Weak ferromagnetism and short range polar order in NaMnF$_{\mathrm{3}}$ thin films

The orthorhombically distorted perovskite NaMnF3 has been predicted to become ferroelectric if an a $=$ c distortion of the bulk \textit{Pnma} structure is imposed. In order to test this prediction, NaMnF$_{\mathrm{3}}$ thin films were grown on SrTiO$_{\mathrm{3}}$ (100) 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\'{e}el temperature $T_{N} \quad =$ 66 K. For the dielectric studies, NaMnF$_{\mathrm{3}}$ films were grown on a 30 nm SrRuO$_{\mathrm{3}}$ (100) 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.