Monte Carlo Simulations of the site-diluted 3d XY model with superexchange interaction: application to Fe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Cl -- Zn[S$_2$CN(C$_2$H$_5$)$_2$]$_2$ diluted magnets

A simple site-diluted classical XY model is proposed to study the magnetic properties of the ferromagnetic polycrystalline Fe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Cl diluted with diamagnetic Zn[S$_2$CN(C$_2$H$_5$)$_2$]$_2$. An extra superexchange interaction is assumed between next-nearest-neighbors on a simple cubic lattice, which are induced by a diluted ion. The critical properties are obtained by Monte Carlo simulations using a hybrid algorithm, single histograms procedures and finite-size scaling techniques. Quite good fits to the experimental results of the ordering temperature are obtained, namely its much less rapidly decreasing with dilution than predicted by the standard diluted 3$d$ XY model, and the change in curvature around $86\%$ of the magnetic Fe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Cl compound.

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