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Element-Resolved Thermodynamics of Magnetocaloric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>LaFe</mml:mi><mml:mrow><mml:mn>13</mml:mn><mml:mo>โ</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Si</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math>
By combination of two independent approaches, nuclear resonant inelastic X-ray scattering and first-principles calculations in the framework of density functional theory, we determine the element-resolved vibrational density of states in the ferromagnetic low temperature and paramagnetic high temperature phase of LaFe$_{13-x}$Si$_x$. This allows us to derive the lattice and electronic โฆ