Lattice dynamics and spin-phonon coupling in orthorhombic ${\text{Eu}}_{1-x}{\text{Ho}}_x{\text{MnO}}_3(x\le 0.3)$ studied by Raman spectroscopy

${\text{Eu}}_{1-x}{\text{Ho}}_x{\text{MnO}}_3$ 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 $A_g\left(4\right)$ mode as a measure to evaluate the orthorhombic distortion angle $\theta$. 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 $\approx 650{\text{cm}}^{-1}$ is a phonon of $B_{3g}$ symmetry and ascribe it to the $B_{3g}\left(1\right)$ 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.

Figure 1

Left: ideal cubic $R{\text{MnO}}_3$ perovskite unit cell. All axes are parallel to the Mn-O bonds. Right: orthorhombic distorted perovskitelike unit cell with tilted ${\text{MnO}}_6$ octahedra and with axes labeled in the Pnma notation. The $a$ and $c$ axes are rotated by ${45}^{\circ }$ relative to the cubic unit cell and elongated by a factor of $\sqrt{2}$; the $b$ axis is elongated by a factor of 2. The oxygen ions in the ${\text{MnO}}_2$ planes are denoted as O(2), and the apical ones as O(1).

Figure 2

Raman spectra of ${\text{Eu}}_{0.9}{\text{Ho}}_{0.1}{\text{MnO}}_3$ and ${\text{Eu}}_{0.7}{\text{Ho}}_{0.3}{\text{MnO}}_3$ for the polarization configurations $b(c,a)\overline{b}$ ($B_{2g}$ modes allowed) and $b(c,c)\overline{b}$ ($A_g$ modes allowed) at $T=5$ K.

Figure 3

Raman spectrum for ${\text{Eu}}_{0.9}{\text{Ho}}_{0.1}{\text{MnO}}_3$ at 10 K in the $a(c,b)\overline{a}$ configuration. The assignment of $B_{3g}$ modes according to [14, 34] is indicated in blue.

Figure 4

Temperature dependence of phonon frequencies in ${\text{Eu}}_{0.9}{\text{Ho}}_{0.1}{\text{MnO}}_3$ and ${\text{Eu}}_{0.7}{\text{Ho}}_{0.3}{\text{MnO}}_3$. The spin-ordered phases are labeled according to literature [27]. The frequency error bars were obtained from Lorentzian peak fits. For those modes, for which no error bars are visible, they are below the size of the data point symbols. Red lines: fit according to decay-induced $T$ dependence. The deviation in the low-$T$ range is due to spin-phonon coupling. Green arrows indicate the maximum magnitude of SPC-induced shift in the low-$T$ phase.

Figure 5

SPC-induced relative frequency shift of all observed modes vs temperature. The vertical dashed lines indicate the magnetic transition temperatures. Middle row: ${\text{Eu}}_{0.9}{\text{Ho}}_{0.1}{\text{MnO}}_3$; bottom row: ${\text{Eu}}_{0.7}{\text{Ho}}_{0.3}{\text{MnO}}_3$. For comparison, data of pure $\text{Eu}{\text{MnO}}_3$ was added from Issing et al. [20] (top row).