Physical reasons to find a soft mode.

A soft mode has imaginary frequency, represented as negative values. The reasons for obtaining the imaginary modes could be as follows:

• To find a soft modes can mean that in the current structure the crystal is unstable at T=0. It can be stable at another structure (unit cell) and space group. The most negative mode, called soft mode, indicates the suggested lower symmetry structure. One may figure out the necessery displacements, which lead to lower symmetry phase. For that calculate the polarization vectors for the soft mode, and analize them. Notice, however, that in this situation the used supercell should be also a multiplication (or should have the same shape) of the searched low symmetry phase. This is a very tool to search structural Landau type phase transitions.
• If the crystal is magnetic, and there exists some phonon-magnetic coupling, the phonon dispersion curves may depend whether one treats the crystal as non-magnetic, or ferro-, or antiferromagnetically. Magnetic structure lowers the crystal structure, thus the phonons should be considered in lower symmetry crystallographic space group describing to magnetic structure. It involves as a rule to calculate more non-equivalent atoms, more lists of Hellmann-Feynman forces. The remaining procedure is standard. This approach could remove the fake soft modes.
• If in the crystal exhibits strong electron correlation, then the electronic band structures, and phonons must be calculated within the LDA+U, or GGA+U approach. The soft mode, present at U=0, may disappear at U>0. This is so because the force constants may depend on the U value.
• If the crystal possesses a long interaction range, essentially longer then half of the linear size of the supercell, then missing force constants to the far away atoms can cause fake soft modes usualy for acoustic modes in vicinity of Γ point. An increase of supercell size, if possible, may resolve this problem.