Observation of a Magnetopiezoelectric Effect in the Antiferromagnetic Metal ${\mathrm{EuMnBi}}_2$

We have experimentally studied a magnetopiezoelectric effect predicted recently for magnetic metals with low crystal symmetries. In ${\mathrm{EuMnBi}}_2$ with antiferromagnetic Mn moments at 77 K, dynamic displacements emerge along the $a$ direction upon application of ac electric fields in the $c$ direction and increase in proportion to the applied electric fields. Such displacements are not observed along the $c$ direction of ${\mathrm{EuMnBi}}_2$ or ${\mathrm{EuZnBi}}_2$ with nonmagnetic Zn ions. As temperature increases from 77 K, the displacement signals decrease and disappear at about 200 K, above which electric conduction changes from coherent to incoherent. These results demonstrate the emergence of the magnetopiezoelectric effect in a magnetic metal lacking inversion and time-reversal symmetries.

Figure 1

(a) Schematic illustration of crystal structure for ${\mathrm{EuMnBi}}_2$, together with the magnetic structure of Mn ions below the antiferromagnetic transition temperature ($T_N$) [19, 20]. (b) Schematic illustration of measurement setup for the magnetopiezoelectric effect. (c) Temperature dependence of interlayer resistivity ${\rho }_{zz}$ for ${\mathrm{EuMnBi}}_2$ and ${\mathrm{EuZnBi}}_2$. (Inset) Temperature derivative of resistivity for ${\mathrm{EuMnBi}}_2$ around $T_N(=315\mathrm{K})$. See Supplemental Material [22] for in-plane resistivity ${\rho }_{xx}$ of ${\mathrm{EuMnBi}}_2$.

Figure 2

Frequency dependence of displacement signals measured at 77 K with (red color) and without (black color) voltage application to (a),(b) ${\mathrm{EuMnBi}}_2$ and (c) ${\mathrm{EuZnBi}}_2$ samples. Here, the voltage of 6-kHz frequency and 5-V amplitude (10-V peak-to-peak amplitude) was applied along the $c$ direction of the samples. The displacement along the $a$ direction was measured for (a) ${\mathrm{EuMnBi}}_2$ and (c) ${\mathrm{EuZnBi}}_2$, while that along the $c$ direction was measured for ${\mathrm{EuMnBi}}_2$ in (b). (Top row) Sample pictures are also shown; red points correspond to the laser spots.

Figure 3

(a) Frequency dependence of the displacement signals measured with various voltage amplitudes for ${\mathrm{EuMnBi}}_2$ at 77 K. Here, the displacements were measured along the $a$ direction while the voltage of 6-kHz frequency was applied to the $c$ direction. (b) Frequency dependence of the displacement signals measured for ${\mathrm{EuMnBi}}_2$ at various temperatures. Here, the displacements were measured along the $a$ direction, while the voltage of 6-kHz frequency and 5-V amplitude was applied to the $c$ direction.

Figure 4

(a) Voltage dependence of the displacement signal measured at 6 kHz (red circles). See Fig. 3 for raw data. The background levels (black triangles) correspond to the averaged displacements around 6 kHz without voltage application. The dotted line is a guide for eyes. (b) Temperature dependence of the displacement signal measured at 6 kHz (red circles). See Fig. 3 for raw data. The background levels (black triangles) correspond to the averaged displacements around 6 kHz without voltage application.