Hybrid quasiparticles within the orthorhombic or hexagonal topology of RMO$_{3}$ (R$=$Nd,Pr,Tm,Er; M$=$Mn,Cr) under strong magnetic fields

We report on magnetoelectric quasiparticles that originate from electronic Coulomb and exchange correlations using a Bruker IFS125-HR interferometer at 0.5 cm$^{-1}$ resolution in the THz beamline of the electron storage ring BESSYII in Berlin. Orthorhombic NdMnO$_{3}$ and hexagonal TmMnO$_{3}$ have quasiparticles at energies of zone center magnons. In both cases, increasing the applied field, the $\sim$ 20 cm$^{-1}$ line matching the lowest energy magnon, has its intensity reduced sharply while bands associated in TmMnO$_{3}$ to magnon--acoustical phonon dispersion crossing and gap opening behave differently. The line at $\sim$ 48 cm$^{-1}$, the higher branch of the phonon gap, shows a Zeeman splitting-like behavior, while the lower branch at $\sim$ 31 cm$^{-1}$ has weak field dependences. The asymmetric envelope peaking at $\sim$ 35 cm$^{-1}$ in NdMnO$_{3}$ weakens, softens, and evolves at 8 T into two unresolved bands suggesting field induced TA$+$magnon coupling materializing a condition for a multiferroic state. Metastable orthorhombic ErMnO$_{3}$ has two bands at 5 K which resembles those of NdMnO$_{3}$. A remarkable 35 cm$^{-1}$ Zeeman splitting at 5 K in PrCrO$_{3}$ is tentatively associated to Cr$^{3+}$ electrons in a distorted polarizable p-d bond. ErCrO$_{3}$ shows such a feature at 50 cm$^{-1}$ as well additional zero field splitting at 8 and 9 cm$^{-1}$ in the spin reorientation phase.