Magnetic structure and multiferroicity of Sc-substituted hexagonal YbFeO$_3$

Hexagonal rare-earth ferrite RFeO$_3$ family represents a unique class of multiferroics exhibiting weak ferromagnetism, and a strong coupling between magnetism and structural trimerization is predicted. However, the hexagonal structure for RFeO$_3$ remains metastable in conventional condition. We have succeeded in stabilizing the hexagonal structure of polycrystalline YbFeO$_3$ by partial Sc substitution of Yb. Using bulk magnetometry and neutron diffraction, we find that Yb$_{0.42}$Sc$_{0.58}$FeO$_3$ orders into a canted antiferromagnetic state with the Neel temperature $T_N$ ~ 165 K, below which the $Fe^{3+}$ moments form the triangular configuration in the $ab$-plane and their in-plane projections are parallel to the [100] axis, consistent with magnetic space group $P$6$_{3}$$cm$. It is determined that the spin-canting is aligned along the $c$-axis, giving rise to the weak ferromagnetism. Furthermore, the $Fe^{3+}$ moments reorient toward a new direction below reorientation temperature $T_R$ ~ 40 K, satisfying magnetic subgroup $P$6$_{3}$, while the $Yb^{3+}$ moments order independently and ferrimagnetically along the $c$-axis at the characteristic temperature $T_{Yb}$ ~ 15 K. Interestingly, reproducible modulation of electric polarization induced by magnetic field at low temperature is achieved, suggesting that the delicate structural distortion associated with two-up/one-down buckling of the Yb/Sc-planes and tilting of the FeO$_5$ bipyramids may mediate the coupling between ferroelectric and magnetic orders under magnetic field. The present work represents a substantial progress to search for high-temperature multiferroics in hexagonal ferrites and related materials.