Understanding the anomalous magnetic heat capacity and thermopower of MnTe above the Néel temperature using cluster mean-field theory

MnTe is an antiferromagnetic (AFM) semiconductor with exotic thermoelectric properties. Experiments have shown anomalously large thermopower and magnetic heat capacity above the transition temperature T_N where the magnetic Néel order disappears. Thermopower is directly proportional to the specific heat. Hence, we study the specific heat of the system, both experimentally and theoretically. Using different approaches such as spin-wave theory (SWT), mean-field approximation (MFA), and cluster mean-field theory (CMFT), we study the effects of the thermal fluctuations below and above T_N. While SWT is reliable at low temperatures, it overestimates the values at high temperatures and fails to determine the transition temperature. MFA and CMFT show strong staggered magnetization below T_N due to the dominant AFM inter-layer interactions. The MFA shows an increasing specific heat followed by a sudden drop at T_N, different from the experimental data. However, including magnetic fluctuations through CMFT explains the transition temperature and shows a finite specific heat in the disordered phase, agreeing with the experimental results. Therefore, the enhanced specific heat in the disordered phase can be explained only by the large correlations between the nearest-neighbor inter-layer spins.