Can a material have negative phonon modes in the phonon spectrum but still exist?

Question

I came across a paper which talks about $Cs_2SnI_6$ the material is well researched and there are dozens of experimental papers which say that the material exists in Fm3m space group(FCC), the particular paper I am talking about talks about the phase transition from cubic to monocilinic as the tempreature decreases although this theoretical calculation does not really go with experimental evidence. My point is that the they show the phonon band structure as

where the red lines show unstable modes. So is this calculation wrong(as I have heard this would be a dynamically unstable mode, but the material does exist) or can materials with negative phonon modes also exist?

P.S there are studies which talk about the anharmonic lattice dynamics of Cs2SnI6 saying that the material shows quite a lot of anharmonicity.

Answer 1

My answer will be a more general one about soft modes and not too specifically-related to the system OP cited as these ideas are probably generally applicable to other structures.

Firstly, I would say that phonon calculations can be qualitatively "wrong" if the soft modes arise from convergence problems rather than anything physical. This could be a result of

• Poor electronic convergence. The forces might not be well-converged.
• Poor geometry relaxation convergence. The forces might not small enough, which would be problematic for say computing the force constants matrix with finite differences.
• Poor supercell convergence. The phonon dispersion values at the $\mathbf{q}$-points commensurate with the supercell used may not exhibit soft modes, but Fourier interpolating those points for values in between those commensurate $\mathbf{q}$-points may lead to artificial soft modes that might disappear when larger supercells are used. (see this Q&A)

If the soft modes are still present, they can be physically interpreted as indicative of dynamical instability as OP pointed out. This Q&A provides a comprehensive discussion relevant to OP's question. In short, we can rationalize the experimental observation of a structure with a soft mode by thinking of the structure as a saddle point in the potential energy landscape that could become a minima in the free energy landscape above some critical temperature.