Systematics of electromagnons in the spiral spin-ordered states of $R{\text{MnO}}_3$

Electromagnon, magnetic excitation driven by an electric field of light, has been investigated for a series of perovskite manganites $R{\text{MnO}}_3$. Two distinct excitations commonly appear in the spiral spin-ordered state, and systematic changes in their peak positions and spectral weights were observed as a function of the radius of the $R$-ion or equivalently of spin-exchange interaction energies. By comparing the results with the spin-wave calculation based on the Heisenberg model, the higher-lying excitation is assigned to the zone-edge magnon. The strong electric-dipole activity of these magnetic excitations is discussed in terms of dynamic coupling among the collective modes.

Figure 1

(Color online) (a) The optical conductivity spectra ${\sigma }_1\left(\omega \right)$ below 20 meV of ${\text{Gd}}_{0.7}{\text{Tb}}_{0.3}{\text{MnO}}_3$ along the $a$ axis. The results displayed with the symbols (below $\sim 8\text{meV}$) are taken from Ref. 13. The inset shows ${\sigma }_1\left(\omega \right)$ of ${\text{Gd}}_{0.7}{\text{Tb}}_{0.3}{\text{MnO}}_3$ at 10 K and of ${\text{GdMnO}}_3$ at 15 K, both of which are in the $A$-AFM state. (b) Temperature-dependent spectral weight of the electromagnons obtained by integrating ${\sigma }_1\left(\omega \right)$ up to 12.5 meV.

Figure 2

(Color online) The optical conductivity spectra ${\sigma }_1\left(\omega \right)$ of $R{\text{MnO}}_3$ in the spiral spin (ferroelectric) state and the paramagnetic/paraelectric state for (a) $R={\text{Gd}}_{0.7}{\text{Tb}}_{0.3}$, (b) ${\text{Gd}}_{0.5}{\text{Tb}}_{0.5}$, (c) ${\text{Gd}}_{0.1}{\text{Tb}}_{0.9}$, (d) ${\text{Tb}}_{0.41}{\text{Dy}}_{0.59}$, and (e) Dy. In each curve, the symbols correspond to the results obtained by THz time-domain spectroscopy and the solid and dashed lines by Fourier-transform spectroscopy. The results displayed with the symbols for $R={\text{Gd}}_{0.7}{\text{Tb}}_{0.3}$ are taken from Ref. 13.

Figure 3

(Color online) (a) Peak positions of the electromagnons (modes $A$ and $B$) as a function of the radius of the $R$ ions. Open symbols are zone-edge magnon energies as the energy of mode $B$ obtained by the spin-wave theory using two sets of exchange energies; parameters for Cal.1 (Cal.2) are shown by open (closed) symbols in Fig. 4b. (b) SW of the electromagnon; the respective SW for modes $A$ and $B$ and their total sum. The values are the differences between the SWs at 10 and 50 K. The result for $R={\text{Gd}}_{0.7}{\text{Tb}}_{0.3}$ is omitted since the lowest temperature for the available data is 16 K, which is rather high compared to 10 K considering the strong temperature dependence of the spectral weight. The solid lines are merely guides for the eyes.

Figure 4

(Color online) (a) Sketch of the crystal structure of $R{\text{MnO}}_3$ in the $ab$ plane with $R$ ion omitted. Exchange energies of $J_{ab}$ (ferromagnetic) and $J_b$ (antiferromagnetic) are indicated. The arrows correspond to the local spins and their oscillations with an excitation of the magnon at $q=\left(0,1,0\right)$. (b) $\left|J_{ab}\right|$, $J_b$, and $J_c/\left|J_{ab}\right|$ as a function of the radius of the $R$ ions. The open symbols correspond to the first parameter set obtained by using structural data reported by Alonso et al. (Ref. 20), and closed symbols correspond to the second set estimated to reproduce the neutron scattering and the magnetic-resonance experiments (Ref. 16). [(c) and (d)] Magnon dispersions along the $b$ axis with the parameters corresponding to $R={\text{Gd}}_{0.7}{\text{Tb}}_{0.3}$, Tb, and Dy.