Antiferromagnetism and geometric frustration in tetrahedral lattice hydroxyhalides M₂(OH)₃X

A systematic study of magnetic susceptibility measurements is carried out on distorted tetrahedral lattice hydroxyhalides Fe₂(OH) ₃Cl, Mn₂(OH)₃Cl, Mn₂(OH) ₃Br, and Co₂(OH)₃Br, following our recent finding of coexisting antiferromagnetic order and disorder in Cu ₂(OH)₃Cl (clinoatacamite). These transition metal hydroxyhalides are found to undergo antiferromagnetic transitions, at T _N ≤ 14K for Fe₂(OH)₃Cl, at two successive transitions of T_N1 ≤ 3.4K and T_N2 ≤ 2.7K for Mn ₂(OH)₃Cl, at T_N1 ≤ 3.3K and T_N2 ≤ 2.4K for Mn₂(OH)₃Br, and at T_N ≤ 5K for Co₂(OH)₃Br, respectively. All hydroxychlorides show coexisting glassiness below the magnetic transitions; meanwhile, the glassiness is not found in the hydroxybromides. The distorted tetrahedral lattice for the magnetic ions consists of stacked layers of triangular lattice planes and Kagome lattice planes, with the magnetic ions on the Kagome lattice planes being bonded by the halogen ions. The contrasting behaviours in Mn₂(OH) ₃Cl and Mn₂(OH)₃Br suggest that the glassiness arises from competing magnetic interactions in the tetrahedron, specifically on the Kagome lattice planes.