Simple hysteresis loop model for rock magnetic analysis

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A simple phenomenological model founded on Lorentzian functions is evaluated on the first derivative of magnetic hysteresis loops from several artificial samples with iron oxide/oxyhydroxide mixtures imitating natural sediments. The approach, which shows that hysteresis loops can be described by elementary analytical functions and provides estimates of magnetization parameters to a satisfactory degree of confidence, is applied with the help of standard data analysis software. Distorted hysteresis loops (wasp-waisted, goose-necked and pot-bellied shaped) from simulations and artificial samples from a previous work are reproduced by the model which allows to straightforwardly unmix the ferromagnetic signal from different minerals like magnetite, greigite, haematite and goethite. The analyses reveal that the contribution from the ferrimagnetic fraction, though present in a minor concentration (≤2.15 wt%), dominates the magnetization.

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  1. Bertotti G., 1998. Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers. First Edition. Academic Press, San Diego, CA.

  2. Carter-Stiglitz B., Moskowitz B. and Jackson M., 2001. Unmixing magnetic assemblages and the magnetic behavior of bimodal mixtures. J. Geophys. Res.-Solid Earth., 106, 26397–26411.

  3. Channell J.E.T. and McCabe C., 1994. Comparison of magnetic hysteresis parameters of unremagnetized and remagnetized limestones. J. Geophys. Res.-Solid Earth, 99, 4613–4623.

  4. Dunlop D.J. and Özdemir Ö., 1997. Rock Magnetism: Fundamentals and Frontiers. Cambridge University Press, Cambridge, U.K.

  5. Dunlop D., 2002a. Theory and application of the Day plot (Mrs/Ms versus Hcr/Hc). 1. Theoretical curves and tests using titanomagnetite data. J. Geophys. Res.-Solid Earth, 107(B3), 2056.

  6. Dunlop D., 2002b. Theory and application of the Day plot (Mrs/Ms versus Hcr/Hc). 2. Application to data for rocks, sediments and soils. J. Geophys. Res.-Solid Earth, 107(B3), 2057.

  7. Fabian K., 2003. Some addtional parameters to estimate domain state from isothermal magnetization measurements. Earth Planet. Sci. Lett., 213, 337–345.

  8. Heslop D., 2015. Numerical strategies for magnetic mineral unmixing. Earth Sci. Rev., 150, 256–284.

  9. Heslop D. and Roberts A.P., 2012. A method for unmixing magnetic hysteresis loops. J. Geophys. Res.-Solid Earth, 117, B03103.

  10. Hodgdon M.L., 1988. Mathematical theory and calculations of magnetic hysteresis curves. IEEE Trans. Magn., 24, 3120–3122.

  11. Jackson M., Worm H.-U. and Banerjee S.K., 1990. Fourier analysis of digital hysteresis data: rock magnetic applications. Phys. Earth. Planet. Inter, 65, 78–87.

  12. Jackson M., Rochette P., Fillion G., Banerjee S. and Marvin J., 1993. Rock magnetism of remagnetized Paleozoic carbonates: low-temperature behavior and susceptibility characteristics. J. Geophys. Res.-Solid Earth, 98, 6217–6225.

  13. Jackson M. and Solheid P., 2010. On the quantitative analysis and evaluation of magnetic hysteresis data. Geochem. Geophys. Geosyst, 11, Q04Z15

  14. Jiles D.C. and Atherton D.L., 1984. Theory of ferromagnetic hysteresis. J. Appl. Phys., 55, 2115–2120.

  15. Jiles D.C. and Thoelke J.B., 1989. Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops. IEEE Trans. Magn., 25, 3928–3930.

  16. Josephs R.M, Crompton D.S. and Krafft C.S., 1986. Characterization of magnetic oxide recording media using Fourier analysis of static hysteresis loops. IEEE Trans. Mag, 22, 653–655.

  17. Kobayashi S., Miura K., Narita Y. and Takahashi S., 2018. Magnetic investigations of steel degradation using a magnetic hysteresis scaling technique. Metals, 8, 1–12.

  18. Kwun H. and Burkhardt G.L., 1987. Effects of grain size, hardness, and stress on the magnetic hysteresis loops of ferromagnetic steels. J. Appl. Phys., 61, 1576–1579.

