Specific Heat Anomalies in Solids Described by a Multilevel Model

Specific heat measurements constitute one of the most powerful experimental methods to probe fundamental excitations in solids. After the proposition of Einstein's model, more than one century ago (Annalen der Physik \textbf{22}, 180 (1907)), several theoretical models have been proposed to describe experimental results. Here we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels $\Delta_i$ = $(E_i$ $-$ $E_{0})$ and the degeneracy of each energy level $g_i$, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of $\Delta_2$/$\Delta_1$ $\thickapprox$ 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.