纳米盘状NiFe磁体的微磁学研究
摘要
本文通过微磁学方法进行理论计算并与实验进行比较,分析了直径在200～700nm的NiFe合金薄膜的退磁过程及各个阶段的磁化分布特性,由于涡旋在整个过程中起着非常重要的作用,所以我们较为系统地研究了涡旋的产生、移动和消失机制,并进一步将不同位置和数目的缺陷引入磁体,分析了它对涡旋钉扎作用的影响。最后在动态模拟周期性振荡场作用于薄膜软铁磁圆盘的基础上,我们不但发现涡旋位置与场分量都作相同的周期性运动,并且归纳出二者之间存在恒定的相位差。
The study of magnetization processes in magnetic materials has been in thelast fifty years the focus of considerable research for its application to magneticrecording technology. In fact, the design of nowadays widespread magnetic stor-age devices, such as the hard-disks which are within computers on our desktopsand laptops, requires the knowledge of the “microscopic”phenomena occurringwithin magnetic media.
Meanwhile, magnetic systems with reduced dimensions has attracted a greatdeal of interest for their various potential applications such as high-density pat-terned recording media ,Magnetoresistive Random Access Memory (MRAM) andultrasmall magnetic field sensors. Prior to the technological applications men-tioned above, it is indispensable to understand well fundamental properties of theindividual magnetic elements with reduced dimentions.
More and more applications required the spatial scale of magnetic media inthe order of, more or less, hundred nanometers, magnetic phenomena has to beanalyzed by theoretical models with appropriate resolution. This is the case of mi-cromagnetics, which is a continuum theory that stands between quantum theorieslike ab-initio and macroscopic theories. On the other hand, with the read/write fre-quency increased to GHz and more, dynamic effects cannot be neglected, and thetime resolution of our observation should be on the order of picosecond. It is alsothe micromagnetics, which can simulate the ultra-fast magnetic recording deviceson the framework of magnetization dynamics.
With the motivation mentioned above, we simulate the demagnetization pro-cesses of submicron-sized NiFe ferromagnetic disks of different shapes. The result
exhibit a magnetic vortex structure, which dominate almost the whole process.This peculiar configuration has been investigated both by Lorentz and magneticforce microscopy on a lot of literatures, which revealed an in-plane spin configu-ration, which closed the magnetic ?ux and a small region of perpendicular magne-tization at the vortex core.From our simulation, it became quite clear that the magnetization reversal ofdisks involves vortex formation, propagation, and annihilation. Although micro-magnetic calculations and experimental carried out previously suggest that vortexformation is preceded by ”C” ”S” and ”W” state in different shape disks, we showhere the detailed mechanism. Different scenarios of vortex nucleation could beuncovered and confirmed by micromagnetic calculations.We study the interaction between magnetic vortices and artificial point defectsin submicron-sized Nife disk by using micromagnetics, which illustrate the inter-action of Pinning and Attracting by plotting the magnetic moment distribution.With the location of the defect changed perpendicular to the direction of the exter-nal field, vortex core will be pinned at the defect on most of the case, though thenucleation field are not the same. Changing defect location parallel to the externalfield will only alternate the degree of the attraction between defect and vortex.A dynamic micromagnetic finite-element simulation on the dynamic responseof a soft-magnetic disc exposed to an oscillatory field applied in the disc planewas presented. The simulation was started in an original-vortex state, and then thevortex core moved around an elliptical orbit and the magnetization vector changedits direction as the same frequency. As for the two resonant oscillations mentionedabove, we concluded that they have a invariable phase difference.
The study of magnetization processes in magnetic materials has been in thelast fifty years the focus of considerable research for its application to magneticrecording technology. In fact, the design of nowadays widespread magnetic stor-age devices, such as the hard-disks which are within computers on our desktopsand laptops, requires the knowledge of the “microscopic”phenomena occurringwithin magnetic media.
Meanwhile, magnetic systems with reduced dimensions has attracted a greatdeal of interest for their various potential applications such as high-density pat-terned recording media ,Magnetoresistive Random Access Memory (MRAM) andultrasmall magnetic field sensors. Prior to the technological applications men-tioned above, it is indispensable to understand well fundamental properties of theindividual magnetic elements with reduced dimentions.
