Classical (Heisenberg) simulations show that the total magnetization of the lowest-energy states of clusters made of antiferromagnetically coupled chromium atoms is planar, rather than collinear, depending on the arrangement of the atoms. Although the model Hamiltonian is not restrictive, many cluster configurations of various numbers of atoms do not use all three directions for the spins. This result confirms the conclusion drawn from the local-spin DFT calculation by Kohl and Bertsch that clusters of N≤13 have non-collinear magnetic moments. The present simulations show non-collinear spin ordering also for bigger clusters, designed to be as spherical as possible following the bcc arrangement, when atoms interact both with the nearest and next-nearest neighbours. Depending on the signs of the coupling constants frustration appears. The advantage of the discrete model, despite the simplicity, is that very large clusters and magnetization at finite temperatures can be studied. This model predicts that clusters with specific numbers of atoms interacting only with the nearest neighbours have collinear spins as in the bulk. We also apply the model to simulate the destruction of the anti-ferromagnetic ordering by thermal fluctuations. This model shows no unique magnetization of mixed Fe
0.67, which is consistent with experimental observations.
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