  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. Stre\v{c}ka 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.
