We report on the impact of magnetoelastic coupling on the magnetocaloric properties of ${\mathrm{LaFe}}_{11.4}{\mathrm{Si}}_{1.6}{\mathrm{H}}_{1.6}$ in terms of the vibrational (phonon) density of states (VDOS), which we determined with ${}^{57}\mathrm{Fe}$ nuclear resonant inelastic x-ray scattering (NRIXS) measurements and with density functional theory (DFT) based first-principles calculations in the ferromagnetic (FM) low-temperature and paramagnetic (PM) high-temperature phase. In experiments and calculations, we observe pronounced differences in the shape of the Fe-partial VDOS between nonhydrogenated and hydrogenated samples. This shows that hydrogen not only shifts the temperature of the first-order phase transition, but also affects the elastic response of the Fe subsystem significantly. In turn, the anomalous redshift of the Fe VDOS, observed by going to the low-volume PM phase, survives hydrogenation. As a consequence, the change in the Fe-specific vibrational entropy $\mathrm{\Delta }{S}_{\mathrm{lat}}$ across the phase transition has the same sign as the magnetic and electronic contribution. DFT calculations show that the same mechanism, which is a consequence of the itinerant electron metamagnetism associated with the Fe subsystem, is effective in both the hydrogenated and the hydrogen-free compounds. Although reduced by 50% as compared to the hydrogen-free system, the measured change $\mathrm{\Delta }{S}_{\mathrm{lat}}$ of $(3.2\pm 1.9)\frac{\mathrm{J}}{\mathrm{kg}\mathrm{K}}$ across the FM-to-PM transition contributes with $\sim 35$% significantly and cooperatively to the total isothermal entropy change $\mathrm{\Delta }{S}_{\mathrm{iso}}$. Hydrogenation is observed to induce an overall blueshift of the Fe VDOS with respect to the H-free compound; this effect, together with the enhanced Debye temperature observed, is a fingerprint of the hardening of the Fe sublattice by hydrogen incorporation. In addition, the mean Debye velocity of sound of ${\mathrm{LaFe}}_{11.4}{\mathrm{Si}}_{1.6}{\mathrm{H}}_{1.6}$ was determined from the NRIXS and the DFT data.

• Received 3 January 2019
• Revised 25 October 2019
• Accepted 17 December 2019

DOI:https://doi.org/10.1103/PhysRevB.101.064415