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The magnetic properties of the alkaline earth oxocuprate BaCu3O4 areinvestigated. We show that the characteristic Cu3O4 layers of this material canbe described with diamond chains of antiferromagnetically coupled Cu 1/2 spinswith only a weak coupling between two adjacent chains. These Cu3O4 layers seemto represent a so far unique system of weakly coupled one-dimensional magneticobjects where the local AF ordering of the Cu2+ ions leads to an actual netmagnetic moment of an isolated diamond chain. We demonstrate a magnetictransition at a high N\'eel temperature T_{N}=336 K.

BaCu3O4: High Temperature Magnetic Order in One-Dimensional S=1/2 Diamond-Chains