Anomalous lattice specific heat and rattling phonon modes in quadruple perovskites

Experimental data on the specific heat $C_p$ of quadruple perovskites ACu${}_3$Fe${}_2$Re${}_2$O${}_{12}$ (A = Mn, Cu, La, Ce, Dy) are presented, demonstrating an anomalous concave-down $C_p\mathrm{/}T$ vs. $T^2$ curve and a bell-shaped feature in $\beta (T)=(C_p-\gamma T)\mathrm{/}{T}^3$ plotted against $T$ on a logarithmic scale. This feature is most pronounced for A = Cu and Mn. These findings can be explained by the rattling phenomenon, previously identified in other systems such as filled skutterudites and $\beta$-pyrochlores. Using first-principles DFT+U calculations, the presence of a rattling mode in A = Mn system is directly confirmed. A qualitative interpretation of the rattling mechanism in terms of a pseudo-Jahn-Teller effect is proposed.