More and more applications required the spatial scale of magnetic media inthe order of, more or less, hundred nanometers, magnetic phenomena has to beanalyzed by theoretical models with appropriate resolution. This is the case of mi-cromagnetics, which is a continuum theory that stands between quantum theorieslike ab-initio and macroscopic theories. On the other hand, with the read/write fre-quency increased to GHz and more, dynamic effects cannot be neglected, and thetime resolution of our observation should be on the order of picosecond. It is alsothe micromagnetics, which can simulate the ultra-fast magnetic recording deviceson the framework of magnetization dynamics.
With the motivation mentioned above, we simulate the demagnetization pro-cesses of submicron-sized NiFe ferromagnetic disks of different shapes. The result
exhibit a magnetic vortex structure, which dominate almost the whole process.This peculiar configuration has been investigated both by Lorentz and magneticforce microscopy on a lot of literatures, which revealed an in-plane spin configu-ration, which closed the magnetic ?ux and a small region of perpendicular magne-tization at the vortex core.From our simulation, it became quite clear that the magnetization reversal ofdisks involves vortex formation, propagation, and annihilation. Although micro-magnetic calculations and experimental carried out previously suggest that vortexformation is preceded by ”C” ”S” and ”W” state in different shape disks, we showhere the detailed mechanism. Different scenarios of vortex nucleation could beuncovered and confirmed by micromagnetic calculations.We study the interaction between magnetic vortices and artificial point defectsin submicron-sized Nife disk by using micromagnetics, which illustrate the inter-action of Pinning and Attracting by plotting the magnetic moment distribution.With the location of the defect changed perpendicular to the direction of the exter-nal field, vortex core will be pinned at the defect on most of the case, though thenucleation field are not the same. Changing defect location parallel to the externalfield will only alternate the degree of the attraction between defect and vortex.A dynamic micromagnetic finite-element simulation on the dynamic responseof a soft-magnetic disc exposed to an oscillatory field applied in the disc planewas presented. The simulation was started in an original-vortex state, and then thevortex core moved around an elliptical orbit and the magnetization vector changedits direction as the same frequency. As for the two resonant oscillations mentionedabove, we concluded that they have a invariable phase difference.
引文
[1] Werner Scholz. Scalable Parallel Micromagnetic Solvers for Magnetic Nanostructures. PhDthesis, Institute of Solid State Physics, Vienna University of Technology, 2003.
[2] K. J. Strnat, G. Hoffer, J. Oson, and W. Ostertag. A family of cobaltbased permanent magnetmaterials. Journal of Applied Physics, 1967, vol. 38, pp. 1001–1002.
[3] M. Sagawa, S. Fujimura, N. Togawa, H. Yamamoto, and Y. Matsuura. New material for perma-nent magnets on a base of Nd and Fe. Journal of Applied Physics, 1984, vol. 55, pp. 2083–2087.
[4] G. C. Hadjipanayis, R. C. Hazelton, and K. R. Lawless. Cobalt-free permanent magnet materialsbased on iron-rare-earth alloys. Journal of Applied Physics, 1984, vol. 55(6), pp. 2073–2077.
[5] S. R. Das. Coming soon: Terabit hard disk drives. IEEE Spectrum, February 2003, vol. 40, pp.19–21.
[6] 戴道生等. 《铁磁学》上册. 科学出版社, 1987, 第一版.
[7] W.F. Brown. Theory of the approach to magnetic saturation. Physical Review, 1940, vol. 48, p.736.
[8] W.F. Brown. Micromagnetics. Interscience, New York, 1963.
[9] W.F. Brown. Magnetostatic principles in ferromagnetism. Interscience, New York, 1962.
[10] Werner Scholz, Josef Fidler, Thomas Schre?, et al. Scalable parallel micromagnetic solvers formagnetic nanostructures. Computational Materials Science, 2003, vol. 28, p. 366.
[11] M. Donahue and D. Porter. Object oriented micromagnetic framework (oommf) home page.Available from http://math.nist.gov/oommf/, October 2002.
[12] M.R. Scheinfein. LLG(Landau-Lifshitz-Gilbert) micromagnetics simulator home page. Avail-able from http://llgmicro.home.mindspring.com/, 2003.
