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Contrary to a text-book picture of magnetization processes, many examples are known both in theory and in experiment to exhibit step-like structures (magnetization plateaus) which are "quantized" at rational values of magnetization. The appearance of these plateaus is a direct consequence of the formation of spin-gapped states and normally they are accompanied by magnetic superstructures (e.g. crystalline order of magnons). We re-examine this issue from a geometrical viewpoint. By using semiclassical approach, we derive an effective hamiltonian for generic (antiferromagnetic) spin systems in high magnetic fields. The model contains all-important Berry-phase term, whose topological interference determines whether plateaus are allowed at a given value of magnetization or not. On the other hand, this interference effects may cause multiple-vortex condensation and thereby leads to featureless plateau states with topological orders. Possible extension (microscopic models, other gauge groups, etc.) will be discussed, too. |
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