Hexagonal manganites are another interesting class of manganites and are depicted by the general formula RMnO₃ where R is typically a rare earth ion such as Y and Ho. These materials simultaneously exhibit ferroelectricity and antiferromagentic ordering of magnetic Mn ions. In general, rare earth elements having smaller ionic radii, tend to stabilize hexagonal phase of manganites, RMnO₃¹⁹ (R = Sc, Y, Ho, Er, Tm, Yb, Lu) with space group P6₃ cm.²⁰ In spite of having a chemical formula, ABO₃, similar to the perovskites, hexagonal manganites have altogether different crystal and electronic structure. In contrast to the conventional perovskites, hexagonal manganites have their Mn³⁺ ions with 5-fold coordination, located at the center of an MnO₅ trigonal bi-prism. R ions, on the other hand, have 7-fold coordination unlike the cubic coordination in perovskites.  The MnO₅ bi-prisms are two dimensionally arranged in space and are separated by a layer of R³⁺ ions. Figure 8.3 shows a schematic representation of YMnO₃ unit cell showing ionic arrangements within the structure.

Crystal field level scheme of Mn³⁺ ions in hexagonal RMnO₃ is also different from that of Mn³⁺ ions with octahedral coordination.  Here, the d- levels are split into two doublets and an upper singlet. As a result, four d-electrons of Mn³⁺ occupy two lowest lying doublets and unlike Mn³⁺ ion in octahedral coordination, there is no degeneracy present. Consequently, Mn³⁺ ions in these compounds are not Jahn-Teller ions.²²

Hexagonal RMnO₃ are found to possess considerably high ferroelectric transition temperature (> 500 K). However, their Neel temperature is far below the room temperature. Table 1 lists the ferroelectric and magnetic transition temperatures, spontaneous polarization (P_S) and effective paramagnetic moment μ_eff of some common RMnO₃ along with their structural parameters.

The mechanism of ferroelectricity in these compounds also differs from that of the conventional perovskite oxides. In case of YMnO₃, it was observed that off-centering of   Mn³⁺ ion from the center of the MnO₅ biprism is very small and cannot be considered to contribute toward ferroelectricity.²² Apparently it turns out that R ions (Y, here) contributes most toward ferroelectricity by having large R-O dipole moments. However, in reality, ferroelectricity in these materials has different origin and can be considered as accidental by-product. Similar to BO₆ octahedra in perovskite oxides (ABO₃), MnO₅ trigonal biprism in RMnO₃, tilts and rotates in order to ensure closest packed structure. Such tilting of MnO₅ trigonal biprism results in loss of inversion symmetry in the structure and brings about ferroelectricity.²² Since the mechanisms of ferroelectric and magnetic ordering in the above materials are quite different in nature, giant effect of magnetoelectric coupling is understandably not present.²²