Pressure-induced ferroelastic phase transition in SnO$_2$ from density functional theory

We studied the high-pressure ferroelastic transition of rutile- to CaCl$_2$-type SnO$_2$ within density functional theory and Landau free energy theory. Softening mechanism of B_{1g}\) mode (order parameter \emph{Q}) and the coupling mechanism between the soft B_{1g}\) mode and the soft transverse acoustic (TA) mode (strain \varepsilon\)) are clarified by calculating Landau energy map around the ground state. It is found that the Sn-O-Sn bending induced soft B_{1g}\) mode effectively reduces the excess energy increase caused by bond stretching, which however always leads to SnO$_6$ octahedral distortion. The octahedral distortion is subsequently minimized by lattice distortion strain \varepsilon\), which interacts with the soft B_{1g}\) mode to further increase the stability of system.