Raman spectroscopy of the magnetic coupling in Gd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>i</mml:mi></mml:math>-MAX

We report the investigation of electronic collective modes in rare-earth- (RE) based magnets ${({\mathrm{Mo}}_{2/3}{\mathrm{RE}}_{1/3})}_{2}\mathrm{AlC}$ (also known as RE-$i$-MAX phases), where $\mathrm{RE}=\mathrm{Gd}$, Yb, and Dy, using single crystal samples. In particular, a detailed investigation of the Raman spectra of Gd-$i$-MAX samples at low temperatures, with a focus on the phonon behavior in relation to the antiferromagnetic (AFM) phase transition at 26 K is presented. Significant shifts in the central frequencies of several low-frequency phonon modes were observed below 25 K, correlating with the N\'eel transition. Integrated Raman intensity measurements indicated a reduction in the electronic background below the AFM transition temperature, suggesting the opening of a magnetic gap. Our analysis showed no new phonon modes. Therefore, we do not see any indication of a Brillouin zone folding of phonon mode on cooling. However, the hardening of all phonon modes at low temperatures points to a strong spin-phonon coupling effect. Using a temperature-dependent model of phonon frequency, we determined the spin-phonon coupling constant $\ensuremath{\lambda}$ to be less than 0.1 ${\mathrm{cm}}^{\ensuremath{-}1}$ for all frequencies, which is of the same order of magnitude as found in other antiferromagnetic materials such as ${\mathrm{MnF}}_{2}$ and ${\mathrm{FeF}}_{2}$ with ${T}_{N}=68$ K and ${T}_{N}=78$ K, respectively, but significantly lower than that of CuO with ${T}_{N}=213$ K.