Thermodynamics of the exactly solvable spin-electron tetrahedral chain

An exactly solvable spin-electron tetrahedral chain, where the Ising spins localized at nodal lattice sites regularly alternate with three equivalent lattice sites available for one mobile electron is considered. The system with ferromagnetic interaction between the Ising spins and electrons exhibits an enhanced magnetocaloric effect (MCE) in the limit $H/|J|\to 0$ when the entropy is very small, whereas the system with antiferromagnetic interaction between the Ising spins and electrons exhibits an enhanced MCE around the field $H/J=1$ when the entropy is sufficiently close to the value $S/2N = \ln[(1+\sqrt{5})/2]$. We study the thermodynamics of the system in these field regions.