The field-induced re-entrant phase in multiferroic hexagonal $\mathrm{Ho}\mathrm{Mn}{\mathrm{O}}_3$ is investigated to lower temperatures by dc magnetization, ac susceptibility, and specific heat measurements at various magnetic fields. Two new phases have been unambiguously identified below the Néel transition temperature, $T_N=76\mathrm{K}$, for magnetic fields up to 50 kOe. The existence of an intermediate phase between the $P{\underset{̱}{\mathit{6}}}_3\underset{̱}{\mathit{c}}m$ and $P{\underset{̱}{\mathit{6}}}_3\mathit{c}\underset{̱}{m}$ magnetic structures (previously predicted from dielectric measurements) was confirmed and the magnetic properties of this phase have been investigated. At low temperatures $(T<5\mathrm{K})$ a dome shaped phase boundary characterized by a magnetization jump and a narrow heat capacity peak was detected between the magnetic fields of 5 kOe and 18 kOe. The transition across this phase boundary is of first order and the magnetization and entropy jumps obey the magnetic analogue of the Clausius-Clapeyron relation. Four of the five low-temperature phases coexist at a tetracritical point at 2 K and 18 kOe. The complex magnetic phase diagram so derived provides an informative basis for unraveling the underlying driving forces for the occurrence of the various phases and the coupling between the different orders.

• Received 24 August 2004

DOI:https://doi.org/10.1103/PhysRevB.71.014438