Visualization of weak ferromagnetic domains in multiferroic hexagonal ferrite thin film*

Hexagonal $\textit{h}$-LuFeO$_3$ thin film has been reported to be a room-temperature multiferroic [1]. Extensive studies on high quality MBE thin films revealed a magnetoelectric phase with weak ferromagnetism emerges below $T_N\sim 147$\,K [2]. However, the direct observation of weak ferromagnetic domain structures is still lacking. Here we report cryogenic magnetic force microscopy (MFM) results on 200 nm thick $\textit{h}$-LuFeO$_3$ film grown by molecular-beam epitaxy (MBE) on (111)-oriented yttria-stablized cubic zirconia (YSZ) substrates. Labyrinth-like weak ferromagnetic domain structures were observed with a domain size $\sim 1\,\mu m$ and domain wall width $\sim 0.4\,\mu m$. Field-dependent MFM data indicates the coercive field is $\sim 2.66$\,T at 50\,K and $\sim 3.15$\,T at 6\,K. [1] W. Wang et al., Phys. Rev. Lett. 110, 237601(2013). [2] J. A. Moyer et al., APL MATER. 2, 012106 (2014).