Spin heat capacity of monolayer and AB-stacked bilayer MoS2 in the presence of exchange magnetic field

Dirac theory and Green's function technique are carried out to compute the spin dependent band structures and corresponding electronic heat capacity (EHC) of monolayer (ML) and AB-stacked bilayer (BL) molybdenum disulfide (MoS2) two-dimensional (2D) crystals. We report the influence of induced exchange magnetic field (EMF) by magnetic insulator substrates on these quantities for both structures. The spin-up (down) subband gaps are shifted with EMF from conduction (valence) band to valence (conduction) band at both Dirac points in the ML because of the spin-orbit coupling (SOC) which leads to a critical EMF in the K point and EHC returns to its initial states for both spins. In the BL case, EMF results split states and the decrease (increase) behavior of spin-up (down) subband gaps has been observed at both K and K′ valleys which is due to the combined effect of SOC and interlayer coupling. For low and high EMFs, EHC of BL MoS2 does not change for spin-up subbands while increases for spin-down subbands.