Colour groups and spin waves symmetry analysis of the spin wave spectrum in hexagonal manganites LMnO3 (L = Er, Ho, Lu, Sc, Tm, Y)

Interplay between spin dynamics and crystal field in the multiferroic compound HoMnO3

“…The details are given in appendix II. According to [43], for the Mn magnetic orders with zero propagation vector corresponding to the four different one dimensionnal Γ i , the spin wave representation may be decomposed into τ = A 2 B 1 E 1 E 2 where we use the irreducible representations of the C 6v (6mm) point group. For Ho 4b and 2a crystal field excitations, their decompositions are already given in Fig.10, in the local point groups associated to the two different sites: C 3 (3) for Ho 4b, and C 3v (3m) for Ho 2a.…”

“…Its character table is given in table III. The symmetry of the different Mn spin waves have been reported in [43] with Kovalev notation. We will rather use Mulliken notation.…”

“…To simplify calculations, the spin wave analysis has been performed in a more symmetric space group than C 3 6v , namely D 4 6h , which means neglecting some oxygen displacements and therefore some weak magnetic anisotropies. From [43], it follows that the spin wave representation can be decomposed into A 2g B 1g E 1g E 2g . Going back to the lower symmetric C 3 6v space group, gerade und ungerade modes are no longer relevant so that the spin wave decomposition becomes A 2 B 1 E 1 E 2 .…”

Inelastic neutron scattering study of spin waves in the garnet with a triangular magnetic structure

“…It is more useful to neglect weak interactions resulting in small splittings of the SW branches and to find the approximate spectra. This can be done within the exchange approximation for the spin-wave Hamiltonian [11]. The symmetry analysis was performed using the stabilizer concept proposed in references [10,11].…”

“…This can be done within the exchange approximation for the spin-wave Hamiltonian [11]. The symmetry analysis was performed using the stabilizer concept proposed in references [10,11].…”