The anisotropic triangular lattice of the crednerite system Cu(Mn1-xCux)O2 is used as a basic model for studying the influence of spin disorder on the ground state properties of a two-dimensional frustrated antiferromagnet. Neutron diffraction measurements show that the undoped phase (x=0) undergoes a transition to antiferromagnetic long-range order that is stabilized by a frustration-relieving structural distortion. Small deviation from the stoichiometric composition alters the magnetoelastic characteristics and reduces the effective dimensionality of the magnetic lattice. Upon increasing the doping level, the interlayer coupling changes from antiferromagnetic to ferromagnetic. As the structural distortion is suppressed, the long-range magnetic order is gradually transformed into a two-dimensional order.
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