Critical Slowing Down near the Multiferroic Phase Transition in ${\mathrm{MnWO}}_4$

By using broadband dielectric spectroscopy in the radio frequency and microwave range, we studied the magnetoelectric dynamics in the multiferroic chiral antiferromagnet ${\mathrm{MnWO}}_4$. Above the multiferroic phase transition at $T_{N2}\approx 12.6\mathrm{K}$ we observe a critical slowing of the corresponding magnetoelectric fluctuations resembling the soft-mode behavior in canonical ferroelectrics. This electric-field-driven excitation carries much less spectral weight than ordinary phonon modes. Also, the critical slowing down of this mode scales with an exponent larger than 1, which is expected for magnetic second-order phase transition scenarios. Therefore, the investigated dynamics have to be interpreted as the softening of an electrically active magnetic excitation, an electromagnon.

Figure 1

Schematic ($H,T$) diagram for the multiferroic phase in ${\mathrm{MnWO}}_4$ (see also Refs. [15, 16]). The red arrows denote the two ways used in this study to approach the phase transition, namely, temperature driven in zero field and magnetic-field driven at $T=12\mathrm{K}$.

Figure 2

Real part $\mathrm{\Delta }{ϵ}^{\prime }(T)$ (only the ferroelectric contribution, upper panel) and imaginary part ${ϵ}^{\prime \prime }(T)$ (lower panel) of the complex dielectric permittivity for frequencies between 30 MHz and 1 GHz around the multiferroic phase transition. For comparison, the inset shows similar measurements in a canonical proper ferroelectric (Ca-Sr-propionate) taken from Ref. [19]. Note that the scales differ by 4 orders of magnitude due to the small ferroelectric moment in ${\mathrm{MnWO}}_4$.

Figure 3

Upper frames: Spectra of the real and imaginary part of the complex permittivity $ϵ(f{)}^{*}$ for exemplary temperatures slightly above $T_{N2}$. Solid lines are guides to the eye. Lower frame: Critical temperature dependence of the relaxation rate (circle, left scale) ${\omega }_c(T)=2\pi f_p$ as extracted from the position $f_p$ of the peaks in the loss spectra (upper frame). The scattered line (green) is a fit using the expression $f_p\propto {[(T-T_{N2)}/T_{N2}]}^{\gamma }$ with $\gamma =\nu z\approx 1.3$. Right scale (star): The inverse of the real part of the permittivity measured at $f=30\mathrm{MHz}$.

Figure 4

Real part $\mathrm{\Delta }{ϵ}^{\prime }(T)$ (upper frame) and imaginary part ${ϵ}^{\prime \prime }(T)$ (lower frame) of the complex permittivity for frequencies between 30 MHz and 1 GHz (see Fig. 2) as function of the magnetic field at $T=12\mathrm{K}$. The inset shows the critical magnetic field dependence of the relaxation rate ${\omega }_c=1/{\tau }_c$ (left scale, circle). The solid line is a fit due to $f_p\propto [(H-H_c)/H_c{]}^{{\gamma }_H}$ at $H_c\approx 7.3\mathrm{T}$ with ${\gamma }_H=\nu z_H\approx 1.3$. The right scale of the inset (star) refers to the inverse of $\mathrm{\Delta }{ϵ}^{\prime }(T)$ measured at $f=30\mathrm{MHz}$.