Determining the vibrational entropy change in the giant magnetocaloric material LaFe_(11.6)Si_(1.4) by nuclear resonant inelastic x-ray scattering

摘要

Magnetocaloric LaFe_(13-x), Si,-based compounds belong to the outstanding materials with potential for efficient solid-state refrigeration. We have performed temperature-dependent (57)~Fe nuclear resonant inelastic x-ray scattering measurements (in a field μ_0lH of ~0.7 T) of the vibrational (phonon) density of states, VDOS, in LaFen6Si|4 across the metamagnetic isostructural first-order phase transition at Tc ~ 192 K from the low-temperature ferromagnetic (FM) to the high-temperature paramagnetic (PM) phase, in order to determine the change in thermodynamic properties of the Fe lattice at T_c. The experimental results are compared with density-functional-theory-based first-principles calculations using the fixed-spin moment approach. Our combined experimental and theoretical results reveal distinct and abrupt changes in the VDOS of the Fe sublattice across Tc, occurring within a small temperature interval of △T ≤ 12 K around T_c. This indicates that strong magnetoelastic coupling fat the atomic scale) is present up to T_c, leading to a pronounced lattice softening (phonon redshift) in the PM phase. These changes originate from the itinerant electron magnetism associated with Fe and are correlated with distinct modifications in the Fe-partial electronic density of states D(E_f) at the Fermi energy E_F. From the experimental VDOS we can infer an abrupt increase (jump) in the Fe-partial vibrational entropy △S_(vib) of +6.9 ± 2.6 J/(kg K)and in the vibrational specific heat △C_(vib), of +2.7 ± 1.6 J/(kg K)upon heating. The increase in magnitude of the vibrational entropy | △S_(vib)| = 6.9 J/(kg K) of the Fe sublattice at T_c upon heating is substantial, if compared with the magnitude of the isothermal entropy change |△5_(iso)| of 14.2 J/(kg K) in a field change AB from 0 to 1 T, as obtained from isothermal magnetization measurements on our sample and using the Maxwell relation. We demonstrate that △S_(vib) obtained by nuclear resonant inelastic x-ray scattering is a sizable quantity and contributes directly and cooperatively to the total entropy change △5_(iso) at the phase transition of LaFe_(13-x) Si_x.