Spin-phonon interaction and short range order in $\mathrm{M}{\mathrm{n}}_3\mathrm{S}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_6$

The vibrational properties of ferrimagnetic $\mathrm{M}{\mathrm{n}}_3\mathrm{S}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_6$ single crystals are investigated using Raman spectroscopy and density functional theory calculations. Eighteen Raman-active modes are identified, fourteen of which are assigned according to with the trigonal symmetry. Four additional peaks, obeying the $A_{1g}$ selection rules, are attributed to the overtones. The unconventional temperature evolution of the $A_{1g}^5$ mode self-energy suggests a competition between different short-range magnetic correlations that significantly impact the spin-phonon interaction in $\mathrm{M}{\mathrm{n}}_3\mathrm{S}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_6$. The research provides a comprehensive insight to the lattice properties, studies their temperature dependence and shows the arguments for existence of competing short-range magnetic phases in $\mathrm{M}{\mathrm{n}}_3\mathrm{S}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_6$.