Schottky anomaly observed in P NMR for P-doped Si

The Schottky anomaly, which happens when the heat capacity of nuclei is comparable to that of electrons, was observed in NMR for phosphorous doped silicon. The anomaly appears as an abnormal double exponential decay in the nuclear spin relaxation at very low temperature and high magnetic field. The initial fast exponential decay is the usual relaxation due to the interaction with free electrons but the slow decay in the 2nd stage is the process where the combined system of the nuclear spins and free electrons lose their energy to the liquid He bath. The double exponential decay diasppears above 1 K, where the heat capacity of the free electrons exceeds that of the nuclear spins. The result of the numerical calculation based on the assumption of the Schottky anomaly is also in consistence with the experimental observation.