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2005 | 3 | 2 | 209-220

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Classical simulations of magnetic structures for chromium clusters: Size effects


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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.










Physical description


1 - 6 - 2005
1 - 6 - 2005


  • Department of Atomic Physics, University of Sofia, 5 James Bourchier Blvd., 1126, Sofia, Bulgaria
  • Institute for Theoretical Physics, Cologne University, D-50923, Köln, Euroland


  • [1] I.M.L. Billas, A. Châtelain and W.A. de Heer: “Magnetism of Fe, Co and Ni clusters in molecular beams”J. Magn. Magn. Matter., Vol. 168, (1997), pp. 64–84. http://dx.doi.org/10.1016/S0304-8853(96)00694-4[Crossref]
  • [2] F. Aguilera-Granja, S. Bouarab, M.J. López, A. Vega, J.M. Montejano-Carrizales, M.P. Iñiguez and J.A. Alonso. “Magnetic moments of Ni clusters”, Phys. Rev. B, Vol. 57, (1998), pp. 12469–12475. http://dx.doi.org/10.1103/PhysRevB.57.12469[Crossref]
  • [3] P. Borrmann, B. Diekmann, E.R. Hilf and D. Tománek: “Thermodynamics of finite magnetic two-level systems”Surf. Rev. Lett., Vol. 3, (1996), pp. 463–467. http://dx.doi.org/10.1142/S0218625X96000838[Crossref]
  • [4] T. Oda, A. Pasquarello and R. Car: “Fully Unconstrained Approach to Noncollinear Magnetism: Application to Small Fe Clusters”Phys. Rev. Lett., Vol. 80, (1998), pp. 3622–3625. http://dx.doi.org/10.1103/PhysRevLett.80.3622[Crossref]
  • [5] C. Kohl and G.F. Bertsch: “Noncollinear magnetic ordering in small chromium clusters”, Phys. Rev. B, Vol. 60, (1999), pp. 4205–4211. http://dx.doi.org/10.1103/PhysRevB.60.4205[Crossref]
  • [6] N.S. Yartseva, S.V. Yartsev, V.M. Uzdin and C. Demangeat: “Interface defects and formation of non-collinear magnetic ordering in Fe/Cr multilayers”, Comp. Mat. Sci., Vol. 17, (2000), pp. 468–472. http://dx.doi.org/10.1016/S0927-0256(00)00071-9[Crossref]
  • [7] P. Entel, E. Hoffmann, H.C.H.E.F. Wassermann, V. Crisan, H. Ebert and H. Akai: “Collinear and noncollinear Magnetism in Transition Metal Alloys”, J. Phys. Soc. Japan Suppl. A, Vol. 69 (2000), pp. 112–116.
  • [8] N. Douarche, F. Calvo, P.J. Jensen and G.M. Pastor: “Model simulations of groundstate and finite-temperature properties of disordered magnetic nanostructures”Eur. Phys. J. D, Vol. 24 (2003), pp. 77–80. http://dx.doi.org/10.1140/epjd/e2003-00128-3[Crossref]
  • [9] C. Kittel.Introduction to Solid State Physics, Wiley, New York, 1986.
  • [10] V.M. Uzdin, W. Keune, H. Schror and M. Walterfang: “Fe/Cr interface magnetism: Correlation between hyperfine fields and magnetic moments”, Phys. Rev. B, Vol. 63, (2001), pp. 104407-1–104407-15. http://dx.doi.org/10.1103/PhysRevB.63.104407
  • [11] S. Uzdin, V. Uzdin and C. Demangeat: “Non-collinear structure of Cr trimer on the surface of non-magnetic metals”, Comp. Mat. Sci., Vol. 17, (2000), pp. 441–444. http://dx.doi.org/10.1016/S0927-0256(00)00065-3[Crossref]
  • [12] I. Dragieva, C. Deleva, M. Mladenov and I. Markova-Deneva: “Self-Organization of Magnetic Nanoparticles and Inclusion of Hydrogen by Borohydride Reduction”, Chemical Monthly, Vol. 133, (2002), pp. 807–814. http://dx.doi.org/10.1007/s007060200052[Crossref]
