Terahertz and infrared spectroscopic evidence of phonon-paramagnon coupling in hexagonal piezomagnetic YMnO${}_3$

Terahertz and far-infrared electric and magnetic responses of hexagonal piezomagnetic YMnO${}_3$ single crystals are investigated. Antiferromagnetic resonance is observed in the spectra of magnetic permeability ${\mu }_a$ [H$\left(\omega \right)$ oriented within the hexagonal plane] below the Néel temperature $T_N$. This excitation softens from 41 to 32 ${\text{cm}}^{-1}$  upon heating and finally disappears above $T_N$. An additional weak and heavily-damped excitation is seen in the spectra of complex dielectric permittivity ${\varepsilon }_c$ within the same frequency range. This excitation contributes to the dielectric spectra in both antiferromagnetic and paramagnetic phases. Its oscillator strength significantly increases upon heating toward room temperature, thus providing evidence of piezomagnetic or higher-order couplings to polar phonons. Other heavily-damped dielectric excitations are detected near 100 ${\text{cm}}^{-1}$  in the paramagnetic phase in both ${\varepsilon }_c$ and ${\varepsilon }_a$ spectra, and they exhibit similar temperature behavior. These excitations appearing in the frequency range of magnon branches well below polar phonons could remind electromagnons, however their temperature dependence is quite different. We have used density functional theory for calculating phonon dispersion branches in the whole Brillouin zone. A detailed analysis of these results and of previously published magnon dispersion branches brought us to the conclusion that the observed absorption bands stem from phonon-phonon and phonon-paramagnon differential absorption processes. The latter is enabled by strong short-range in-plane spin correlations in the paramagnetic phase.

Figure 1

Complex THz spectra of YMnO${}_3$ taken at various temperatures. The polarization of the THz beam is indicated above the plots. The resonance feature near $\sim$40 ${\text{cm}}^{-1}$ corresponds to the doubly-degenerated AFM mode contributing to the magnetic permeability ${\mu }_a$ spectra.

Figure 2

Temperature dependence of the complex permittivity ${\varepsilon }_c$ and permeability ${\mu }_a$ spectra calculated from data plotted in Fig. 1. The solid ${\varepsilon }_c$ curves at 100 and 140 K result from the oscillator fit.

Figure 3

Temperature dependences of parameters of the resonances observed in magnetic ${\mu }_a$ and dielectric ${\varepsilon }_c$ spectra. Closed circles: frequency of the AFM resonance. Solid squares and open triangles: eigenfrequency ${\omega }_{\text{diel}1}$ and oscillator strength $\Delta \varepsilon {\omega }_{\text{diel}1}^2$, respectively, of the mode observed in the dielectric spectra in Fig. 2. The dotted line shows the population increase of an energy level at 66 ${\text{cm}}^{-1}$  following the Bose-Einstein statistics.

Figure 4

Example of the experimental FTIR transmittance and reflectivity spectra of 348-$\mu$m-thick YMnO${}_3$ crystal with polarization $\mathbf{E}\parallel \mathbf{c}$ obtained at 120 K. Dashed-dotted blue line: theoretical transmittance spectrum obtained from parameters of the FTIR reflectivity fit (without considering modes observed by THz spectroscopy); solid red line: simultaneous fit of the FTIR transmission and THz spectra. Dashed green line is the result of a fit of the reflectivity using the parameters obtained from the fit of FIR and THz transmittance. One can see that the reflectivity spectrum is not sensitive enough to detect the weak broad modes near 40 and 100 ${\text{cm}}^{-1}$. Oscillations in the experimental reflectivity spectrum observed below 80 ${\text{cm}}^{-1}$  are caused by the diffraction of FIR beam on a small sample.

Figure 5

The measured THz loss spectra of YMnO${}_3$ (symbols) and those obtained from the fits of FTIR transmittance and reflectivity spectra. Below $T_N=70$ $\text{K}$, the spectra correspond to imaginary parts of the permittivity-permeability product. Above $T_N$, the spectra correspond to the dielectric losses. Polarizations of electric and magnetic components of IR or THz beams are indicated. Dashed lines are the fits of room-temperature FTIR reflectivity spectra without taking into account the IR and THz transmittance spectra. The marked peaks above 150 ${\text{cm}}^{-1}$ are due to phonons; the origin of lower frequency absorption bands is discussed in the text.

Figure 6

Temperature dependence of the (a) permittivity and (b) dielectric loss measured at 20 ${\text{cm}}^{-1}$  with polarization $\mathbf{E}\perp \mathbf{c}$ (red solid lines) and $\mathbf{E}\parallel \mathbf{c}$ (black dashed lines).

Figure 7

Dispersion branches of phonons (theoretical; black solid lines) and magnons (experimental[35] at 7 $\text{K}$; red dashed lines). The red-dotted line indicates the presumable dispersion of the paramagnon near the $M$ point. The symbols shown at the BZ edges indicate the polarization of the phonons at the BZ boundary: $a$ and $c$ stand for phonons polarized within the hexagonal plane and in the perpendicular direction, respectively. In the $\Gamma$-point, the $E_1$ and $A_1$ phonons observed experimentally[30] are marked by green and blue points, respectively; other modes are silent. Blue arrows with assignment ${\omega }_{\text{diel}1}$ and ${\omega }_{\text{diel}2}$ indicate phonon-paramagnon excitations observed in the dielectric loss spectra of ${\varepsilon }_c^{\prime \prime }$. Green arrow marked as ${\omega }_{\text{diel}3}$ indicates a broad multiphonon absorption observed in the ${\varepsilon }_a^{\prime \prime }$ loss spectra (see Fig. 5).