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The hierarchy of the coupling strengths in a physical system often engendersan effective model at low energies where the decoupled high-energy modes areintegrated out. Here, using neutron scattering, we show that the spinexcitations in the breathing pyrochlore lattice compound CuInCr$_4$S$_8$ arehierarchical and can be approximated by an effective model of correlatedtetrahedra at low energies. At higher energies, intra-tetrahedron excitationstogether with strong magnon-phonon couplings are observed, which suggests thepossible role of the lattice degree of freedom in stabilizing the spintetrahedra. Our work illustrates the spin dynamics in CuInCr$_4$S$_8$ anddemonstrates a general effective-cluster approach to understand the dynamics onthe breathing-type lattices.

Hierarchical excitations from correlated spin tetrahedra on the breathing pyrochlore lattice