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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 CuInCr$_4$S$_8$ are hierarchical and can be approximated by an effective model of correlated tetrahedra at low energies. At higher energies, intra-tetrahedron 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 CuInCr$_4$S$_8$ and demonstrates a general effective-cluster approach to understand the dynamics on the breathing-type lattices.
The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material Ba
The low energy spin excitation spectrum of the breathing pyrochlore Ba3Yb2Zn5O11 has been investigated with inelastic neutron scattering. Several nearly resolution limited modes with no observable dispersion are observed at 250 mK while, at elevated
Fractonic phases of matter are novel quantum ground states supporting sub-dimensional emergent excitations with mobility restrictions and/or immobile fractons. The ground state degeneracy of such phases is sub-extensive and depends on the geometry of
We study a spin-ice Kondo lattice model on a breathing pyrochlore lattice with classical localized spins. The highly efficient kernel polynomial expansion method, together with a classical Monte Carlo method, is employed in order to study the magneti
Reproducing the electronic structure of AM$_4$X$_8$ lacunar spinels with a breathing pyrochlore lattice is a great theoretical challenge due to the interplay of various factors. The character of the M$_4$X$_4$ cluster orbitals is critically influence