Magnetocaloric $${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$$-based compounds belong to the outstanding materials with potential for efficient solid-state refrigeration. We have performed temperature-dependent $$^{57}\mathrm{Fe}$$ nuclear resonant inelastic x-ray scattering measurements (in a field $${{\mu}}_{0}H$$ of $${\sim}0.7$$ T) of the vibrational (phonon) density of states, VDOS, in $${\mathrm{LaFe}}_{11.6}{\mathrm{Si}}_{1.4}$$ across the metamagnetic isostructural first-order phase transition at $${T}_{C}{\sim}192$$ 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 $${T}_{C}$$, occurring within a small temperature interval of $$\mathrm{{\Delta}}T{\le}12$$ K around $${T}_{C}$$. This indicates that strong magnetoelastic coupling (at 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 $$\mathrm{{\Delta}}{S}_{\mathrm{vib}}$$ of $$+6.9\pm{}2.6$$ J/(kg K) and in the vibrational specific heat $$\mathrm{{\Delta}}{C}_{\mathrm{vib}}$$ of $$+2.7\pm{}1.6$$ J/(kg K) upon heating. The increase in magnitude of the vibrational entropy $$|\mathrm{{\Delta}}{S}_{\mathrm{vib}}|=6.9$$ J/(kg K) of the Fe sublattice at $${T}_{C}$$ upon heating is substantial, if compared with the magnitude of the isothermal entropy change $$|\mathrm{{\Delta}}{S}_{\mathrm{iso}}|$$ of 14.2 J/(kg K) in a field change $$\mathrm{{\Delta}}B$$ from 0 to 1 T, as obtained from isothermal magnetization measurements on our sample and using the Maxwell relation. Finally, we demonstrate that $$\mathrm{{\Delta}}{S}_{\mathrm{vib}}$$ obtained by nuclear resonant inelastic x-ray scattering is a sizable quantity and contributes directly and cooperatively to the total entropy change $$\mathrm{{\Delta}}{S}_{\mathrm{iso}}$$ at the phase transition of $${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$$.
Landers, J., Salamon, S., Keune, W., Gruner, M. E., Krautz, M., Zhao, J., Hu, M. Y., Toellner, T. S., Alp, E. E., Gutfleisch, O., & Wende, H. (2018). Determining the vibrational entropy change in the giant magnetocaloric material <math><msub><mrow><mi mathvariant='normal'>LaFe</mi></mrow><mrow><mn>11.6</mn></mrow></msub><msub><mrow><mi mathvariant='normal'>Si</mi></mrow><mrow><mn>1.4</mn></mrow></msub></math> by nuclear resonant inelastic x-ray scattering. Physical Review B, 98(2). https://doi.org/10.1103/PhysRevB.98.024417
Landers, J., Salamon, S., Keune, W., et al., "Determining the vibrational entropy change in the giant magnetocaloric material <math><msub><mrow><mi mathvariant='normal'>LaFe</mi></mrow><mrow><mn>11.6</mn></mrow></msub><msub><mrow><mi mathvariant='normal'>Si</mi></mrow><mrow><mn>1.4</mn></mrow></msub></math> by nuclear resonant inelastic x-ray scattering," Physical Review B 98, no. 2 (2018), https://doi.org/10.1103/PhysRevB.98.024417
@article{osti_1480690,
author = {Landers, J. and Salamon, S. and Keune, W. and Gruner, M. E. and Krautz, M. and Zhao, J. and Hu, M. Y. and Toellner, T. S. and Alp, E. E. and Gutfleisch, O. and others},
title = {Determining the vibrational entropy change in the giant magnetocaloric material <math><msub><mrow><mi mathvariant='normal'>LaFe</mi></mrow><mrow><mn>11.6</mn></mrow></msub><msub><mrow><mi mathvariant='normal'>Si</mi></mrow><mrow><mn>1.4</mn></mrow></msub></math> by nuclear resonant inelastic x-ray scattering},
annote = {Magnetocaloric ${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$-based compounds belong to the outstanding materials with potential for efficient solid-state refrigeration. We have performed temperature-dependent $^{57}\mathrm{Fe}$ nuclear resonant inelastic x-ray scattering measurements (in a field ${{\mu}}_{0}H$ of ${\sim}0.7$ T) of the vibrational (phonon) density of states, VDOS, in ${\mathrm{LaFe}}_{11.6}{\mathrm{Si}}_{1.4}$ across the metamagnetic isostructural first-order phase transition at ${T}_{C}{\sim}192$ 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 ${T}_{C}$, occurring within a small temperature interval of $\mathrm{{\Delta}}T{\le}12$ K around ${T}_{C}$. This indicates that strong magnetoelastic coupling (at 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 $\mathrm{{\Delta}}{S}_{\mathrm{vib}}$ of $+6.9\pm{}2.6$ J/(kg K) and in the vibrational specific heat $\mathrm{{\Delta}}{C}_{\mathrm{vib}}$ of $+2.7\pm{}1.6$ J/(kg K) upon heating. The increase in magnitude of the vibrational entropy $|\mathrm{{\Delta}}{S}_{\mathrm{vib}}|=6.9$ J/(kg K) of the Fe sublattice at ${T}_{C}$ upon heating is substantial, if compared with the magnitude of the isothermal entropy change $|\mathrm{{\Delta}}{S}_{\mathrm{iso}}|$ of 14.2 J/(kg K) in a field change $\mathrm{{\Delta}}B$ from 0 to 1 T, as obtained from isothermal magnetization measurements on our sample and using the Maxwell relation. Finally, we demonstrate that $\mathrm{{\Delta}}{S}_{\mathrm{vib}}$ obtained by nuclear resonant inelastic x-ray scattering is a sizable quantity and contributes directly and cooperatively to the total entropy change $\mathrm{{\Delta}}{S}_{\mathrm{iso}}$ at the phase transition of ${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$.},
doi = {10.1103/PhysRevB.98.024417},
url = {https://www.osti.gov/biblio/1480690},
journal = {Physical Review B},
issn = {ISSN 2469-9950},
number = {2},
volume = {98},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2018},
month = {07}}
Argonne National Lab. (ANL), Argonne, IL (United States); Leibniz Inst. for Solid State and Materials Research (IFW Dresden), Dresden (Germany); Technical Univ. of Darmstadt (Germany); Univ. of Duisburg-Essen (Germany)
Sponsoring Organization:
German Research Foundation (DFG); USDOE; USDOE Office of Science (SC)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 374, Issue 2074https://doi.org/10.1098/rsta.2015.0308
