always applied along the tetragonal $c$-axis of the sample. Specific heat was measured with two methods, as shown in Fig. 7.

Measurements at quasi-constant temperature were made using a developed ac technique, Fig. 7a. A small sample, $\approx1$ mg, was mounted onto a home-made calorimeter consisting of a Si platform furbished with an amorphous-metal thin film heater and a bare Cernox thermometer. The calorimeter was attached to the temperature regulation block and was held in a cryogenic vacuum system inside a refrigerator. The sample heater is driven by one lock-in amplifier running at frequency $f$, and the temperature is detected with a second lock-in locked to the frequency of 2$f$. In both cases a peak is observed at the transitions. The observed anomalies in $C_{p}$ map the known phase boundaries in DTN quite well. In the $C_{p}$ versus $H$ curves a double peak is apparent, with the peak near $H_{c2}$ far larger than the peak near $H_{c1}$. A comprehensive theory of the specific heat has been developed. Quantum fluctuations present near $H_{c1}$, but not near $H_{c2}$, reduce the kinetic energy of the magnons, causing a strong mass renormalization near the two transitions, $m(H_{2})/m(H_{1})\approx 3$. This effect, closely described by analytical 