Phonon softening in paramagnetic bcc Fe and relationship with pressure-induced phase transition

Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transition pathway, exhibits strong softening under isotropic volume compression. The frequency of this mode becomes zero by $2\%$ volume decrease within the harmonic approximation. This result is not consistent with the experimental fact that phase transition from the PM bcc to hcp phases does not occur under volume compression. The seeming contradiction can be explained only when anharmonic behavior of the N$_4^-$ mode is taken into consideration; a potential energy curve along the N$_4^-$ mode becomes closer to a double-well shape for the PM phase under the volume compression. On the other hand, softening of the longitudinal mode at the 2/3[111] point under the volume compression is also found for the PM phase, which indicates the pressure-induced bcc-fcc phase transition along this mode. Such behaviors are not seen in ferromagnetic (FM) bcc Fe, implying that the magnetic structure plays essential roles on the phase transition mechanism.