Journal of Nanoparticle Research

, Volume 10, Issue 3, pp 487–497 | Cite as

Determination of the anisotropy constant and saturation magnetization of magnetic nanoparticles from magnetization relaxation curves

  • Ivan Volkov
  • Maxim Chukharkin
  • Oleg Snigirev
  • Alexander Volkov
  • Saburo Tanaka
  • Coenrad Fourie
Research Paper


We have developed a new method for the determination of the anisotropy constant and saturation magnetization of magnetic nanoparticles. This method deals with the approximation of magnetization relaxation curves measured upon application and further fast switching off the dc magnetizing field. The relaxation process is registered in the time interval from 6 μs to several minutes by using a scanning high-T C SQUID-microscope equipped with a specially designed electronic circuit composed of a fast solid-state switch and a low-inductance magnetizing coil. The algorithm for calculating the approximation data is based on the activation Néel–Arrhenius law and takes into account the size distribution of the nanoparticles and the angular distribution of their easy axes. The performance of the method is demonstrated on dilute (∼0.2 vol%) ensembles of near-spherical Fe3O4 nanoparticles with a mean size of 7.7 nm and a standard deviation of 45% as determined from transmission electron microscopy data.


Magnetic nanoparticles SQUIDs Anisotropy Relaxation phenomena Néel–Arrhenius law Measurements Instrumentation 



This work was supported by the Russian Foundation for Basic Research under the projects # 06-02-16776-a and # 07-02-91227-YaF_a.


