Rattling Phonon Modes in Quadruple Perovskites

Rattling phonon modes are known to be origin of various anomalous physical properties such as superconductivity, suppression of thermal conductivity, enhancement of specific heat etc. By means of DFT+$U$ calculations we directly show presence of the rattling mode in the quadruple perovskites CuCu${}_3$V${}_4$O${}_{12}$ and CuCu${}_3$Fe${}_2$Re${}_2$O${}_{12}$ and argue that this can develop in others as well. It is demonstrated that Cu ions at $A$ sites vibrate in the center of the icosahedral oxygen O${}_{12}$ cages and the corresponding potential has a complicated form with many local minima.