Magnetic monopole relaxation effects probed by modulation calorimetry in small spin-ice samples

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.