Spin-phonon coupling and isotope-related pseudo-molecule vibrations in layered Cr$_2$Ge$_2$Te$_6$ ferromagnet

TL;DR

This work probes spin-phonon coupling in the layered ferromagnet CGT by combining high-resolution, polarization-resolved Raman spectroscopy with first-principles phonon calculations. All 10 predicted Raman-active modes ($5A_g$ and $5E_g$) are observed, and a quantitative map of mode-dependent spin-phonon coupling is obtained across magnetic transitions near $T_C$ and $T^*$. A novel Ge-Ge pseudo-molecule, isotope-based model explains the fine structure of the $A_g^5$ mode, linking Ge isotope configurations to discrete Raman features and yielding a Ge-Ge force constant of about $K \approx 187$ N/m. The results underscore strong magneto-elastic effects in CGT and demonstrate isotope-driven vibrational fine structure as a probe of geochemical and spin dynamics in van der Waals ferromagnets, with implications for spintronic device concepts.

Abstract

The vibrational structure of chromium germanium telluride (Cr$_2$Ge$_2$Te$_6$, CGT) is investigated and a strong spin-phonon coupling is revealed. The measured high-resolution Raman scattering (RS) spectra are composed of the 10 Raman-active modes: 5A$_\textrm{g}$ and 5E$_\textrm{g}$, predicted by calculation using the density functional theory and identified using polarization-resolved RS measurements. We also studied the effect of temperature on the RS spectra of CGT from 5~K to 300~K. A strong magneto-phonon coupling in CGT is revealed at temperatures of about 150~K and 60~K, which are associated with the appearance of the local magnetic order in the material and the transition to the complete ferromagnetic phase, respectively. Moreover, a unique shape of the A$_g^5$ mode composed of a set of very narrow Raman peaks is simulated using a model that takes into account vibrations of Ge-Ge pseudo-molecules for various Ge isotopes.

Figures (14)

• Figure 1: The schematic representation of (a) perspective with rombohedral axis, (b) side, and (c) top views with hexagonal axis of the atomic structure of the CGT crystal. The black shapes represent the unit cells.
• Figure 2: Phonon dispersion of bulk CGT crystal in rhombohedral primitive cell with ferromagnetic order. The $\Gamma$ point corresponds to center of the Brillouin zone.
• Figure 3: Raman Scattering spectra of the 24 nm thick CGT flake measured at 5 K with co-linear (XX) and cross-linear (XY) polarization using excitation energy 1.58 eV and excitation power of 1 mW. The horizontal scale was adjusted with breaks for clarity.
• Figure 4: False-color map of the temperature evolution of the RS spectra of the exfoliated 24-nm thick CGT flake under 1.58 eV excitation with 1 mW power. The white horizontal dash-dot line denotes Curie temperature ($T_C$) of CGT. The horizontal scale was adjusted with breaks for clarity.
• Figure 5: Temperature evolutions of the (a) Raman shifts, (b) linewidths and (c) integrated intensities of the selected four Raman modes, $i.e.$ A$_g^1$, E$_g^2$, A$_g^3$, E$_g^4$ measured on the exfoliated 24-nm thick CGT flake. The black vertical dash-dot line corresponds to the Curie temperature ($T_C$), while the red vertical doted line denote the second phase change temperature ($T^*$). The gray curves are result of fitting using Balkanski model (Eg. \ref{['balkanski']}) to the data measured only above the $T_1$, $i.e.$ in the paramagnetic phase.