Both Ba$_4$Mn$_3$O$_{10}$ and Sr$_4$Mn$_3$O$_{10}$ crystallize in an orthorhombic crystal structure consisting of corrugated layers containing Mn$_3$O$_{12}$ polydedra. The thermal variation of magnetic susceptibility of the compositions consists of a broad hump like feature indicating the presence of low dimensional magnetic correlation. We have systematically investigated the magnetic data of these compounds and found that the experimental results match quite well with the two dimensional Heisenberg model of spin-spin interaction. The two dimensional nature of the magnetic spin-spin interaction is supported by the low temperature heat capacity data of Ba$_4$Mn$_3$O$_{10}$. Interestingly, both the samples show dielectric anomaly near the magnetic ordering temperature indicating multiferroic behavior.
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