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Monte Carlo study of the magnetic properties of frozen and non-interacting nanoparticles

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Abstract

The transition from the blocked to the superparamagnetic regime in non-interacting and frozen magnetite nanoparticles with diameters of about 10 nm was studied using the Monte Carlo method with the Metropolis algorithm. The behavior of the blocking temperature (T B) was analyzed for different nanoparticle systems. For ensembles of homogeneous nanoparticles, T B showed a linear dependence on the exchange constant, which is the main factor that determines T B. Comparatively, the dependence of T B on the magnetocrystalline anisotropy constant was much weaker and nonlinear. It was observed that T B decreases with the decreasing particle size following a finite-size scaling theory. Systems of nanoparticles with a core/dead-layer structure exhibited a lower T B than the corresponding homogeneous nanoparticles. It was verified that the presence of a thin, hard layer on the nanoparticles surface, where the exchange interaction was improved, produced a significant increase in the blocking temperature.

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References

  • Als-Nielsen J, Dietricht OW, Kunnmann W, Passell L (1971) Critical Behavior of the Heisenberg Ferromagnets EuQ and EuS. Phys Rev Lett 27:741–744

    Article  Google Scholar 

  • Arantes FR, Figueiredo, Neto AM, Cornejo DR (2011) Magnetic behavior of 10 nm-magnetite particles diluted in lyotropic liquid crystals. J Appl Phys 109:07E315.1–07E315.3. doi:10.1063/1.3549616

    Article  Google Scholar 

  • Batlle X, Labarta A (2002) Finite-size effects in fine particles: magnetic and transport properties. J Phys D 35:R15–R42

    Article  Google Scholar 

  • Berger L, Labaye Y, Tamine M, Coey JMD (2008) Ferromagnetic nanoparticles with strong surface anisotropy: spin structures and magnetization processes. Phys Rev B 77:104431.1–104431.10. doi:10.1103/PhysRevB.77.104431

    Article  Google Scholar 

  • Bertotti G (1998) Hysteresis in magnetism for physicists, materials scientists and engineers. Academic Press, San Diego

    Google Scholar 

  • Chen K, Ferrenberg AM, Landau DP (1993) Static critical behavior of three-dimensional classical Heisenberg models: a high-resolution Monte Carlo study. Phys Rev B 48:3249–3256

    Article  Google Scholar 

  • Chen X, Sahoo S, Kleemann W, Cardoso S, Freitas PP (2004) Universal and scaled relaxation of interacting magnetic nanoparticles. Phys Rev B 70:172411.1–172411.4. doi:10.1103/PhysRevB.70.172411

    Google Scholar 

  • Daou TJ, Grenèche JM, Pourroy G, Buathong S, Derory A, Ulhaq-Bouillet C, Donnio B, Guillon D, Begin-Colin S (2008) Coupling agent effect on magnetic properties of functionalized magnetite-based nanoparticles. Chem Mater 20:5869–5875. doi:10.1021/cm801405n

    Article  Google Scholar 

  • Demortière A, Panissod P, Pichon BP, Pourroy G, Guillon D, Donnio B, Bégin-Colin S (2011) Size-dependent properties of magnetic iron oxide nanocrystals. Nanoscale 3:225–232. doi:10.1039/c0nr00521e

    Article  Google Scholar 

  • Hergt R, Dutz S, Müller R, Zeisberger M (2006) Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy. J Phys 18:S2919–S2934. doi:10.1088/0953-8984/18/38/S26

    Google Scholar 

  • Iglesias O, Labarta A (2001) Finite-size and surface effects in maghemite nanoparticles: Monte Carlo simulations. Phys Rev B 63:184416.1–184416.11. doi:10.1103/PhysRevB.63.184416

    Article  Google Scholar 

  • Iglesias O, Labarta A (2005) Influence of surface anisotropy on the hysteresis of magnetic nanoparticles. J Magn Magn Mater 290:738–741. doi:10.1016/j.jmmm.2004.11.358

    Article  Google Scholar 

  • Kesserwan H, Manfredi G, Bigot J-Y, Hervieux P-A (2011) Magnetization reversal in isolated and interacting single-domain nanoparticles. Phys Rev B 84:172407.1–172407.5

    Article  Google Scholar 

  • Kittel C (1995) Introduction to solid state physics, 7th edn. Wiley, New York

    Google Scholar 

  • Kodama RH (1999) Magnetic nanoparticles. J Magn Magn Mater 200:359–372

    Article  Google Scholar 

  • Landau DP (1976) Finite-size behavior of the simple-cubic Ising lattice. Phys Rev B 14:255–262

    Article  Google Scholar 

  • Landau DP, Binder K (2000) A guide to Monte Carlo simulations in statistical physics. Cambridge University Press, Cambridge

    Google Scholar 

  • Leblanc MD, Plumer ML, Whitehead JP, Mercer JI (2010) Transition temperature and magnetic properties of the granular Ising model in two dimensions studied by Monte Carlo simulations: impact of intragrain spin structure. Phys Rev B 82:174435.1–174435.8. doi:10.1103/PhysRevB.82.174435

    Article  Google Scholar 

  • Leite VS, Figueiredo W (2006) Mean-field and Monte Carlo calculations of the equilibrium magnetic properties of uniaxial ferromagnetic particles. Phys Lett A 359:300–307. doi:10.1016/j.physleta.2006.06.039

