Magnetization, specific heat, and thermal conductivity of hexagonal ErMnO$_3$ single crystals

We report a study of magnetism and magnetic transitions of hexagonal ErMnO$_3$ single crystals by magnetization, specific heat and heat transport measurements. Magnetization data show that the $c$-axis magnetic field induces three magnetic transitions at 0.8, 12 and 28 T. The specific heat shows a peak at 2.2 K, which is due to a magnetic transition of Er$^{3+}$ moments. For low-$T$ thermal conductivity ($\kappa$), a clear dip-like feature appears in $\kappa(H)$ isotherm at 1--1.25 T for $H \parallel ab$; while in the case of $H \parallel c$, a step-like increase is observed at 0.5--0.8 T. The transition fields in $\kappa(H)$ are in good agreement with those obtained from magnetization, and the anomaly of $\kappa$ can be understood by a spin-phonon scattering scenario. The natures of magnetic structures and corresponding field-induced transitions at low temperatures are discussed.