The temperature dependence of nuclear resonant X-Ray spectra of magnetic iron and cementite

Abstract

From low temperatures through the Curie temperatures, the phonon density of states (DOS) was measured for bcc ⁵⁷Fe, and the partial phonon DOS was measured for cementite, ⁵⁷Fe₃C, by nuclear resonant inelastic x-ray scattering (NRIXS). Nuclear forward scattering (NFS) was used to determine the state of magnetization of ⁵⁷Fe₃C. The changes in phonon DOS with magnetization were assessed, and a linear relationship was found between the temperature dependences of the magnetization and the non-quasiharmonic shifts of phonon frequencies. Following the quasiharmonic approximation (QHA) for non-harmonic phonons, a magnetic quasiharmonic theory is developed to account for how phonon frequencies are altered by changes in magnetization. The formalism explains well the discrepancy between the free energy measurements and predictions of the QHA for both bcc iron and cementite. The physical origin of the magnetic Grüneisen parameters remains a challenge.

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