High-Frequency-Relaxation Measurements of Magnetic Specific Heats

The recent development of cryogenic tunnel-diode oscillators has been used to improve and extend the high-frequency-relaxation (HFR) method for measuring the magnetic specific heat $C_M$. The method, originally due to Casimir and du Pré, uses purely magnetic measurements to determine $C_M$ directly, without the usual correction for the generally much larger lattice contribution to the total heat capacity, and it thus allows accurate estimates of $C_M$ over wide ranges of temperature. At temperatures that are high compared with the onset of magnetic ordering, $C_M$ can be fitted to a series expansion of the form $\frac{C_M}{R}=\frac{C_2}{T^2}+\frac{C_3}{T^3}+ \mathbf{\cdots }$, where $R=N{k}_B$ and $N$ is the number of magnetic spins, and in suitable cases this can be related to microscopic spin-spin interaction parameters. Additional information can also be obtained from the field dependence of $C_M$, which can be related to the temperature dependence of the isothermal susceptibility. The central experimental requirement for this method is an accurate determination of the field and temperature dependence of the differential susceptibility in the MHz frequency range, and a fairly detailed discussion of a suitable system is given. Examples of materials for which this technique has been used succesfully include rare-earth halides, hydroxides, and garnets, but many other materials should satisfy the conditions under which this method can be applied. A review of these conditions is given and the criteria for choosing suitable measuring fields, frequencies, and temperatures are summarized.