  We investigate the temperature response of the alkali-metal rattling modes in
{\beta}-pyrochlores, AOs2O6 (A = K, Rb, Cs), from the results of ab initio
molecular dynamics (MD) simulations performed at 20 K, 100 K, and 300 K. Our
results show that the temperature response of the T1u mode is clearly different
from that of the T2g mode for all three pyrochlores. In this regard, two
features are of particular note for both K and Rb; (1) the T1u mode exhibits a
distinctly stronger softening response with decreasing temperature compared to
the T2g mode, and (2) the T1u mode becomes stronger and sharper with decreasing
temperature. These two findings suggest that the T1u mode is significantly more
anharmonic and sensitive to the cage dynamics than the T2g mode. Examination of
the local potentials around the alkali-metal atoms reveals that K has the
flattest and most anharmonic potential at all temperatures while Cs exhibits
the narrowest potential. The temperature dependence of the local potentials
reveals that, for K, the potential at a higher temperature is not a simple
extrapolation to higher energy of that at a lower temperature. Instead, we find
significant reconstruction of the potential at different temperatures. Finally,
we explore the temperature response of the coupling between the alkali metals
and find a complex temperature dependence which suggests that the origin of the
coupling may be more complex than a pure Coulomb interaction. We also find an
unexpected increase in the static disorder of the system at low temperatures
for the K and Rb pyrochlores.
