By using broadband linear and nonlinear dielectric spectroscopy we studied the magnetoelectric dynamics in the chiral antiferromagnet MnWO4. 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=10 K but unexpectedly decays again on approaching the lower, first-order phase boundary at T_N1=7.6K. 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=1.8. The rise of the effective dynamical coercive field on cooling below the TN2 is much stronger compared to the usual ferroelectrics and can be described by a power law E_c ~{ u}^1/2. The latter questions the feasibility of fast-switching devices based on this type of material.
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