Dielectric properties and magnetostriction of the collinear multiferroic spinel CdV${}_2$O${}_4$

By studying the dielectric properties of the geometrically frustrated spinel CdV${}_2$O${}_4$, we observe ferroelectricity developing at the transition into the collinear antiferromagnetic ground state. In this multiferroic spinel, ferroelectricity is driven by local exchange striction and not by the more common scenario of spiral magnetism. The experimental findings are corroborated by ab initio calculations of the electric polarization and the underlying spin and orbital order. The results point toward a charge rearrangement due to dimerization, where electronic correlations and the proximity to the insulator-metal transition play an important role.

Figure 1

Schematic view of (a) the V-O ionic arrangements with spin magnetic structure (see black arrows) and short (long) V-V bond lengths highlighted by dashed (bold solid) lines; (a${}^{\prime }$) oxygen-induced dipoles (see ellipses) and long bond-length V-O (see black lines)—symmetry inequivalent oxygens are denoted with different symbols/colors; (b) calculated polarization according to DFT+$U$ (left) and HSE schemes (right); V and O arrangement for (c) $\uparrow \uparrow \uparrow \uparrow$ and (c${}^{\prime }$) $\uparrow \uparrow \downarrow \downarrow$ spin ordering along [101] or [011]; (d) values of ${\alpha }_1$, ${\beta }_2$, ${\alpha }_2$, and ${\beta }_1$ angles as a function of $U_{\text{eff}}$.

Figure 2

Thermal expansion $\alpha$ in the whole temperature range (a) and in the vicinity of the magnetic transition (a1). The complex dielectric permittivity ${\varepsilon }^{*}$ of CdV${}_2$O${}_4$ is displayed as real part ${\varepsilon }^{\prime }$ (b) and as dielectric loss ${\varepsilon }^{″}$ (c) for different frequencies between 82 Hz and 0.3 MHz measured with a stimulus of $~$1 V/mm. The data displayed in frame (b1) were measured in the vicinity of the magnetic transition at 1 Hz in external fields of zero and 10 T. Frame (b2) shows the small dielectric anomaly at the structural transition below 100 K.

Figure 3

Electric polarization (a) measured via the pyrocurrent under cooling with a rate of 2 K/min in an electric poling field of 220 V/mm and under heating with the same rate in zero external field. Frame (b) displays the linear component of the dielectric permittivity measured with a stimulus of 220 ${\mathrm{V}}_{\text{rms}}$/mm. The corresponding (third-order) nonlinear component $\left|{\varepsilon }_{\text{nl}}\right|$ normalized on the linear term is displayed in (c); the “floor” of roughly $0.8\times {10}^{-4}$ can be attributed to the harmonic distortion of the high-voltage amplifier.