Domain dynamics in the multiferroic phase of ${\mathrm{MnWO}}_4$

By using broadband linear and nonlinear dielectric spectroscopy we studied the magnetoelectric dynamics in the chiral antiferromagnet ${\mathrm{MnWO}}_4$. In the multiferroic phase the dielectric response is dominated by the dynamics of domains and domain walls which is strongly dependent on the stimulating electric field. The mean switching time reaches values in the minute range in the middle of the multiferroic temperature regime at $T\approx 10$ K but unexpectedly decays again on approaching the lower, first-order phase boundary at $T_{N1}\approx 7.6$ K. The switchability of the ferroelectric domains denotes a pinning-induced threshold and can be described considering a growth-limited scenario with an effective growth dimension of $d\approx 1.8$. The rise of the effective dynamical coercive field on cooling below the $T_{N2}$ is much stronger compared to the usual ferroelectrics and can be described by a power law $E_c\propto {\nu }^{1/2}$. The latter questions the feasibility of fast-switching devices based on this type of material.

Figure 1

Schematic sketch of the magnetically ordered phases in ${\mathrm{MnWO}}_4$ [24].

Figure 2

Real part of the dielectric permittivity ${\varepsilon }^{\prime }$ of ${\mathrm{MnWO}}_4$ for different frequencies between 100 mHz and 100 MHz in equidistant spacing measured with a stimulus of $\sim$1 V/mm and as a function of temperature around the multiferroic transition at $T_{N2}\approx 12.6$ K. The inset shows a zoom on higher frequencies.

Figure 3

Electric-field-dependent polarization $P\left(E\right)$ measured for $E\parallel b$ at temperatures below $T_{N2}$. The dotted curve was measured using a time-dependent stimulus $E\left(t\right)$ with a triangular profile and an effective frequency of $\nu \approx 6$ mHz. The other $P\left(E\right)$ loops were reconstructed from the first 10 orders of the nonlinear permittivity measured with sinusoidal stimulation at frequencies between 300 mHz and 300 Hz. The inset shows the $P\left(E\right)$ loops for the switchable net polarization after subtraction of the quasistatic dielectric background $\propto {\varepsilon }_{\infty }$.

Figure 4

Top panel: Spectra of the nonlinear orders ${\varepsilon }_n$ of permittivity measured using a stimulus of $E_{ac}=1$ kV/mm at $T=9.8$ K. The first-order component is displayed as $\Delta {\varepsilon }_1^{\prime }={\varepsilon }_1^{\prime }-{\varepsilon }_{\infty }$ (blue), the dielectric loss ${\varepsilon }_1^{\prime \prime }$ (red), and the magnitude $|\Delta {\varepsilon }_1|=\sqrt{\Delta {\varepsilon }^{\prime 2}+{\varepsilon }^{\prime \prime 2}}$ (light gray). Also displayed is the magnitude of the second- and third-order permittivities $|{\varepsilon }_2|$ and $|{\varepsilon }_3|$ which denotes the nonlinear character of the dielectric response within the multiferroic phase. Bottom panel: The frequency dependence of the switched polarization $P_{sw}$ and the ratio ${\varepsilon }_1^{\prime \prime }/\left|\Delta {\varepsilon }_1\right|\approx E_c/E_{Eac}$. The dashed line (green) represents a fit to $P_{sw}\left(\nu \right)$ following the Ishibashi-Orihara model [31] with a dimensionality parameter $d\approx 1.8$ as described in the text.

Figure 5

Real and imaginary part of the first-order component of the nonlinear permittivity measured for frequencies between 0.3 Hz and 3 kHz at two different stimuli of 100 (left column) and 1000 V/mm (right column). The additional data shown in the bottom right panel (asterisks) originate from integrated pyrocurrent measurements and trace the temperature dependence of the spontaneous polarization. The dashed line is a fit according to a mean-field-like square-root behavior.

Figure 6

Switchable polarization $P_{sw}$ measured for frequencies between 0.3 Hz and 3 kHz at a stimulus of 1 kV/mm. Left panels: Temperature dependence at zero field and ${\mu }_{0}H=7.3$ T. Right panel: Magnetic field dependence at $T=12$ K.

Figure 7

Dielectric loss spectra (left panel) measured for a stimulus of 1000 V/mm. From the maxima in these spectra a temperature-dependent mean switching time can be evaluated (right panel). The right frame also displays the corresponding results for an applied magnetic field of 7.3 T (red symbols).

Figure 8

Contour plot of the switchability $\Delta \left|\varepsilon \right|E_{ac}/P_S$. The solid line is a fit according to the modified Ishibashi-Orihara model [31] for the frequency dependence of the coercive field as described in the text. The small open circles show the position of the maxima in the dielectric loss spectra for the corresponding stimulus.