    Article  Google Scholar 

  • Leostean C, Pana O, Turcu R, Soran ML, Macavei S, Chauvet O, Payen C (2011) Comparative study of core–shell iron/iron oxide gold covered magnetic nanoparticles obtained in different conditions. J Nanopart Res 13:6181–6192. doi:10.1007/s11051-011-0313-3

    Article  Google Scholar 

  • Lu A-H, Salabas EL, Schüth F (2007) Magnetic nanoparticles: synthesis, protection, functionalization, and application. Angew Chem Int 46:1222–1244. doi:10.1002/anie.200602866

    Article  Google Scholar 

  • Mao Z, Chen X (2010) Magnetic relaxation in disordered exchange interacting systems with random anisotropy. Solid State Commun 150:2227–2230. doi:10.1016/j.ssc.2010.09.038

    Article  Google Scholar 

  • Mejía-López J, Mazo-Zuluaga J (2011) Energy contributions in magnetite nanoparticles: computation of magnetic phase diagram, theory, and simulation. J Nanopart Res 13:7115–7125. doi:10.1007/s11051-011-0629-z

    Article  Google Scholar 

  • Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44:335–341. doi:10.1080/01621459.1949.10483310

    Article  Google Scholar 

  • Neuberger T, Schöpf B, Hofmann H, Hofmann M, von Rechenberg B (2005) Superparamagnetic nanoparticles for biomedical applications: possibilities and limitations of a new drug delivery system. J Magn Magn Mater 293:483–495. doi:10.1016/j.jmmm.2005.01.064

    Article  Google Scholar 

  • Nie Z, Petukhova A, Kumacheva E (2010) Properties and emerging applications of self-assembled structures made from inorganic nanoparticles. Nat Nanotech 5:15–25. doi:10.1038/nnano.2009.453

    Article  Google Scholar 

  • Peczak P, Ferrenberg AM, Landau DP (1991) High-accuracy Monte Carlo study of the three-dimensional classical Heisenberg ferromagnet. Phys Rev B 43:6087–6093

    Article  Google Scholar 

  • Porto M (2002a) Effect of positional disorder in systems of ultrafine ferromagnetic particles. Eur Phys J B 26:229–234. doi:10.1140/epjb/e20020084

    Article  Google Scholar 

  • Porto M (2002b) Relative significance of particle anisotropy in systems of ultrafine ferromagnetic particles. J Appl Phys 92:6057–6061. doi:10.1063/1.1513873

    Article  Google Scholar 

  • Porto M (2005) Ordered systems of ultrafine ferromagnetic particles. Eur Phys J B 45:369–375. doi:10.1140/epjb/e2005-00186-3

    Article  Google Scholar 

  • Reiss G, Hütten A (2005) Magnetic nanoparticles: applications beyond data storage. Nat Mater 4:725–726

    Article  Google Scholar 

  • Russ S, Bunde A (2011) Relaxation in ordered systems of ultrafine magnetic particles: effect of the exchange interaction. J Phys 23:126001.1–1260011. doi:10.1088/0953-8984/23/12/126001

    Google Scholar 

  • Sato T, Iijima T, Seki M, Inagaki N (1987) Magnetic properties of ultrafine ferrite particles. J Magn Magn Mater 65:252–256

    Article  Google Scholar 

  • Serantes D, Baldomir D, Pereiro M, Arias JE, Mateo–Mateo C, Buján-Núñez MC, Vázquez-Vázquez C, Rivas J (2008) Interplay between the magnetic field and the dipolar interaction on a magnetic nanoparticle system: a Monte Carlo study. J Non-Cryst Solids 354:5224–5226. doi:10.1016/j.jnoncrysol.2008.07.040

    Article  Google Scholar 

  • Serantes D, Baldomir D, Pereiro M, Hoppe CE, Rivadulla F, Rivas J (2010) Nonmonotonic evolution of the blocking temperature in dispersions of superparamagnetic nanoparticles. Phys Rev B 82:134433.1–134433.6. doi:10.1103/PhysRevB.82.134433

    Article  Google Scholar 

  • Skumryev V, Stoyanov S, Zhang Y, Hadjipanayis G, Givord D, Nogués J (2003) Beating the superparamagnetic limit with exchange bias. Nature 423:850–853

    Article  Google Scholar 

  • Srivastava CM, Srinivasan G, Nanadikar NG (1979) Exchange constants in spinel ferrites. Phys Rev B 19:499–508

    Article  Google Scholar 

  • Stanley HE (1999) Scaling, universality, and renormalization: three pillars of modern critical phenomena. Rev Mod Phys 71:S358–S366

    Article  Google Scholar 

  • Yang HT, Liu HL, Song NN, Du HF, Zhang XQ, Cheng ZH, Shen J, Li LF (2011) Determination of the critical interspacing for the noninteracting magnetic nanoparticle system. Appl Phys Lett 98:153112.1–153112.3. doi:10.1063/1.3574917

    Google Scholar 

Download references

Acknowledgments

The authors thank FAPESP—the São Paulo Research Foundation—for funding this research through processes numbered 2010/01655-2 and 2012/07117-5.

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  1. Instituto de Física, Universidade de São Paulo, Sao Paulo, 05508-090, Brazil

    Fabiana R. Arantes & Daniel R. Cornejo

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  1. Fabiana R. Arantes
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  2. Daniel R. Cornejo
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Correspondence to Daniel R. Cornejo.

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Arantes, F.R., Cornejo, D.R. Monte Carlo study of the magnetic properties of frozen and non-interacting nanoparticles. J Nanopart Res 15, 1859 (2013). https://doi.org/10.1007/s11051-013-1859-z

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