Magnetoelectric phenomena in BaMnF4and BaMn0.99

Dielectric behavior near the N\'eel 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 $T<{T}_{N}$ 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\ensuremath{'} 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 ${l}_{z}\ifmmode\cdot\else\textperiodcentered\fi{}{m}_{x}\ifmmode\cdot\else\textperiodcentered\fi{}P$ are respectively sublattice magnetization, ferromagnetic moment, and electric polarization, is introduced, and it is shown that the dielectric anomaly $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{a}(T)$ 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.