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Monte Carlo simulations of magnetization state of ellipsoidal CoCu particles in disordered self-assembled arrays

  • V.Z.C. Paes (a1), J. Varalda (a1), P. Schio (a2), J.T. Matsushima (a3), E.C. Pereira (a4), A.J.A. de Oliveira (a2) and D.H. Mosca (a1)...


Monte Carlo (MC) simulations of the magnetization states of disordered self-assembled arrays of particles consisting of Co87Cu13 alloy are investigated. The assemblies of magnetic particles with ellipsoidal shapes and volumes ranging from 5 to 50 µm3 exhibit densities of about 3 × 106 particles per mm2. Magnetization was obtained in the framework of Stoner–Wohlfarth model extended to include phenomenological contributions of second-order magnetic anisotropy and coercivity mechanism with distinct configuration of easy axes of magnetization. MC simulations for assemblies containing no more than 100 particles with negligible magnetic interaction between each other and exhibiting saturation magnetization and magnetic anisotropy constant values close to those found for cobalt in bulk are in good agreement with experimental results. We evaluate and validate our computational modeling using samples having particles with different sizes and different angular distributions of the easy axis of magnetization. A simple numerical approach with minimum of parameters was used to take into account the coercive fields of the samples. Reasonable simulation results are generated based on realistic size distributions and angular distributions of easy axis of magnetization.

PACS numbers: 75.30.Gw,75.60-d,75.70-i


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Present address: Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 – Caixa Postal 15051 – CEP 91501-970 – Porto Alegre, RS, Brazil.