[13] M. Schneider and H. Hoffman. Magnetization loops of submicron ferromagnetic permalloy dotarrays. Journal of Applied Physics, 1999, vol. 86, p. 4539.
[14] M. Grimsditch, Y. Jaccard, and I.K. Schuller. Magnetic anisotropies in dot arrays: Shapeanisotropy versus coupling. Physical Review B, 1998, vol. 58, p. 11539.
[15] K. Runge, Y. Nozaki, Y. Otani, H. Miyajima, B. Pannetier, T. Matsuda, and A. Tonomura. High-resolution observation of magnetization processes in 2μm × 2μm × 0.04μm permalloy particles.Journal of Applied Physics, 1996, vol. 79, p. 5075.
[16] D. K. Koltsov, R. P. Cowburn, and M. E. Welland. Micromagnetics of ferromagnetic equilateraltriangular prisms. Journal of Applied Physics, 2000, vol. 88, p. 5315.
[17] C.A.F. Vaz, M. Kla¨ui, J.A.C. Bland, L.J. Heyderman, C. David, and F. Nolting. Fundamentalmagnetic states of disk and ring elements. Journal of Magnetism and Magnetic Materials, 2006,vol. ?, p. unpublished.
[18] Thomas Uhlig, M. Rahm, Christian Dietrich, Rainer Ho¨llinger, Martin Heumann, Dieter Weiss,and Josef Zweck. Shifting and pinning of a magnetic vortex core in a permalloy dot by a magneticfield. Physical Review Letters, December 2005, vol. 95, p. 237205.
[19] T.R. Koehler. Hybrid FEM-BEM method for fast micromagnetic calculations. Physa B: Con-dense Matter, 1997, vol. 233(4), pp. 302–307.
[20] Dennis A. Lindholm. Three-dimensional magnetostatic fields from point-matched integral equa-tions with linearly varying scalar source. IEEE Transactions on Magnetic, 1984, vol. 20(5), pp.2025–2032.
[21] S. Benson, L.C. McInnes, J.J. More′, and J. Sarich. TAO home page. Available from http://www-unix.mcs.anl.gov/tao/, 2001.
[22] Peter Brown, Aaron Collier, Keith Grant, Alan Hindmarsh, Steven Lee, Radu Serban, and CarolWoodward. SUNDIALS home page. Available from http://www.llnl.gov/CASC/sundials/, 2002.
[23] G. Karypis. METIS home page. Available from http://www-users.cs.umn.edu/ karypis/metis/,2002.
[24] MPICH. home page. Available from http://www-unix.mcs.anl.gov/mpi/mpich/, 2003.
[25] S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M. Knepley, L.C. McInnes, B.F. Smith, andH. Zhang. PETSc home page. Available from http://www.mcs.anl.gov/petsc/, 2001.
[26] K. Yu. Guslienko and V. Novosad. Magnetization reversal due to vortex nucleation, displacement,and annihilation in submicron ferromagnetic dot arrays. Physical Review B, 2001, vol. 65, p.024414.
[27] T. Shinjo, T. Okuno, et al. Magnetic vortex core observation in circular dots of permalloy. Sci-ence, August 2000, vol. 298, p. 930.
[28] Taras Pokhil, Dian Song, and Janusz Nowak. Spin vortex states and hysteretic properties ofsubmicron size nife elements. Journal of Applied Physics, May 2000, vol. 87(9), pp. 6319–6321.
[29] M. Rahm, M. Schneider, J. Biberger, R. Pulwey, J. Zweck, and D. Weiss. Vortex nucleation insubmicrometer ferromagnetic disks. Applied Physics Letters, June 2003, vol. 82(23), p. 4110.
[30] Jonathan Kin Ha, Riccardo Hertel, and J. Kirschner. Micromagnetic study of magnetic configu-rations in submicron permalloy disks. Physical Review B, June 2003, vol. 67(1), p. 224432.
[31] Jonathan Kin Ha, Riccardo Hertel, and J. Kirschner. Configurational stability and magnetiza-tion processes in submicron permalloy disks. Physical Review B, February 2003, vol. 67(1), p.064418.
[32] M. Schneider, H. Hoffmann, S. Otto, Th. Haug, and J. Zweck. Stability of magnetic vorticesin ?at submicron permalloy cylinders. Journal of Applied Physics, August 2002, vol. 92(3), p.1466.
