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We present neutron scattering results on the magnetic excitations in thespinel compounds Li$_x$[Mn$_{1.96}$Li$_{0.04}$]O$_4$ (x= 0.2, 0.6, 0.8, 1.0).We show that the dominant excitations below T ~ 70 K are determined by clustersof Mn^4+ ions, and that these excitations mimic the E/T-scaling found inquantum critical systems that also harbor magnetic clusters, such asCeRu$_{0.5}$Fe$_{1.5}$Ge$_2$. We argue that our results for this classicalspinel compound show that the unusual response at low temperatures as observedin quantum critical systems is (at least) partially the result of thefragmentation of the magnetic lattice into smaller units. This fragmentation inquantum critical systems is the direct and unavoidable result of intrinsicdisorder.

physical review. b, condensed matter and materials physics

Magnetic excitations in the spinel compound  Li$_x$[Mn$_{1.96}$Li$_{0.04}$]O$_4$ (x= 0.2, 0.6, 0.8, 1.0): how a classical  system can mimic quantum critical scaling