Geometric Magnetic Frustration in ${\mathrm{Ba}}_2{\mathrm{Sn}}_2{\mathrm{Ga}}_3{\mathrm{ZnCr}}_7{O}_{22}$: A Two-Dimensional Spinel Based Kagomé Lattice

The properties of a two-dimensional geometrically frustrated magnetic material based on the Kagomé net, ${\mathrm{Ba}}_2{\mathrm{Sn}}_2{\mathrm{ZnGa}}_3{\mathrm{Cr}}_7{\mathrm{O}}_{22}$, are reported. The Kagomé net is fully filled with magnetic ions. A Curie-Weiss theta ${\theta }_W=-312\mathrm{}\mathrm{K}$ is found with a spin glass transition at approximately 1.5 K, indicating strong geometrical magnetic frustration. This compound is the most two dimensional of a structural series with the geometrically frustrated materials ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ and ${\mathrm{SrCr}}_8{\mathrm{Ga}}_4{\mathrm{O}}_{19}$. The comparison of their properties tests the influence of different degrees of coupling between Kagomé layers on magnetic frustration within a single chemical and structural family.