We have performed a combined experimental and theoretical investigation of the vibrational properties of ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$ Heusler alloys. Sn-partial vibrational density of states (VDOS) of ${}^{119}\mathrm{Sn}$ was measured by nuclear resonant inelastic x-ray scattering at temperatures of 15 and 300 K, while magnetism and local environment of Sn was resolved by ${}^{119}\mathrm{Sn}$ Mössbauer spectroscopy. Using density functional theory, we associate the peaks in the VDOS with particular features in the element-resolved phonon dispersion of $\mathrm{L}{2}_1$ ordered ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$. The good agreement between theory and experiment in the low-energy region provides the evidence that the inversion of optical modes at $\mathrm{\Gamma }$ involving the displacement of Ni and the heavier main group element atoms, which was predicted previously for other Ni-Mn-based Heusler compounds, is also a characteristic property of ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$. Introducing different types of magnetic and antisite disorder in our calculations results in a distinctive redistribution and broadening of the Sn-VDOS, suggesting that considering partial disorder further improves the agreement with the experiment in particular at the highest phonon energies.

• Received 10 August 2022
• Revised 7 November 2022
• Accepted 10 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.214302