  We use modulation calorimetry to study the heat capacity of small samples (30
nano gram-10 micro gram) of the classical spin-ice compounds Dy2Ti2O7 and
Ho2Ti2O7 at low temperature (0.5-3 K). Using modulation frequencies of 0.1-200
Hz we find a strong frequency dependence in the measured heat capacity and are
able to study thermal relaxation effects on the corresponding timescales.
Performing dynamic Monte Carlo simulations we verify that the specific heat
frequency response has its origin in the slow magnetic monopole dynamics
indigenous to spin ice. We find a timescale of 20ms per Monte Carlo step at 4K
in contrast to 2.5ms mentioned in previous studies by other 1 techniques. Our
study establishes modulation calorimetry as a versatile experimental probe of
dynamic processes in frustrated magnetic materials.