  19. Lagroix F. and Guyodo Y., 2017. A new tool for separating the magnetic mineralogy of complex mineral assemblages from low temperature magnetic behavior. Front. Earth Sci., 5, 61.

  20. Mayergoyz I.D., 1986. Mathematical models of hysteresis. IEEE Trans. Magn., 22, 603–608.

  21. Paterson G.A., Zhao X., Jackson M. and Heslop D., 2018. Measuring, processing and analyzing hysteresis data. Geochem. Geophys. Geosyst., 19, 1925–1945.

  22. Rivas J., Zamarro J.M., Martín E. and Pereira C., 1981. Simple approximation for magnetization curves and hysteresis loops. IEEE Trans. Magn., 17, 1498–1502.

  23. Roberts A.P., Cui Y. and Verosub K.L., 1995. Wasp-waisted hysteresis loops: Mineral magnetic characteristics and discrimination of components in mixed magnetic systems. J. Geophys. Res.-Solid Earth, 100, 909–924.

  24. Tauxe L., 1998. Paleomagnetic Principles and Practice. Modern Approaches in Geophysics 18. Kluwer Academic Publishers, Dordrecht, The Netherlands.

  25. Tauxe L., Mullender T.A.T. and Pick T., 1996. Potbellies, wasp-waists, and superparamagnetism in magnetic hysteresis. J. Geophys. Res.-Solid Earth, 101, 571–583.

  26. Tauxe L., Bertram H.N and Seberino C., 2002. Physical interpretation of hysteresis loops: Micromagnetic modeling of fine particle magnetite. Geochem. Geophys. Geosyst., 3, 1055, DOI: 10.1029/2001GC000241.

  27. Thompson R., 1986. Modelling magnetization data using SIMPLEX. Phys. Earth Planet. Inter., 42, 113–127.

  28. Schmidbauer E. and Schembera N., 1987. Magnetic hysteresis properties and anhysteretic remanent magnetization of spherical Fe3O4 particles in the grain size range 60–160 nm. Phys. Earth Planet. Inter, 46, 77–83.

  29. Stoner E.C. and Wohlfarth E.P., 1948. A mechanism of magnetic hysteresis in heterogeneous alloys. Phil. Trans. R. Soc. London A, 240, 599–642.

  30. Upda S.S. and Lord, W., 1985. A Fourier descriptor model of hysteresis loop phenomena. IEEE Trans. Mag., 21, 2370–2373.

  31. Vasquez C.A., Sapienza F.F., Somacal A. and Fazzito S.Y., 2018. Anhysteretic remanent magnetization: model of grain size distribution of spherical magnetite grains. Stud. Geophys. Geod., 62, 339–351.

  32. von Dobeneck T., 1996. A systematic analysis of natural magnetic mineral assemblages based on modelling hysteresis loops with coercivity-related hyperbolic basis functions. Geophys. J. Int., 124, 675–694.

  33. Wang H., Zhan J., Yu Z., Zhang Y., Yu J., Gui Y., Yu T., Xie J., Zhang H., Ji Y., Zan N., Fu R. and Perin D., 2016. A novel hysteresis model of magnetic field strength determined by magnetic induction intensity for Fe-3% Si electrical steel applied in cigarette making machines. J. Mater., ID 1509498, DOI: 10.1155/2016/1509498.

  34. Willcock S.N.M. and Tanner B.K., 1983. Harmonic analysis of B-H loop. IEEE Trans. Mag., 19, 2265–2270.

  35. Zhang R., Necula C., Heslop D. and Nie J., 2016. Unmixing hysteresis loops of the late Miocene-early Pleistocene loess-red clay sequence. Sci. Rep., 6, 29515.

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Correspondence to Carlos A. Vasquez.

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Vasquez, C.A., Fazzito, S.Y. Simple hysteresis loop model for rock magnetic analysis. Stud Geophys Geod (2020) doi:10.1007/s11200-019-1942-8

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  • magnetic hysteresis loops
  • Lorentzian functions
  • iron oxides/oxyhydroxides
  • rock magnetism