Domain fluctuations near the field-induced incommensurate-commensurate phase transition of ${\text{TbMnO}}_3$

We present temperature- and field-dependent inelastic light-scattering studies of multiferroic ${\text{TbMnO}}_3$. By carefully examining the evolution of magneto-elastic modes in various phases of ${\text{TbMnO}}_3$, our study reveals several features of the field-induced incommensurate-commensurate (IC-C) transition in ${\text{TbMnO}}_3$. We find that, for fields applied along the $b$ axis, there is a coexistence of distinct structural phases in the intermediate field regime $\left(H=4–7\text{T}\right)$ around the IC-C-phase transition. We present evidence for the existence of dynamical fluctuations of the C phase for fields lower than the critical field for $\mathbf{H}$ along the $b$ axis, $H<H_c^b$. Furthermore, we present evidence for strong spin-lattice coupling effects in ${\text{TbMnO}}_3$ in the form of zone-boundary phonon modes that strongly couple to the spins by modulating the exchange interaction in this material.

Figure 1

(Color online) (a) Room temperature Raman spectrum of ${\text{TbMnO}}_3$. (b) Temperature dependence of the zero-field Raman spectra in the $115–155{\text{cm}}^{-1}$ spectral range showing the evolution of the IC mode at $125{\text{cm}}^{-1}$; the dashed line is a guide to the eye. (c) Field dependence of ${\text{TbMnO}}_3$ at $T=10\text{K}$ for $\text{H}\parallel b$ (top) and $\text{H}\parallel a$ (bottom) axes. The C mode is induced at $137{\text{cm}}^{-1}$ for $H>4\text{T}$ along the $b$ axis but is not present up to $H=8\text{T}$ for applied fields along the $a$ axis.

Figure 2

(Color) The established phase diagram for ${\text{TbMnO}}_3$ (from Ref. 2) overlaid with our data for the IC and C modes, represented by green circles and red squares, respectively. The sizes of the circles and squares provide a rough indication of the relative intensity of the IC and C modes, respectively.

Figure 3

(Color) Field dependence of ${\text{TbMnO}}_3$ at (a) 10 and (b) 25 K. Dashed lines illustrate Lorentzian fits to the C and $147{\text{cm}}^{-1}$ modes, used to extract intensity and linewidth parameters for the C mode. (c) Summary of the linewidth (circles) and lifetime (squares) of the C mode as a function of applied field at $T=10\text{K}$. The linewidth values include a $\sim 0.3{\text{cm}}^{-1}$ contribution associated with the instrumental resolution of the instrument.

Figure 4

(Color) Contour plots of the (a) linewidth and (b) intensity of the C mode as a function of temperature and applied field $\left(\mathbf{H}\parallel b\right)$. The dashed lines indicate the established phase boundary lines from Ref. 2. The insets shows summary plots of the (a) linewidth and (b) intensity vs field of the C mode at different temperatures.

Figure 5

(Color online) Field dependence (at $T=10\text{K}$) of the (a) integrated intensity and (b) frequency of the $A_g$ symmetry Tb-phonon mode associated with the IC phase (blue squares), where the phonon frequency is $\sim 147{\text{cm}}^{-1}$, and with the C phase (red circles), where the phonon frequency is $\sim 144{\text{cm}}^{-1}$. The gray shaded area highlights a region of coexistence of the 144 and $147{\text{cm}}^{-1}$ Tb modes, indicating a coexistence of IC and C phases in this intermediate field region. The inset illustrates Lorentzian fits to the raw 10 K spectrum in the intermediate field regime $\left(H=6\text{T}\right)$, showing the coexistence of 144 and $147{\text{cm}}^{-1}$ Tb modes in this region.