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

We present neutron scattering results on the magnetic excitations in the spinel 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 clusters of Mn^4+ ions, and that these excitations mimic the E/T-scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu$_{0.5}$Fe$_{1.5}$Ge$_2$. We argue that our results for this classical spinel compound show that the unusual response at low temperatures as observed in quantum critical systems is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units. This fragmentation in quantum critical systems is the direct and unavoidable result of intrinsic disorder.