Lattice contributions to the anisotropic dielectric response of rare-earth langasites

We investigate the phonon spectrum of pure and rare-earth substituted langasites. For electric fields oriented along the $c$ axis, a strong low-frequency phonon is observed, softening at lower temperature in all samples studied. The dielectric contribution and temperature dependence of this mode is the primary source of the large $\left[\varepsilon \right(0)\sim 100]$ static dielectric permittivity observed in these systems. Softening of this mode with increasing mass of the rare-earth substitutes further suggests that langasites are close to a structural instability at low temperatures. The application of a magnetic field to a diluted Ho-langasite sample reveals a shift in the strong absorption band at THz frequencies associated with this soft lattice mode, suggesting spin-lattice effects may also be at play in these systems.

Figure 1

Crystal structure of langasite. The geometry of the different sites is labeled on the right along with the ions and Wycoff positions.

Figure 2

Reflectance of LGS parallel (a) and perpendicular (b) to the polar $c$ axis at three temperatures as indicated. The arrows in the top panel indicate the four lowest frequency lattice modes in $c$ direction labeled P1–P4. Results for the full spectral range out to 2000 ${\mathrm{cm}}^{-1}$ can be found in the Supplemental Material [22].

Figure 3

Reflectance of LGS parallel to the $c$ axis at three temperatures as indicated. The data points represent the raw measurements, solid lines represent the fit with two oscillators, while dashed lines show fits for one oscillator.

Figure 4

Real (a) and imaginary part (b) of the dielectric permittivity ${\varepsilon }^{*}={\varepsilon }_1+i{\varepsilon }_2$ for LGS at 10, 200, and 300 K for $e\parallel c$. Results for the full spectral range out to 600 ${\mathrm{cm}}^{-1}$ and for $e\parallel b^{*}$ can be found in the Supplemental Material [22].

Figure 5

(a) Dielectric contribution $\mathrm{\Delta }\varepsilon$ of the first four oscillators with $e\parallel c$, demonstrating the dominant contribution of the P1 and P2 phonons. (b) Peak positions of the first four phonons obtained from the fits to ${\varepsilon }_2\left(\omega \right)$. The inset in (a) shows the spectral weight of two lowest phonons.

Figure 6

Comparison of (a) real and (b) imaginary dielectric permittivity of the four different langasite samples at room temperature along the $c$ axis in the low-frequency range.

Figure 7

Parameters of the lowest-frequency phonon as function of atomic number for different rare-earth langasites. For the mixed Ho-LGS a weighted effective number has been utilized. (a) Resonance frequency, (b) dielectric contribution, and (c) spectral weight $\text{SW}=\mathrm{\Delta }\varepsilon {\nu }_{0,1}^2$. A linear trend in ${\nu }_{0,1}$ and in $\mathrm{\Delta }\varepsilon$ for increasing atomic number is given by thin dotted lines. This behavior leads to approximately constant spectral weight of all langasites (horizontal line in the bottom panel). Additional axes for the masses and atomic radii are given for reference.

Figure 8

Magneto-optical THz transmission measurements of Ho-LGS for electric field of light parallel to the $c$ axis. The inset shows the transmission spectrum at 0 T with a fit incorporating a single Lorentz oscillator (solid red curve). The main panel shows the relative change in transmission as magnetic field is applied along the $c$ axis of the sample in Voigt geometry.

Figure 9

Comparison of static dielectric permittivity of all four investigated langasite crystals. Filled circles represent the sum of dielectric contributions of all phonons obtained from the fit to the far-infrared spectra. The orange crosses represent the summed contributions from the two lowest-frequency phonons P1 and P2. The values of ${\varepsilon }_0$ were measured at a frequency of $\nu =10$ kHz. In the LGS plot (top left), the static permittivity agrees closely with that of Mill et al. [1] (black crosses), in the Nd-LGS blue crosses on top of the PPMS data show additional measurements with a backward-wave oscillator performed at 3 ${\mathrm{cm}}^{-1}$.

Figure 10

Overview of the squared frequencies of the lowest oscillator from the fits. Dashed lines are linear extrapolations. These fits intercept the zero line at different temperature, increasing with atomic number.