Field and temperature dependence of electromagnon scattering in ${\text{TbMnO}}_3$ studied by inelastic neutron scattering

Inelastic neutron scattering techniques have been used to study the field-induced multiferroic transition and the temperature dependence of magnetic excitations in ${\text{TbMnO}}_3$. The significant changes in the spin-wave spectra across the field-induced transition perfectly agree with a rotation of the cycloidal spiral plane and with efficient pinning in the commensurate high-field phase. Further analysis of the $\mathbf{Q}$ dependence allows the identification of an electromagnon in the multiferroic high-field phase whose energy and polarization precisely matches previous infrared data. This and the zero-field temperature dependence of a zone-center magnon, which exactly agrees with that of an optically detected excitation, document that the inverse Dzyaloshinskii-Moriya interaction induces an electromagnon hybrid excitation in ${\text{TbMnO}}_3$.

Figure 1

Sketch of the different magnon excitations at the magnetic zone center of the cycloid structure in the LF-IC phase (upper panels) and in the HF-C phase (lower panels). The static spin structure is marked by thick gray, and the local fluctuations by smaller colored arrows. In each of the two phases there are a phason mode (top) and cycloid rotation modes around the $\mathbf{b}$ direction (middle) and around the vector in the cycloid plane perpendicular to $\mathbf{b}$ (bottom). The axis vectors show the oscillation of the spin vector products ${\mathbf{S}}_i\times {\mathbf{S}}_j$.

Figure 2

(a) Schematic phase diagram of ${\text{TbMnO}}_3$ for magnetic fields applied along $\mathbf{b}$ [7]. Points denote the positions of the recorded spin-wave spectra, the line highlights the position of the temperature scan in (b). (b) Neutron intensity of the Bragg peak position ${\mathbf{Q}}_2=\left(2q_{k}1\right)$ as function of temperature in 8 T applied along $\mathbf{b}$. The gray bars indicate the magnetic phase transitions.

Figure 3

Zone center excitations at the magnetic Bragg positions ${\mathbf{Q}}_1=\left(0q_{k}1\right)$ and ${\mathbf{Q}}_2=\left(2q_{k}1\right)$. The spectra were recorded at (a) 12 K and 0 T, (b) 2 K and 0 T, (c) 12 K and 8 T, and (d) 2 K and 8 T, with the magnetic field applied along $\mathbf{b}$. The gray bars denote the positions of the low-energy magnon modes of the Mn order.

Figure 4

Magnetic field dependence of the zone center excitations at the magnetic Bragg positions ${\mathbf{Q}}_1=\left(0q_{k}1\right)$ and ${\mathbf{Q}}_2=\left(2q_{k}1\right)$ for field applied along $\mathbf{b}$ at 2 K.

Figure 5

Temperature dependence of the zone center excitations at the magnetic Bragg positions ${\mathbf{Q}}_1=\left(0q_{k}1\right)$ and ${\mathbf{Q}}_2=\left(2q_{k}1\right)$ in 8 T applied along $\mathbf{b}$.

Figure 6

Intensity mapping of the spin-wave excitations at $T=12$ K (a) and $T=2$ K (b) along the direction [$H$ 0 0] between the magnetic zone centers ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ in 8 T applied along $\mathbf{b}$.

Figure 7

(a) Temperature dependence of the zone center excitations at the magnetic Bragg position ${\mathbf{Q}}_1=\left(0q_{k}1\right)$ in zero magnetic field. The gray line may be used as guide to the eye to follow the position of the two electromagnon excitations. (b) Comparison of magnetic excitations investigated by neutron scattering with IR data from Pimenov et al. (red triangles) [11].