SHAPE DEPENDENCE OF SPECIFIC HEAT OF MAGNETIC SYSTEMS WITH LONG-RANGE INTERACTIONS

The shape dependence of the free energy in an applied field and thereby the specific heat, has been determined for magnetic systems with long-range interactions. For ellipsoidal bodies the specific heat at constant applied field, CH0, can be related to the shape-independent specific heat at constant internal field, CHi, by; C Hi(Hi, T)=CH0(Hi, T)+[DT(∂M/∂T)2H0]/[1-D(∂M/∂H 0)T] where D is the classical demagnitization factor. Detailed experimental knowledge of M(H0, T) and CH 0 (H0, T) is required in order to find the derivatives accurately and to determine CH0 (Hi, T). In dysprosium aluminum garnet (DAG) dipolar interactions account for about 70% of the energy and therefore shape effects should be important. By using new and available magnetothermal data on DAG we have calculated CH i (Hi, T) from the CH0 (H 0, T) measured for two different shapes; we find that the C Hi agree to within experimental error. We also find that the maximum specific heat changes with shape by as much as 40% and the temperature corresponding to this maximum can vary drastically. We conclude that it is important to reduce experimental results to the specific heat for a long thin needle aligned parallel to H0; for this shape CH 0 and CHi are identical. © 1968 The American Institute of Physics.