Contributing Editor: Yang-T. Cheng



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1. Singamanemi, S., Blizyiuk, V.N., Binek, C., and Tsymbal, E.Y.: Magnetic nanoparticles: Recent advances in synthesis, self-assembly and applications. J. Mater. Chem. 21, 16819 (2011).
2. Dormann, J.L., Fiorani, D., and Tronc, E.: Magnetic relaxation in fine-particle systems. Adv. Chem. Phys. 98, 283 (1997).
3. Bolte, M., Eiselt, R., Meier, G., Kim, D-H., and Fischer, P.: Real space observation of dipolar interaction in arrays of Fe microelements. J. Appl. Phys. 99, 08H301 (2006).
4. Abraham, D.W. and Lu, Y.: Observation of switching of magnetic particle arrays with dipole interaction field effects. J. Appl. Phys. 98, 023902 (2005).
5. Ross, C.A., Haratani, S., Castaño, F.J., Hao, Y., Hwang, M., Shima, M., Cheng, J.Y., Vögeli, B., Farhoud, M., Walsh, M., and Smith, H.I.: Magnetic behavior of lithographically patterned particles arrays. J. Appl. Phys. 91, 6848 (2002).
6. Martinez-Boubeta, C., Simeonidis, K., Makridis, A., Angelakeris, M., Iglesias, O., Guardia, P., Cabot, A., Yedra, L., Estrade, S., Peiro, F., Saghi, Z., Midgley, P.A., Conde-Lebora, I., Serantes, D., and Baldomir, D.: Learning from nature to improve the heat generation of iron-oxide nanoparticles for magnetic hyperthermia applications. Sci. Rep. 3, 1652 (2013).
7. Stoner, E.C. and Wohlfarth, E.P.: A mechanism of magnetic hysteresis in heterogenous alloys. Philos. Trans. Roy. Soc. A 240, 599 (1948); reprinted by IEEE Trans. Magn. 27, 3475 (1991).
8. Porro, J.M., Berger, A., Grimsditch, M., Metlushko, V., Ilic, B., and Vavassori, P.: Effect of spatially asymmetric dipolar interactions in the magnetization reversal of closely spaced ferromagnetic nanoisland arrays. J. Appl. Phys. 111, 07B913 (2012).
9. Bisero, D., Cremon, P., Madami, M., Sepioni, M., Tacchi, S., Gubbiotti, G., Carlotti, G., Adeyeye, A.O., Singh, N., and Goolaup, S.: Effect of dipolar interaction on the magnetization state of chains of rectangular particles located either head-to-tail or side-by-side. J. Nanopart. Res. 13, 5691 (2011).
10. Dantas, C.C. and de Andrade, L.A.: Micromagnetic simulations of small arrays of submicron ferromagnetic particles. Phys. Rev. B: Condens. Matter Mater. Phys. 78, 024441 (2008).
11. Hyndman, R., Mougin, A., Sampaio, L.C., Ferre, J., Jameta, J.P., Meyer, P., Mathet, V., Chappert, C., Mailly, D., and Gierak, J.: Magnetization reversal in weakly coupled patterns. J. Magn. Magn. Mater. 240, 34 (2002).
12. García-Otero, J., Porto, M., Rivas, J., and Bunde, A.: Influence of dipolar interaction on magnetic properties of ultrafine ferromagnetic particles. Phys. Rev. Lett. 84, 167 (2000).
13. Aign, T., Meyer, P., Lemerle, S., Jamet, J.P., Ferré, J., Mathet, V., Chappert, C., Gierak, J., Vieu, C., Rousseaux, F., Launois, H., and Bernas, H.: Magnetization reversal in arrays of perpendicularly magnetized ultrathin dots coupled by dipolar interaction. Phys. Rev. Lett. 81, 5656 (1998).
14. Stamps, R.L. and Camley, R.E.: High-frequency response and reversal dynamics of two-dimensional magnetic dot array. Phys. Rev. B: Condens. Matter Mater. Phys. 60, 12264 (1999).
15. Scheinfein, M.R., Schmidt, K.E., Heim, K.R., and Hembree, G.G.: Magnetic order in two-dimensional arrays of nanometer-sized superparamagnets. Phys. Rev. Lett. 76, 1541 (1996).
16. Du, H-F., He, W., Sun, D-L., Fang, Y-P., Liu, H-L., Zhang, X-Q., and Chen, Z-H.: Monte Carlo simulation of magnetic properties of irregular Fe islands on Pb/Si(111) substrate based on the scanning tunneling microscopy image. Appl. Phys. Lett. 96, 132502 (2010).
17. Varalda, J.: Caracterização magnética de filmes de ligas e multicamadas magnéticas (in portuguese). M. Sc. Thesis, Universidade Federal de São Carlos, 2000.
18. Karaagac, O., Kockar, H., and Alper, M.: Electrodeposited cobalt films: The effect of deposition potentials on the film properties. J. Optoelectron. Adv. Mater. 15, 1412 (2013).
19. Szabó, Z. and Iványi, A.: Computer-aided simulation of Stoner-Wohlfarth model. J. Magn. Magn. Mater. 215, 33 (2000).
20. Jamet, M., Wernsdorfer, W., Thirion, C., Dupuis, V., Melinon, P., and Perez, A.: Magnetic anisotropy in single clusters. Phys. Rev. B: Condens. Matter Mater. Phys. 69, 024401 (2004).
21. Paes, V.Z.C., Graff, I.L., Varalda, J., Etgens, V.H., and Mosca, D.H.: The role of magnetoelastic and magnetostrictive energies in the magnetization process of MnAs/GaAs epilayers. J. Phys.: Condens. Matter 25, 046003 (2013).
22. Chen, D-X., Pardo, E., and Sanchez, A.: Demagnetizing factors of rectangular prisms and ellipsoids. IEEE Trans. Magn. 38, 1742 (2002).
23. Zhang, H-W., Zhang, S-Y., Shen, B-G., and Kronmuller, H.: The magnetization behavior of nanocrystalline permanent magnets based on the Stoner–Wohlfarth model. J. Magn. Magn. Mater. 260, 352 (2003).
24. Winter, A., Pascher, H., Krenn, H., Liu, X., and Furdyna, J.K.: Interpretation of hysteresis loops of GaMnAs in the framework of the Stoner–Wohlfarth model. J. Appl. Phys. 108, 043921 (2010).
25. Hrabovsky, D., Vanelle, E., Fert, A.R., Yee, D.S., Redoules, J.P., Sadowski, J., Kanski, J., and Ilver, L.: Magnetization reversal in GaMnAs layers studied by Kerr effect. Appl. Phys. Lett. 81, 2806 (2002).
26. Skomski, R., Hadjipanayis, G.C., and Sellmyer, D.J.: Effective demagnetizing factors of complicated particle mixtures. IEEE Trans. Magn. 43, 2956 (2007).


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Monte Carlo simulations of magnetization state of ellipsoidal CoCu particles in disordered self-assembled arrays

  • V.Z.C. Paes (a1), J. Varalda (a1), P. Schio (a2), J.T. Matsushima (a3), E.C. Pereira (a4), A.J.A. de Oliveira (a2) and D.H. Mosca (a1)...


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