[33] M. Rahm and J. Biberger. Vortex pinning at individual defects in magnetic nanodisks. Journalof Applied Physics, May 2003, vol. 93(10), p. 7429.
[34] M. Rahm, J. Stahl, and D. Weiss. Programmable logic elements based on ferromagnetic nan-odisks containing two antidots. Applied Physics Letters, 2005, vol. 87(18), p. 182107.
[35] M. Rahm, J. Stahl, W. Wegscheider, and D. Weiss. Multistable switching due to magnetic vorticespinned at artificial pinning sites. Applied Physics Letters, June 2004, vol. 85(9), p. 1553.
[36] J. Rothman, M. Kla¨ui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, andR. Speaks. Observation of a bi-domain state and nucleation free switching in mesoscopic ringmagnets. Physical Review B, February 2001, vol. 86(6), p. 1098.
[37] M. Rahm and R. Ho¨llinger. In?uence of point defects on magnetic vortex structures. Journal ofApplied Physics, June 2004, vol. 95(11), p. 6708.
[38] R. Ribo′, M.A. de Riera Pasenau, and E. Escolano. GiD home page, international center fornumerical methods in engineering (CIMNE). Available from http://gid.cimne.upc.es, 2002.
[39] R. Hertel and J. Kirschner. Resonant modes of vortex structures in soft-magnetic nanodiscs.Journal of Magnetism and Magnetic Materials, 2004, vol. 272-276, pp. 655–656.
[2] K. J. Strnat, G. Hoffer, J. Oson, and W. Ostertag. A family of cobaltbased permanent magnetmaterials. Journal of Applied Physics, 1967, vol. 38, pp. 1001–1002.
[3] M. Sagawa, S. Fujimura, N. Togawa, H. Yamamoto, and Y. Matsuura. New material for perma-nent magnets on a base of Nd and Fe. Journal of Applied Physics, 1984, vol. 55, pp. 2083–2087.
[4] G. C. Hadjipanayis, R. C. Hazelton, and K. R. Lawless. Cobalt-free permanent magnet materialsbased on iron-rare-earth alloys. Journal of Applied Physics, 1984, vol. 55(6), pp. 2073–2077.
[5] S. R. Das. Coming soon: Terabit hard disk drives. IEEE Spectrum, February 2003, vol. 40, pp.19–21.
[6] 戴道生等. 《铁磁学》上册. 科学出版社, 1987, 第一版.
[7] W.F. Brown. Theory of the approach to magnetic saturation. Physical Review, 1940, vol. 48, p.736.
[8] W.F. Brown. Micromagnetics. Interscience, New York, 1963.
[9] W.F. Brown. Magnetostatic principles in ferromagnetism. Interscience, New York, 1962.
[10] Werner Scholz, Josef Fidler, Thomas Schre?, et al. Scalable parallel micromagnetic solvers formagnetic nanostructures. Computational Materials Science, 2003, vol. 28, p. 366.
[11] M. Donahue and D. Porter. Object oriented micromagnetic framework (oommf) home page.Available from http://math.nist.gov/oommf/, October 2002.
[12] M.R. Scheinfein. LLG(Landau-Lifshitz-Gilbert) micromagnetics simulator home page. Avail-able from http://llgmicro.home.mindspring.com/, 2003.
[13] M. Schneider and H. Hoffman. Magnetization loops of submicron ferromagnetic permalloy dotarrays. Journal of Applied Physics, 1999, vol. 86, p. 4539.
[14] M. Grimsditch, Y. Jaccard, and I.K. Schuller. Magnetic anisotropies in dot arrays: Shapeanisotropy versus coupling. Physical Review B, 1998, vol. 58, p. 11539.
[15] K. Runge, Y. Nozaki, Y. Otani, H. Miyajima, B. Pannetier, T. Matsuda, and A. Tonomura. High-resolution observation of magnetization processes in 2μm × 2μm × 0.04μm permalloy particles.Journal of Applied Physics, 1996, vol. 79, p. 5075.
[16] D. K. Koltsov, R. P. Cowburn, and M. E. Welland. Micromagnetics of ferromagnetic equilateraltriangular prisms. Journal of Applied Physics, 2000, vol. 88, p. 5315.
