in (b) and also in (c) with solid rounded square representing spin-spiral plane. Dashed rounded square indicates the possible tilting of spin-spiral plane as revealed in this study (see text). (d) ESR signal taken at room temperature under various directions of $H$ confined within the $ac$ plane. ${\theta }_H$ is defined as the angle between the $a$ axis and $H$ direction. Each dashed line represents a fitted curve with a single Lorentzian resonance. (e) Angle dependence of $g$ factor.

Figure 2

(Color online) Temperature dependence of (a) magnetic susceptibility $\chi$, (b) dielectric constant $ϵ$, and (c) electric polarization $P$. In (d) and (e), $H$ dependences of magnetization $M$, $ϵ$, and $P$ under $H\parallel b$ are indicated. Large and small arrows denote corresponding ordinate scale of physical quantity and direction of field scans, respectively. (f) $H\text{−}T$ phase diagram for $H\parallel b$. Circles, squares, triangles are the data points obtained from $M$, $ϵ$, and $P$ profiles, respectively. Open (closed) symbols are taken from $T$- $\left(H\right)$ increasing runs.

Figure 3

(Color online) $P\text{−}E$ hysteresis loop for ${\text{CuCl}}_2$ measured with $E\parallel z$. Electric field was swept at the rate of $13\text{kV}/\text{m}\text{sec}$.

Figure 4

(Color online) (a) $H$ dependence of $M$ taken under various directions of $H$ around the $b$ axis. The base lines of data are arbitrarily shifted. (b) Angle dependence of $\chi$ measured under $H\perp b$. Dashed lines indicate the fits with sinusoidal function. [(c)–(e)] Corresponding development of $z$ component of $ϵ$ $\left({ϵ}_z\right)$ as well as $z$ and $a$ components of $P$ ($P_z$ and $P_a$). Before measurements of $P$, the specimen was cooled at ${\theta }_H=0$ with poling $E$ applied along the $z$ axis. Dashed lines indicate the behavior expected from Eq. (2). Arrows indicate the direction of $H$ rotation.

Figure 5

(Color online) (a) Trace of $P_a$ and $P_z$ under $H$ rotating around the $b$ axis. [(b) and (c)] Magnitude and direction of $P$ as a function of $H$ angle. Arrows indicate the direction of $H$ rotation. The data are taken from Figs. 4d, 4e, and the setup for measurements is shown in (d). ${\theta }_P$ $\left({\theta }_H\right)$ is defined as the angle between $P$ $\left(H\right)$ direction and the $a$ axis. [(e) and (f)] The expected relationship between $P$, $H$, and spin-spiral plane (depicted as rounded square).