The spin dynamics of uranium ions in the non-Fermi liquid compounds URu2-xRexSi2, for x=0.2 to 0.6, have been investigated using inelastic neutron scattering. The wave vector (q) dependence of the magnetic scattering provides evidence of short-range antiferromagnetic correlations at low temperatures for x=0.2,0.25, but the scattering is nearly q independent at x=0.35,0.6. The magnetic response, S(omega), obtained from the q-independent part of neutron scattering, varies as omega(-alpha) with a composition-dependent exponent alpha=0.2-0.5. The dynamic magnetic susceptibility chi(')(q,omega) of the q-independent part exhibits omega/T scaling for the energy transfer h omega between 3.5 and 17 meV in the temperature (T) range of 5-300 K at all the compositions. This scaling, which indicates local quantum criticality, breaks down in the q range, 0.6-1.1 A(-1) at x=0.2 and 0.25, that is dominated by short-range antiferromagnetic correlations. The appearance of power laws in the magnetic response measured by inelastic neutron scattering over a wide Re doping region indicates a disorder driven non-Fermi liquid mechanism for the low-temperature physical properties in these compounds.
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