  The orthorhombically distorted perovskite NaMnF$_{3}$ has been predicted to
become ferroelectric if an $a=c$ distortion of the bulk $Pnma$ structure is
imposed. In order to test this prediction, NaMnF$_{3}$ thin films were grown on
SrTiO$_{3}$ (001) single crystal substrates via molecular beam epitaxy. The
best films were smooth and single phase with four different twin domains.
In-plane magnetization measurements revealed the presence of antiferromagnetic
ordering with weak ferromagnetism below the N\'eel temperature $T_N=66$ K. For
the dielectric studies, NaMnF$_{3}$ films were grown on a 30 nm SrRuO$_{3}$
(001) layer used as a bottom electrode grown via pulsed laser deposition. The
complex permittivity as a function of frequency indicated a strong Debye-like
relaxation contribution characterized by a distribution of relaxation times. A
power-law divergence of the characteristic relaxation time revealed an
order-disorder phase transition at 8 K. The slow relaxation dynamics indicated
the formation of super-dipoles (superparaelectric moments) that extend over
several unit cells, similar to polar nanoregions of relaxor ferroelectrics.
