Micromagnetic Modelling of Hysteresis in Permalloy Thin Films with Non-Magnetic Defects

Inna Lobanova, Stéphane Labbé, Stéphane Despréaux


In this paper, we present the results of numerical micromagnetic modelling of the domain wall pinning on non-magnetic defects in a ferromagnetic thin sheet of permalloy. We compared the influence of different distribution of non-magnetic inclusions on the magnetization reversal in case of uniaxial anisotropy. It is shown that the non-magnetic defects help to resolve vortex singularities and play a role of pinning states. It is demonstrated that the defects located on the sides of the sheet favor the transition into the single-domain state. By varying the in-plane anisotropy constant, we observed that the defects located in the center lead to higher coercivity,  when the domain wall width is comparable to the size of the sample, but narrowing of domain wall width leads to a change of energetically favorable distribution of defects and the highest  is when defects are located on the sides. It is shown that the defects located in the corner of the sheet serve as nucleation points for the magnetization reversal process and have a lower threshold for unpinning of the domain walls.


Domain walls movement; Hysteresis; Micromagnetic modelling; Soft magnetic materials; Spintronics.

Article Metrics

Abstract view : 32 times
PDF - 11 times

Full Text:



S. Parkin, X. Jiang, C. Kaiser, A. Panchula, K. Roche and M. Saman, Magnetically engineered spintronic sensors and memory, Proceedings of the IEEE, 91, 2003, 661-680.

D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit and R. P. Cowburn, Magnetic domain-wall logic, Science, 309, 2005, 688-1692.

C. Chappert, A. Fert and F. V. Dau, The emergence of spin electronics in data storage, Nature Materials, 6, 2007, 813- 823.

T. L. Jin, M. Ranjbar, S. K. He, W. C. Law, T. J. Zhou, W. S. Lew, X. X. Liu and S. N. Piramanayagam, Tuning magnetic properties for domain wall pinning via localized metal diffusion, Scientific Reports, 7, 2017, 1-7.

S. Parkin and S. H. Yang, Memory on the racetrack, Nature Nanotech, 10, 2015, 195-198.

R. D. Shull, Y. P. Kabanov, V. S. Gornakov, P. J. Chen and V. I. Nikitenko, Shape critical properties of patterned Permalloy thin films, Journal of Magnetism and Magnetic Materials, 400, 2016, 191-199

M. C. Giordano, S. E. Steinvall, S. Watanabe, A. F. Morral and D. Grundler, Ni80Fe20 nanotubes with optimized spintronic functionalities prepared by atomic layer deposition, Nanoscale, 13, 2021, 13451-13462.

A. Hubert and R. Schaefer, Magnetic domains: The analysis of magnetic microstructures. Berlin, Heidelberg: Springer Verlag, 2009.

D. Toscano, J. Silva, P. Z. Coura, R. A. Dias, B. V. Costa and S. A. Leonel, Magnetic vortex behavior and its dynamics in nano-magnets in the presence of impurities, Physics Procedia, 28, 2012, 99-104.

T. Takashita, N. Nakamura and Y. Ozaki, Influence of iron powder properties on hysteresis loss of iron powder core, JFE technical report, 21, 2016, 78-84.

W. Brown Jr., Micromagnetics, John Wiley and Sons, 1963.

W. Döring, Micromagnetics, Physics Handbook, Springer, USA, 1966.

J. Fidler and T. Schrefl, Micromagnetic modelling - the current state of the art, Journal of Physics D: Applied Physics, 33, 2000, 135-156.

I. Betancourt, G. Hrkac and T. Schrell, Micromagnetic simulation of domain wall dynamics in permalloy nanotubes at high frequencies, Journal of Applied Physics, 104, 2008, 023915.

B. Belyaev and A. Izotov, Micromagnetic calculation of magnetostatic oscillation modes of an orthogonally magnetized disk of yttrium iron garnet, Physics of the Solid State, 55, 2013, 2491-2500.

J. Leliaert and J. Mulkers, Tomorrow’s micromagnetic simulations, Journal of Applied Physics, 125, 2019, 180901.

B. Belyaev, A.V. Izotov, G. V. Skomorokhov and P. N. Solovev, Micromagnetic analysis of edge effects in a thin magnetic film during local excitation of magnetization oscillations, Russian Physics Journal, 63, 2020, 837-843.

L. Landau and E. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys Z Sowjetunion, 8, 1935, 153-169.

S. Labbé, Numerical simulation of high-frequency behavior of ferromagnetic materials, Ph.D. Dissertation, University Paris 13, Paris, France,1998.

S. Labbé and P. Leca, Fast solver for the Maxwell quasistatic equations: block-Toeplitz matrix, Application to micromagnetism, CR Acad Sci Paris, 327, 1998, 415-420.

S. Labbé and P. Y. Bertin, Microwave polarizability of ferrite particles with non-uniform magnetization, Journal of Magnetism and Magnetic Materials, 206, 1999, 93-105.

S. Labbé, Fast computation for large magnetostatic systems adapted for Micromagnetism, SIAM Journal of Scientific Computing, 26, 2005, 2160-2175.

D. Lee, Fast multiplication of a recursive block Toeplitz matrix by a vector and its application, Journal of Complexity, 2, 1986, 295-305.

E. Pellicer, E. Rossinyol, M. Cabo, A. Lopez-Ortega and M. Estrader, Oxide-matrix based nanocomposite materials for advanced magnetic and optical functionalities, in Advances in Nanocomposites - Synthesis, Characterization and Industrial Applications, InTech, 2011, 343-358.

X. Wen, S. Kelly, J. Andrew and D. Arnold, Nickel-zinc ferrite/permalloy (Ni0.5Zn0.5Fe2O4/Ni Fe) soft magnetic-nanocomposites fabricated by electro-infiltration, AIP Advances, 6, 2016, 056111.

M. Rahm, J. Biberger, V. Umansky and D. Weiss, Vortex pinning at individual defects in magnetic nanodisks, Journal of Applied Physics, 93, 2003, 7429-7431.

M. Rahm, J. Stahl, W. Wegscheider and D. Weiss, Multistable switching due to magnetic vortices pinned at artificial pinning sites, Applied Physics Letters, 85, 2004, 1553-1555.


  • There are currently no refbacks.