Hexagonal Manganites—(RMnO₃): Class (I) Multiferroics with Strong Coupling of Magnetism and Ferroelectricity

Table 2

Magnetic symmetries of the Mn³⁺ spins in hexagonal manganites, according to [93, 95].

Irrep.	Model	Angle Φ	Space group	Example
Γ1	𝛽2	90°	𝑃63𝑐𝑚
Γ2	𝛽1	0°	𝑃63𝑐𝑚
Γ3	𝛼1	0°	𝑃63𝑐𝑚	YMnO3
Γ4	𝛼2	90°	𝑃63𝑐𝑚	ErMnO3
Γ2↔Γ1	𝛽1↔𝛽2	0^∘<Φ<90^∘	𝑃63
Γ3↔Γ4	𝛼1↔𝛼2	0^∘<Φ<90^∘	𝑃63	LuMnO3
Γ2↔Γ4	𝛽1↔𝛼2	0^∘<Φ<90^∘	𝑃3𝑐
Γ3↔Γ1	𝛼1↔𝛽2	0^∘<Φ<90^∘	𝑃3𝑐