Temperature Dependent Magnon-Phonon Coupling in bcc Fe from Theory and Experiment

An ab initio based framework for quantitatively assessing the phonon contribution due to magnon-phonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnon-phonon interaction is an order of magnitude larger than the phonon shift due to lattice expansion, demonstrating the strong impact of magnetic short-range order even significantly above the Curie temperature. The framework closes the previous simulation gap between the ferro- and paramagnetic limits.

Figure 1

Sketch of the developed method coupling the energetics of the magnetic system with explicit DFT force constant calculations (displaced spin in the middle of each sketch). The gray and green arrows indicate the local magnetic spins for each atom and the interatomic forces (restoring forces when displacing the center atom), respectively. The explicit force constant calculations are carried out for the two limits of completely ordered [17] (left side) and fully disordered spins [16] (right side). The force constants for the intermediate temperature regime (dashed squares) are obtained by coupling the two limits with quantum Monte Carlo simulations for the magnetic subsystem [19] which explicitly include long- and short-range-order effects (see text for details).

Figure 2

Phonon density-of-states (DOS) and phonon dispersion of bcc Fe at three different temperatures. Symbols indicate experimental data obtained by neutron scattering experiments [11]. The light-gray shaded area within the phonon dispersion plots indicates the range between $\alpha =1$ (FM limit) and $\alpha =0$ (PM limit). The orange to red thick lines indicate the theoretical predictions for the corresponding $\alpha$ value (given to the right). The left panel shows the theoretical DOS (colored) and the DOS obtained by fitting the neutron spectra by a Born—von Kármán fit [28] (dark gray shaded area).

Figure 3

Temperature dependence of phonon frequencies for different modes comparing theoretical (solid red lines) with experimentally deduced frequencies (open circles) [12]. Dashed red lines show the ferromagnetic quasiharmonic results (no phonon-magnon coupling). Where available, neutron scattering data from Ref. [11] are included (filled black squares).