  1. Aharoni A (1996) Ferromagnetism. Oxford University Press, OxfordGoogle Scholar
  2. Bacri J, Perzynski R, Salin D, Cabuil V, Massart R (1990) Ionic ferrofluids: a crossing of chemistry and physics. J Magn Magn Mater 85:27–32CrossRefGoogle Scholar
  3. Brown W (1963) Thermal fluctuations of a single-domain particle. Phys Rev 130:1677–1686CrossRefGoogle Scholar
  4. Caizer C (2003) Saturation magnetization of γ-Fe2O3 nanoparticles dispersed in a silica matrix. Physica B 327:27–33CrossRefGoogle Scholar
  5. Cannas C, Concas C, Falqui A, Gatteschi D, Musinu A, Piccaluga G, Sangregorio C, Spano G (2001) Superparamagnetic behavior of γ-Fe2O3 nanoparticles dispersed in a silica matrix. Phys Chem Chem Phys 3:832–838CrossRefGoogle Scholar
  6. Chikazumi S (1964) Physics of magnetism. Wiley, New YorkGoogle Scholar
  7. Duarte EL, Itri R, Lima E, Baptista MS, Berquo TS, Goya GF (2006) Large magnetic anisotropy in ferrihydrite nanoparticles synthesized from reverse micelles. Nanotechnology 17:5549–5555CrossRefGoogle Scholar
  8. Fiorani D (ed) (2005) Surface effects in magnetic nanoparticles. SpringerGoogle Scholar
  9. Garcia-Otero J, Porto M, Rivas J, Bunde A (1999) Influence of the cubic anisotropy constants on the hysteresis loops of single-domain particles: a Monte Carlo study. J Appl Phys 85:2287–2292CrossRefGoogle Scholar
  10. Held GA, Grinstein G, Doyle H, Sun Sh, Murray C (2001) Competing interactions in dispersions of superparamagnetic nanoparticles. Phys Rev B 64:012408-1–012408-4CrossRefGoogle Scholar
  11. Jamet M, Wernsdorfer W, Thirion C, Mailly D, Dupuis V, Mélinon P, Pérez A (2001) Magnetic anisotropy of a single cobalt nanocluster. Phys Rev Lett 86:4676–4679CrossRefGoogle Scholar
  12. Kadau K, Gruner M, Entel P, Kreth M (2003) Modeling structural and magnetic phase transitions in iron-nickel nanoparticles. Phase Transit 76:355–365CrossRefGoogle Scholar
  13. Kodama R (1999) Magnetic nanoparticles. J Magn Magn Mater 200:359–372CrossRefGoogle Scholar
  14. Lin XM, Sorensen CM, Klabunde KJ, Hajipanayis GC (1999) Control of cobalt nanoparticle size by the germ-growth method in inverse micelle system: size-dependent magnetic properties. J Mater Res 14:1542–1547CrossRefGoogle Scholar
  15. Luis F, Petroff F, Torres JM, Garcia LM, Bartolome J, Carrey J, Vaures A (2002) Magnetic relaxation of interacting Co clusters: crossover from two- to three-dimensional lattices. Phys Rev Lett 88:217205-1–217205-4Google Scholar
  16. McCallum RW (2005) Determination of the saturation magnetization, anisotropy field, mean field interaction, and switching field distribution for nanocrystalline hard magnets. J Magn Magn Mater 292:135–142CrossRefGoogle Scholar
  17. Moser A, Takano K, Margulies DT, Albrecht M, Sonobe Y, Ikeda Y, Sun Sh, Fullerton EE (2002) Magnetic recording: advancing into the future. J Phys D: Appl Phys 35:R157–R167CrossRefGoogle Scholar
  18. Mørup S (1990) Mossbauer effect in small particles. Hyperfine Interactions 60:959–974CrossRefGoogle Scholar
  19. Muxworthy AR, McClelland E (2000) Review of the low-temperature magnetic properties of magnetite from a rock magnetic perspective. Geophys J Int 140:101–114CrossRefGoogle Scholar
  20. Néel L (1949) Théorie du trainage magnétique. Ann Geophys 5:99Google Scholar
  21. Néel L (1954) J Phys Radium 15:376Google Scholar
  22. Osborn JA (1945) Demagnetizing factors of the general ellipsoid. Phys Rev 67:351–357CrossRefGoogle Scholar
  23. Pankhurst QA, Binns C, Maher M, Kechrakos D, Trohidou K (2002) Magnetic behavior of nanostructured films assembled from preformed Fe clusters embedded in Ag. Phys Rev B 66:184413-1–184413-12Google Scholar
  24. Pankhurst QA, Connolly J, Jones SK, Dobson J (2003) Application of magnetic nanoparticles in biomedicine. J Phys D: Appl Phys 36:R167–R181CrossRefGoogle Scholar
  25. Poddar P, Telem-Shafir T, Fried T, Markovich G (2002) Dipolar interactions in two- and three-dimensional magnetic nanoparticle arrays. Phys Rev B 66:060403-1–060403-4CrossRefGoogle Scholar
  26. Si Sh, Li Ch, Wang X, Yu D, Peng Q, Li Y (2005) Magnetic monodisperse Fe3O4 nanoparticles. Cryst Growth Des 5:391–393CrossRefGoogle Scholar
  27. Song T, Roshko RM, Dahlberg E (2001) Modelling the irreversible response of magnetically ordered materials: a Preisach-based approach. J Phys: Condens Matter 13:3443–3460CrossRefGoogle Scholar
  28. Stoner E, Wohlfarth E (1991) A mechanism of magnetic hysteresis in heterogeneous alloys. IEEE Trans Magn 27:3475–3518 (reprinted from (1948) Philos Trans R Soc London A240:599–642).Google Scholar
  29. Suess D, Schrefl T, Fidler J (2001) Reversal modes, thermal stability and exchange length in perpendicular recording media. IEEE Trans Magn 37:1664–1666CrossRefGoogle Scholar
  30. Vargas JM, Socolovsky LM, Knobel M, Zanchet D (2005) Dipolar interactions and size effects in powder samples of colloidal iron oxide nanoparticles. Nanotechnology 16: S285–S290CrossRefGoogle Scholar
  31. Volkov I, Chukharkin M, Snigirev O, Ranchinski M (2003) YBCO submicron Josephson junctions on bicrystal substrates. IEEE Trans Appl Supercond 13:861–864CrossRefGoogle Scholar
  32. Volkov IA, Chukharkin ML, Snigirev OV, Volkov AV, Moskvina MA, Gudoshnikov SA, Kerimov AK (2005) HTS SQUID microscopy for measuring the magnetization relaxation of magnetic nanoparticles. IEEE Trans Appl Supercond 15:3874–3878CrossRefGoogle Scholar
  33. Vonsovsky SV (1974) Magnetism. Wiley, New YorkGoogle Scholar
  34. Weller D, Moser A (1999) Thermal effect limits in ultrahigh density magnetic recording. IEEE Trans Magn 35:4423–4439CrossRefGoogle Scholar
  35. Woods SI, Kirtley JR, Sun Sh, Koch RH (2001) Direct investigation of superparamagnetism in Co nanoparticle films. Phys Rev Lett 87:137205-1–137205-4CrossRefGoogle Scholar
  36. Zeng H, Li J, Liu JP, Wang ZL, Sun Sh (2002) Exchange-coupled nanocomposite magnets by nanoparticle self-assembly. Nature 420:395–398CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Ivan Volkov
    • 1
  • Maxim Chukharkin
    • 1
  • Oleg Snigirev
    • 1
  • Alexander Volkov
    • 2
  • Saburo Tanaka
    • 3
  • Coenrad Fourie
    • 4
  1. 1.Physics DepartmentLomonosov Moscow State UniversityMoscowRussia
  2. 2.Chemical DepartmentLomonosov Moscow State UniversityMoscowRussia
  3. 3.Toyohashi University of TechnologyToyohashiJapan
  4. 4.Department of Electrical and Electronic EngineeringUniversity of StellenboschStellenboschSouth Africa

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