  • [13] A. Proykova and R. Stephen Berry: “Surface effects in order-disorder transformations in molecular clusters”, Eur. Phys. J. D, Vol. 9 (1999), pp. 445–450. http://dx.doi.org/10.1007/s100530050476[Crossref]
  • [14] A. Proykova: “The Role of Metastable States in the Temperature Driven Phase Changes of Molecular Nanoclusters”, Vacuum, Vol. 68 (1), (2002), pp. 97–104. http://dx.doi.org/10.1016/S0042-207X(02)00292-0[Crossref]
  • [15] H.-J. Schmidt and M. Luban: “Classical ground states of symmetric Heisenberg spin systems”, J. Phys. A: Math. Gen., Vol. 36, (2003), pp. 6351–6357. http://dx.doi.org/10.1088/0305-4470/36/23/306[Crossref]
  • [16] N. Fujima: “Non-Collinear Magnetic Moments of Five-Atom Transition-Metal Clusters”, Journal of the Physical Society of Japan, Vol. 71(6), (2002), pp. 1529–1534. http://dx.doi.org/10.1143/JPSJ.71.1529[Crossref]
  • [17] K. Binder (Ed.):Applications of the Monte Carlo Method in Statistical Physics, Springer-Verlag, Heidelberg-Berlin, 1984.
  • [18] A. Proykova, R. Radev, F.-Y. Li and R. Stephen Berry: “Structural Transformations in Small Molecular Clusters”, J. Chem. Phys., Vol. 110, (1999), pp. 3887–3896 (in particular Fig. 5). http://dx.doi.org/10.1063/1.478248[Crossref]
  • [19] H. Cheng and L. Wang: “Dimer Growth, Structural Transition, and Antiferromagnetic Ordering of Small Chromium Clusters”, Phys. Rev. Lett., Vol. 77, (1996), pp. 51–54. http://dx.doi.org/10.1103/PhysRevLett.77.51[Crossref]
  • [20] E.H. Lieb, T. Schultz and D.C. Mattis: “Two soluble models of an antiferromagnetic chain”, Annals of Phys. (N.Y.), Vol. 16, (1961), pp. 407–466. http://dx.doi.org/10.1016/0003-4916(61)90115-4[Crossref]
  • [21] M. Axenovich and M. Luban: “Exact ground state properties of the classical Heisenberg model for giant magnetic molecules”, Phys. Rev. B, Vol. 63 (2001), pp. 100407-1–100407-4. http://dx.doi.org/10.1103/PhysRevB.63.100407
  • [22] J.B. Kortright and Sang-Koog Kim: “Ferromagnetic to Antiferromagnetic Transition inFe x Cr 1-x Films with Composition: A Transmission MCD Study,” Lawrence Berkeley National Laboratory, 1998. http://www-als.lbl.gov/als/compendium/AbstractManager/uploads/Fexcr1-x.pdf
  • [23] P. Bodeker, A. Hucht, A. Schreyer, J. Borchers, F. Guthoff and H. Zabel: “Reorientation of Spin Density Waves in Cr(001) Films Induced by Fe(001) Cap Layers”, Phys. Rev. Lett., Vol. 81, (1998), pp. 914–917. http://dx.doi.org/10.1103/PhysRevLett.81.914[Crossref]
  • [24] P. Olsson, I.A. Abrikosov, L. Vitos and J. Wallenius: “Ab initio formation energies of Fe−Cr alloys”, Journal of Nuclear Materials, Vol. 321, (2003), pp. 84–90. http://dx.doi.org/10.1016/S0022-3115(03)00207-1[Crossref]
  • [25] Eric E. Fullerton, K.T. Riggs, C.H. Sowers and S.D. Bader: “Suppression of Biquadratic Coupling in Fe/Cr(001) Superlattices below the Neél Transition of Cr”, Phys. Rev. Lett., Vol. 75, (1995), pp. 330–333. http://dx.doi.org/10.1103/PhysRevLett.75.330[Crossref]

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