Abstract
An overview of the theoretical advances in description of the magnetic ordering and its stability in two-dimensional quasiperiodic tilings with strongly localized magnetic moments is presented. It is demonstrated that combination of the magnetic frustration and the quasiperiodic order of atoms leads to noncollinear ground states. An experimental and theoretical evidence for the possibility of coexistence of stable, magnetically ordered subtilings with highly frustrated, glass-like phases in a single sample is given.
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