Shape Dependence of the 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; CHi(Hi, T)=CH0(Hi, T)+[DT(∂M/∂T)H02]/[1−D(∂M/∂H0)T]where D is the classical demagnitization factor. Detailed experimental knowledge of M(H0, T) and CH0 (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 CHi (Hi, T) from the CH0 (H0, T) measured for two different shapes; we find that the CHi 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 CH0 and CHi are identical.