Multiferroic fluoride BaCoF$_{\mathrm{4}}$ Thin Films Grown Via Molecular Beam Epitaxy*

Multiferroic materials exhibit exciting physics related to the simultaneous presence of multiple long-range orders, in many cases consisting of antiferromagnetic (AF) and ferroelectric (FE) orderings. In order to provide a new, promising route for fluoride-based multiferroic material engineering, we grew multiferroic fluoride BaCoF$_{\mathrm{4}}$ in thin film form on Al$_{\mathrm{2}}$O$_{\mathrm{3}}$ (0001) substrates by molecular beam epitaxy. The films grow with the orthorhombic b-axis out-of-plane and with three in-plane structural twin domains along the polar c-axis directions. The FE ordering in thin films was verified by FE remanent hysteresis loops measurements at T $=$ 14 K and by room temperature piezoresponse force microscopy (PFM). An AF behavior was found below Neel temperature T$_{\mathrm{N}} \quad \sim $ 80 K, which is in agreement with the bulk properties. At lower temperatures two additional magnetic phase transitions at 19 K and 41 K were found. First-principles calculations demonstrated that the growth strain applied to the bulk BaCoF$_{\mathrm{4}}$ indeed favors two canted spin orders, along the b- and a-axes, respectively, in addition to the main AF spin order along the c-axis.