Magnetic field induced critical dynamics in magnetoelectric ${\mathrm{TbPO}}_4$

We report on the magnetoelectric dynamics in the linear magnetoelectric antiferromagnet ${\mathrm{TbPO}}_4$ studied by broadband dielectric spectroscopy. For the phase transition into the magnetoelectric antiferromagnetic phase at $T_N\approx 2.3K$, a finite magnetic field $H$ induces critical behavior in the quasistatic permittivity ${\varepsilon }^{\prime }\left(T\right)$. Plotting the corresponding anomaly as a function of $T/T_N\left(H\right)$, we observe the scaling behavior $\Delta {\varepsilon }^{\prime }\propto H^2$, a clear fingerprint of linear magnetoelectric antiferromagnets. Above the phase transition, we find a critical slowing down of the ferroic fluctuations in finite magnetic field. This behavior can be understood via a magnetic field induced relaxational response that resembles the soft-mode behavior in canonical ferroelectrics and multiferroics.