Magnetocaloric effect in molecular spin clusters and their assemblies: model exact and Monte Carlo studies

We study the magnetocaloric effect (MCE) in spin clusters of six spins with site spins $s=1$, $3/2$ and $2$ for different exchange anisotropies. We also study MCE in an assembly of spin clusters, on a chain, a 2-D square lattice and 3-D cubic lattice with spin-dipolar interactions using a Monte Carlo method in spin-1 systems. We compute the magnetic Gr\"uneisen parameter $\Gamma_H$, and study its dependence on exchange anisotropy and spin-dipolar interaction. With increase of exchange anisotropy the maxima in $\Gamma_H$, shifts to higher magnetic fields and becomes a sharp singularity. The first maximum in $\Gamma_H$ shifts to lower fields as we increase spin-dipolar interaction. The behaviour of $\Gamma_H$ on applied magnetic field is also reflected in the magnetic entropy of the systems. The first maximum in $\Gamma_H$ also shifts to lower magnetic field strength as the magnitude of the site spin increases. We also show the dependence of $\Gamma_H$ on dimensionality of the lattice for a fixed lattice constant.