  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.
