Lattice dynamics and spin-phonon coupling in orthorhombicEu1−xHoxMnO3(x≤0.3)studied by Raman spectroscopy

${\text{Eu}}_{1\ensuremath{-}x}{\text{Ho}}_x{\text{MnO}}₃$ with $x<0.5$ has an orthorhombic perovskite structure, where the partial substitution of europium by holmium increases the orthorhombic distortion and changes the low-temperature magnetic structure from canted antiferromagnetic to the multiferroic ground state with cycloidal spin arrangement for $x>0.2$. We employ polarized, temperature-dependent Raman spectroscopy to study the lattice dynamics and spin-phonon coupling (SPC) effects for the two representative compositions $x=0.1$ and $x=0.3$. We observe an enhancement of phonon frequencies by ${\text{Ho}}³⁺$ substitution and we use the ${A}_g(4)$ mode as a measure to evaluate the orthorhombic distortion angle $\ensuremath{\theta}$. SPC manifests itself as mode-specific softening for $T<100$ K, induced by the magnetic ordering of ${\text{Mn}}³⁺$ spins. Furthermore, we present evidence that the hitherto elusive Raman peak at $\ensuremath{\approx}650\phantom{\rule{0.28em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ is a phonon of ${B}_3g$ symmetry and ascribe it to the ${B}_3g(1)$ out-of-phase ${\text{MnO}}₆$-breathing mode. We show that this mode has the strongest SPC effect of all observed phonon modes, a fact which we explain by the participation of the apical O(1) ions, modulating the Mn-O(1)-Mn bond whose SPC contribution was hitherto not accessible. Finally, we present a quantitative evaluation of the SPC contribution by the antiferromagnetic plane-to-plane coupling through the Mn-O(1)-Mn bonds and discriminate if from the in-plane ferromagnetic Mn-O(2)-Mn part.