We have studied the pressure effect on the rattling of tetrahedrite ${\mathrm{Cu}}_{10}{\mathrm{Zn}}_2{\mathrm{Sb}}_4{\mathrm{S}}_{13}$ (CZSS) and type-I clathrate ${\mathrm{Ba}}_8{\mathrm{Ga}}_{16}{\mathrm{Sn}}_{30}$ (BGS) by specific heat and x-ray diffraction measurements. By applying pressure $P$, the rattling energy for CZSS initially decreases and steeply increases for $P>1\mathrm{GPa}$. By contrast, the energy for BGS increases monotonically with $P$ up to 6.5 GPa. An analysis of the pressure-dependent specific heat and x-ray diffraction indicates that the out-of-plane rattling of the Cu atoms in the ${\mathrm{S}}_3$ triangle of CZSS originates from the chemical pressure, unlike the rattling of the Ba ions among off-center sites in an oversized cage of BGS. The rattling in CZSS ceases upon further increasing $P$ above 2 GPa, suggesting that Cu atoms escape away from the ${\mathrm{S}}_3$ triangle plane.

• Received 26 May 2020
• Revised 31 July 2020
• Accepted 14 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.100302