Magnetically induced ferroelectricity in ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$

The tetragonal copper oxide ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ has an unusual crystal structure with a three-dimensional network of well separated ${\mathrm{CuO}}_4$ plaquettes. The spin structure of ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ in the magnetically ordered state below $T_{\text{N}}\sim 43$ K remains controversial. Here we present the results of detailed studies of specific heat, magnetic, and dielectric properties of ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ single crystals grown by the floating zone technique, combined with the polarized neutron scattering and high-resolution x-ray measurements. Down to 3.5 K our polarized neutron scattering measurements reveal ordered magnetic Cu moments which are aligned within the $ab$ plane. Below the onset of the long range antiferromagnetic ordering we observe an electric polarization induced by an applied magnetic field, which indicates inversion symmetry breaking by the ordered state of Cu spins. For the magnetic field applied perpendicular to the tetragonal axis, the spin-induced ferroelectricity is explained in terms of the linear magnetoelectric effect that occurs in a metastable magnetic state. A relatively small electric polarization induced by the field parallel to the tetragonal axis may indicate a more complex magnetic ordering in ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$.

Figure 1

Crystal structure of ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$; green/blue/gray spheres denote Cu/O/Bi atoms.

Figure 2

(a) Temperature dependence of magnetic susceptibility, $\chi$, measured for various magnitudes and directions of the magnetic field. (b) The corresponding temperature dependence of $1/\chi$. The derivative $\left(d\chi /dT\right)$ is shown in the inset of panel (b).

Figure 3

Field dependence of magnetization and magnetic susceptibility with external magnetic field applied along the $c$ and $a$ axes.

Figure 4

Polarization dependence of the magnetic (100) reflection measured at the IN12 spectrometer. The green and blue data points denote the magnetic neutron scattering intensities in the ${\sigma }_{zz}$ and ${\sigma }_{yy}$ spin-flip channels with the $x$ axis being parallel to the scattering vector and $z$ axis being perpendicular to the scattering plane. The lower figure shows the sample temperature at each measuring point of that scan which is always well below $T_{\text{N}}$. The temperature dependence of the magnetic (100) reflection is shown in the inset.

Figure 5

Intensity of the magnetic (100) reflection measured at the DNS spectrometer in zero field (upper plot) and in the magnetic fields $H$ of about 2.5 kG.

Figure 6

Temperature dependence of the lattice parameters. The red dashed line indicates a fit to the data above $T_{\text{N}}$. Below $T_{\text{N}}$ an anomalous increase (decrease) of the $a$ $\left(c\right)$ lattice constant is observable. This observation is in agreement with high-resolution thermal expansion measurements.

Figure 7

Temperature dependence of the specific heat, $C_p\left(T\right)$, for ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ single crystal. The red line represents the background to be subtracted to estimate the change in entropy from the anomaly peak around $T_{\text{N}}$. The upper right inset focuses on $C_p\left(T\right)$ in the region around the magnetic transition, and two sets of $C_p$ data are shown, measured during warming (solid square) and cooling processes (open circles), respectively. The $C_p\left(T\right)$ is also plotted on the log-log scale in the bottom right inset, with a $T^3$ (Debye) fit (red line) to the low temperature part of $C_p\left(T\right)$.

Figure 8

Temperature dependence of dielectric contants: (a) ${\varepsilon }_{ab}$ $(E\perp c$ axis) and (b) ${\varepsilon }_c$ $(E\parallel c$ axis). Also shown is the corresponding dielectric loss $\left(\tan \delta \right)$. All data has been measured in zero field $\left(H=0\right)$. The vertical arrow in (b) marks $T_{\text{N}}$ where the slight kink occurs.

Figure 9

Temperature dependence of in-plane dielectric constants ${\varepsilon }_{ab}$ and corresponding loss for (a) $H\parallel E$ and (b) $H\perp E$. The corresponding dielectric loss $\left(\tan \delta \right)$ is also shown. The measurement frequency amounts to 1 kHz. (c) The magnetic field induced change of the dielectric constant (measured at 1 kHz) at different temperatures (4 K, 40 K, and 50 K).

Figure 10

Temperature dependence of (a) the $c$-axis dielectric constant ${\varepsilon }_c$ and (b) the tan loss for different frequencies measured in a field of $H=9$ T along the $c$ axis. (c) The pyroelectric currents (black and red dots) measured with both positive and negative poling electric fields of 1 MV/m applied. The corresponding polarization $(P_c$, green and blue solid lines) obtained by integrating the pyroelectric currents from above $T_{\text{N}}$.

Figure 11

Temperature dependence of (a) ${\varepsilon }_c$, (b) tan loss, and (c) polarization measured in different fields along the $c$ axis. (d) The magnetic field induced change of ${\varepsilon }_c$ at different temperatures (from 4 K to 45 K). The measuring frequency amounts to 1 kHz.

Figure 12

Temperature dependence of (a) ${\varepsilon }_c$, (b) tan loss, and (c) the polarization measured in different magnetic fields applied along the $a$ direction. (d) The magnetic field induced change in ${\varepsilon }_c$ at different temperatures (from 5 K to 45 K). The measuring frequency is 1 kHz.

Figure 13

Phase diagram of ${\mathrm{Bi}}_2{\mathrm{CuO}}_4$ at 35 K which contains the information about the magnetic field dependence of the electric polarization $P_c$ for two different field directions: (a) $H\parallel a$ and (b) $H\parallel c$.