Magnetic Excitations in Multiferroic ${\mathrm{TbMnO}}_3$: Evidence for a Hybridized Soft Mode

The magnetic excitations in multiferroic ${\mathrm{TbMnO}}_3$ have been studied by inelastic neutron scattering in the spiral and sinusoidally ordered phases. At the incommensurate magnetic zone center of the spiral phase, we find three low-lying magnons whose character has been fully determined using neutron-polarization analysis. The excitation at the lowest energy is the sliding mode of the spiral, and two modes at 1.1 and 2.5 meV correspond to rotations of the spiral rotation plane. These latter modes are expected to couple to the electric polarization. The 2.5 meV mode is in perfect agreement with recent infrared-spectroscopy data giving strong support to its interpretation as a hybridized phonon-magnon excitation.

Figure 1

Raw-data scans at the incommensurate zone center and at the $b$-axis zone boundary in the spiral phase (PANDA and 4F, $k_f=1.5{\AA }^{-1}$) (a); $\mathbf{Q}$ dependence of the signal (b). Full polarization analysis of the magnetic excitations at the incommensurate zone center and at the zone boundary (IN14, $k_f=1.5{\AA }^{-1}$) (c) and (d).

Figure 2

Raw-data scans to determine the magnon dispersion in ${\mathrm{TbMnO}}_3$ along $a$ and $c$ directions starting at the incommensurate zone center (0,0.28,1), (PUMA, $k_i=2.662{\AA }^{-1}$).

Figure 3

Dispersion of the spin-wave excitations in ${\mathrm{TbMnO}}_3$ along the $a$ and the $c$ directions of the $Pbnm$ lattice in the paraelectric sinusoidal phase (a) and in the ferroelectric spiral phase (b). Dispersion along the modulation vector in the spiral and in the SDW phase (c). Polarization of the three low-energy modes at the incommensurate zone center (d): the two $a$-polarized modes, (1) and (2), and the sliding mode of the spiral, (3), see text.

Figure 4

Temperature dependence of the magnetic scattering at the incommensurate zone center determined with unpolarized neutrons (PUMA, $k_i=2.662{\AA }^{-1}$ constant) (a) and with polarized neutrons (IN14, $k_f=1.5{\AA }^{-1}$ constant) (b).