The hierarchy of the coupling strengths in a physical system often engenders an effective model at low energies where the decoupled high-energy modes are integrated out. Here, using neutron scattering, we show that the spin excitations in the breathing pyrochlore lattice compound $\mathrm{Cu}\mathrm{In}{\mathrm{Cr}}_4{\mathrm{S}}_8$ are hierarchical and can be approximated by an effective model of correlated tetrahedra at low energies. At higher energies, intratetrahedron excitations together with strong magnon-phonon couplings are observed, which suggests the possible role of the lattice degree of freedom in stabilizing the spin tetrahedra. Our work illustrates the spin dynamics in $\mathrm{Cu}\mathrm{In}{\mathrm{Cr}}_4{\mathrm{S}}_8$ and demonstrates a general effective-cluster approach to understand the dynamics on the breathing-type lattices.

• Received 23 January 2021
• Revised 26 April 2021
• Accepted 17 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.214418