Unveiling hidden structural instabilities and magnetodielectric effect in manganese fluoroperovskites AMnF3

Recent theoretical studies predict potential multiferroicity in $AB{\mathrm{F}}_{3}$ fluoroperovskites, challenging their experimental confirmations. Here, we show that magnetic manganese fluoroperovskites ${\mathrm{NaMnF}}_{3}$, ${\mathrm{RbMnF}}_{3}$, and ${\mathrm{CsMnF}}_{3}$ reveal clear evidence of intrinsic lattice instability via the temperature behavior of the dielectric permittivity ${\ensuremath{\varepsilon}}_{0}(T)$. Mechanisms of the instability closely correlate with the geometric tolerance factor $t$ and differ from those in oxide perovskites. In particular, a dramatic 170% growth of the permittivity ${\ensuremath{\varepsilon}}_{0}(T)$ takes place at low temperatures in ${\mathrm{NaMnF}}_{3}$ with the smallest tolerance factor $t=0.78$. Below ${T}_{N}$, this growth is accompanied by a huge magnetodielectric effect of about 25%. These findings allow us to call ${\mathrm{NaMnF}}_{3}$ an incipient multiferroic and open up opportunities for designing multiferroics on the basis of fluorides using chemical and strain engineering.