Competing Magnetic Interactions in Magnetoelectric YbMnO$_{3}$

The (\textit{RE)}MnO$_{3}$ (\textit{RE }= \textit{Rare Earth}) series of magnetoelectrics exist as both hexagonal and orthorhombic lattice structures. These have recently attracted much attention due to possible applications in spintronics, in switching, and as media with negative refractive index. YbMnO$_{3}$ is hexagonal with ferroelectricity (Tc$\sim $ 970K) and antiferromagnetism (T$_{N}$: Mn$\sim $80K, Yb$\sim $5K) in the same phase. Here, we report detailed studies of the H-T phase diagram using a high-quality single crystal of YbMnO$_{3}$ grown by floating zone. We examine the magnetically ordered phases of Yb: Yb3+ (2$a)$ via Yb-Yb, and Yb3+ (4$b)$ via Yb-Mn interactions within the hexagonal YbMnO$_{3}$ structure, and report several new features in the magnetic phase diagram. Contrary to recent reports, we observe that the magnetic moment of Yb does not become fully suppressed with external magnetic field, but rather directly transitions from the A$_{1}$ order into the A$_{2 }$order at low temperature.