Evidence for an Electric-Dipole Active Continuum Band of Spin Excitations in Multiferroic ${\mathrm{TbMnO}}_3$

The wide range optical spectra on a multiferroic prototype ${\mathrm{TbMnO}}_3$ have been investigated to clarify the origin of spin excitations observed in the far-infrared region. We elucidate the full band structure, whose high energy edge ($133{\mathrm{cm}}^{-1}$) exactly corresponds to twice of the highest-lying magnon energy. Thus the origin of this absorption band is clearly assigned to two-magnon excitation driven by the electric field of light. There is an overlap between the two-magnon and phonon energy ranges, where the strong coupling between them is manifested by the frequency shift and transfer of oscillator strength of the phonon mode.

Figure 1

(a) The schematic of the spin structure and direction of the spontaneous polarization in the $bc$-plane transverse-spiral (cycloidal) spin state of ${\mathrm{TbMnO}}_3$ in the orthorhombic setting. (b) The magnon dispersion reproduced from Ref 16. Solid lines represent the dispersion calculated by the linear spin wave theory on the $bc$-spiral state with use of spin exchange interaction parameters; $J_1=-0.85\mathrm{meV}$, $J_2=+0.68\mathrm{meV}$, and $J_c=+1.28\mathrm{meV}$ (see text).(c) The ${ϵ}_2$ spectrum with $E^{\omega }\parallel a$ at 12 K. The energy region of the magnon, the 2M excitation, and optical phonon are indicated by arrows. (d) The ${ϵ}_2$ spectra at 12 and 250 K below $290{\mathrm{cm}}^{-1}$, where the magnetic excitation and the lower-lying optical phonon modes are located. The phonon modes in this energy range are denoted as A, B, and C. (e) The ${ϵ}_2$ spectrum at 12 K and for $E^{\omega }\parallel a$ of the 2M band and the lowest optical phonon mode, where the tail of the phonon B is subtracted. Dashed line represents the DOS of the 2M excitation obtained by the linear spin wave theory (see text).

Figure 2

The ${ϵ}_2$ spectra in all the polarization ($E^{\omega }$, $H^{\omega }$) configurations of light, measured at 12, 30, 250 K. $E^{\omega }$ and $H^{\omega }$ represent electric and magnetic fields of light.

Figure 3

Temperature dependence of the ${ϵ}_2$ spectra in $E^{\omega }\parallel a$. Three energy ranges are indicated as I, II, and III. The inset shows the detailed change of the phonon mode A between 110 and $120{\mathrm{cm}}^{-1}$.

Figure 4

(a) Temperature variation of the spectral weight ($N_{\mathrm{eff}}$; see text for the definition) in the respective energy regions, I, II and III (see Fig. 3). $\Delta N_{\mathrm{eff}}$ is defined as the difference from the $N_{\mathrm{eff}}$ value at 250 K. (b) The temperature dependence of the phonon mode frequencies normalized by the respective values at 250 K, where A, B, and C indicates the phonon modes as defined in Fig. 1d. The $\Delta N_{\mathrm{eff}}$ in the energy region I (the lower-energy region of the 2M band) is also shown.