We report cryogenic magnetic force microscopy (MFM) studies of a 200-nm-thick hexagonal ($h$) ${\mathrm{LuFeO}}_3$ film grown by molecular-beam epitaxy on a (111)-oriented yttria-stabilized cubic-zirconia substrate. Labyrinthlike domains $\sim 1.8\mu \mathrm{m}$ in size were observed after zero-field cooling below the Néel temperature, $T_{\mathrm{N}}\approx 147$ K, where weak ferromagnetic order ($P{6}_3$cm) with a canted moment of $M_{\mathrm{S}}\approx 0.02{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ exists. At 6 K, MFM images of the magnetization reversal process reveal a typical domain behavior of a pinning-dominated hard magnet. The pinning strength is substantially reduced at elevated temperature. The temperature dependence of the domain contrast demonstrates that our MFM is able to detect the domain contrast of magnets with tiny magnetic moments ($\sim 0.002{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$). An upper limit of the linear magnetoelectric coefficient of $h-{\mathrm{LuFeO}}_3$ (${\alpha }_{zz}<6\mathrm{ps}/\mathrm{m}$) is estimated by magnetoelectric force microscopy measurements.

• Received 20 January 2017
• Revised 5 April 2017

DOI:https://doi.org/10.1103/PhysRevB.95.134443