  The quasiparticle density of states in correlated and quantum-critical metals
directly probes the effect of electronic correlations on the Fermi surface.
Measurements of the nuclear spin-lattice relaxation rate provide one such
experimental probe of quasiparticle mass through the electronic density of
states. By far the most common way of accessing the spin-lattice relaxation
rate is via nuclear magnetic resonance and nuclear quadrupole resonance
experiments, which require resonant excitation of nuclear spin transitions.
Here we report non-resonant access to spin-lattice relaxation dynamics in
AC-calorimetric measurements. The nuclear spin-lattice relaxation rate is
inferred in our measurements from its effect on the frequency dispersion of the
thermal response of the calorimeter-sample assembly. We use fast,
lithographically-defined nanocalorimeters to access the nuclear spin-lattice
relaxation times in metallic indium from 0.3~K to 7~K and in magnetic fields up
to 35~T.
