Electrocaloric effect in the two spin-1/2 XXZ Heisenberg edge-shared tetrahedra and spin-1/2 XXZ Heisenberg octahedron with Dzyaloshinskii-Moriya interaction

In the present paper, we consider two species of small spin clusters known as; two spin-1/2 Heisenberg edge-shared tetrahedra and spin-1/2 Heisenberg octahedron with the corresponding Dzyaloshinskii-Moriya terms in a longitudinal magnetic field, then we examine magnetization process and electric polarization of the models as functions of magnetic and electric fields at Low temperature using exact numerical diagonalization. Our exact results are in a good agreement with recent analysis carried out by J. Strečka and K. Kar{\v l}ova \cite{str18b,str17a}. It is demonstrated that the polarization behavior coincides the magnetization curves (including sequential intermediate plateaus), also it reflects the respective stepwise changes of ground-state phase transitions. We find that the polarization has significant effects on the magnetic field dependencies of the magnetization. Furthermore, we investigate other isothermal strategies such as cooling rate, magnetocaloric effect (MCE), as well as, electrocaloric effect(ECE) for both models. Since, new electrocaloric materials with high performance is of great interest and importance in condensed matter physics, here, we report on the ECE of the both aforedescribed spin-1/2 Heisenberg small clusters. We conclude that two spin-1/2 Heisenberg edge-shared tetrahedra is a material with significant reversible temperature change capability under an external electric field compared with the spin-1/2 Heisenberg octahedron, and can be used for cooling/heating process.