Structural stability of CuAl$_{2}$O$_{4}$ under pressure

Structural properties of CuAl$_{2}$O$_{4}$, which was recently argued to show unusual suppression of the Jahn-Teller distortions by the spin-orbit coupling, are investigated under pressures up to 6 GPa. Analysis of X-ray powder diffraction experiments shows that CuAl$_{2}$O$_{4}$ gets unstable and decomposes onto CuO and Al$_{2}$O$_{3}$ at pressures $\sim$ 6 GPa and temperature $\sim$ 1000 K. This finding is complemented by the DFT+U+SOC calculations, which demonstrate that this instability is partially driven by a (relatively) large compressibility of strongly Jahn-Teller distorted CuO.