Dielectric behavior near the Néel temperatures of BaMn${\mathrm{F}}_4$ and Ba${\mathrm{Mn}}_{0.99}$${\mathrm{Co}}_{0.01}$${\mathrm{F}}_4$ has been measured. In accord with earlier measurements by Samara and Richards, pure BaMn${\mathrm{F}}_4$ displays a decrease in the $a$-axis dielectric constant for $T<\mathrm{}{T}_N$ which is approximately proportional to the square of the sublattice magnetization. The 1% Co sample exhibits no dielectric anomaly at $T_N$. Whereas the samples have the same structural symmetry ($C_2$ point group), the magnetic symmetry of BaMn${\mathrm{F}}_4$ is 2′ and that of Ba${\mathrm{Mn}}_{0.99}$${\mathrm{Co}}_{0.01}$${\mathrm{F}}_4$ is 2. For the latter symmetry there is no spin canting. Thus, unlike BaMn${\mathrm{F}}_4$, Ba${\mathrm{Mn}}_{0.99}$${\mathrm{Co}}_{0.01}$${\mathrm{F}}_4$ is not a ferromagnet. The present observations confirm our earlier hypothesis that the dielectric anomaly at $T_N$ is an effect due entirely to weak ferromagnetism in a low-symmetry ferroelectric. A Landau theory for the magnetic phase of BaMn${\mathrm{F}}_4$ is presented. A term proportional to $l_z{m}_x{p}^2$, where $l_z·m_x·P$ are respectively sublattice magnetization, ferromagnetic moment, and electric polarization, is introduced, and it is shown that the dielectric anomaly $\Delta {\epsilon }_a\mathrm{}\left(T\right)\mathrm{}$ can have either sign and is proportional to $l_z^{}{}_{}{}^2$, in agreement with experiment. The theory also gives predictions for linear magnetoelectric coefficient and canting angle, and suggests the existence of strong nonlinear magnetoelectric coupling.

• Received 14 June 1979

DOI:https://doi.org/10.1103/PhysRevB.21.2926