[17] C.A.F. Vaz, M. Kla¨ui, J.A.C. Bland, L.J. Heyderman, C. David, and F. Nolting. Fundamentalmagnetic states of disk and ring elements. Journal of Magnetism and Magnetic Materials, 2006,vol. ?, p. unpublished.
[18] Thomas Uhlig, M. Rahm, Christian Dietrich, Rainer Ho¨llinger, Martin Heumann, Dieter Weiss,and Josef Zweck. Shifting and pinning of a magnetic vortex core in a permalloy dot by a magneticfield. Physical Review Letters, December 2005, vol. 95, p. 237205.
[19] T.R. Koehler. Hybrid FEM-BEM method for fast micromagnetic calculations. Physa B: Con-dense Matter, 1997, vol. 233(4), pp. 302–307.
[20] Dennis A. Lindholm. Three-dimensional magnetostatic fields from point-matched integral equa-tions with linearly varying scalar source. IEEE Transactions on Magnetic, 1984, vol. 20(5), pp.2025–2032.
[21] S. Benson, L.C. McInnes, J.J. More′, and J. Sarich. TAO home page. Available from http://www-unix.mcs.anl.gov/tao/, 2001.
[22] Peter Brown, Aaron Collier, Keith Grant, Alan Hindmarsh, Steven Lee, Radu Serban, and CarolWoodward. SUNDIALS home page. Available from http://www.llnl.gov/CASC/sundials/, 2002.
[23] G. Karypis. METIS home page. Available from http://www-users.cs.umn.edu/ karypis/metis/,2002.
[24] MPICH. home page. Available from http://www-unix.mcs.anl.gov/mpi/mpich/, 2003.
[25] S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M. Knepley, L.C. McInnes, B.F. Smith, andH. Zhang. PETSc home page. Available from http://www.mcs.anl.gov/petsc/, 2001.
[26] K. Yu. Guslienko and V. Novosad. Magnetization reversal due to vortex nucleation, displacement,and annihilation in submicron ferromagnetic dot arrays. Physical Review B, 2001, vol. 65, p.024414.
[27] T. Shinjo, T. Okuno, et al. Magnetic vortex core observation in circular dots of permalloy. Sci-ence, August 2000, vol. 298, p. 930.
[28] Taras Pokhil, Dian Song, and Janusz Nowak. Spin vortex states and hysteretic properties ofsubmicron size nife elements. Journal of Applied Physics, May 2000, vol. 87(9), pp. 6319–6321.
[29] M. Rahm, M. Schneider, J. Biberger, R. Pulwey, J. Zweck, and D. Weiss. Vortex nucleation insubmicrometer ferromagnetic disks. Applied Physics Letters, June 2003, vol. 82(23), p. 4110.
[30] Jonathan Kin Ha, Riccardo Hertel, and J. Kirschner. Micromagnetic study of magnetic configu-rations in submicron permalloy disks. Physical Review B, June 2003, vol. 67(1), p. 224432.
[31] Jonathan Kin Ha, Riccardo Hertel, and J. Kirschner. Configurational stability and magnetiza-tion processes in submicron permalloy disks. Physical Review B, February 2003, vol. 67(1), p.064418.
[32] M. Schneider, H. Hoffmann, S. Otto, Th. Haug, and J. Zweck. Stability of magnetic vorticesin ?at submicron permalloy cylinders. Journal of Applied Physics, August 2002, vol. 92(3), p.1466.
[33] M. Rahm and J. Biberger. Vortex pinning at individual defects in magnetic nanodisks. Journalof Applied Physics, May 2003, vol. 93(10), p. 7429.
[34] M. Rahm, J. Stahl, and D. Weiss. Programmable logic elements based on ferromagnetic nan-odisks containing two antidots. Applied Physics Letters, 2005, vol. 87(18), p. 182107.
[35] M. Rahm, J. Stahl, W. Wegscheider, and D. Weiss. Multistable switching due to magnetic vorticespinned at artificial pinning sites. Applied Physics Letters, June 2004, vol. 85(9), p. 1553.
[36] J. Rothman, M. Kla¨ui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, andR. Speaks. Observation of a bi-domain state and nucleation free switching in mesoscopic ringmagnets. Physical Review B, February 2001, vol. 86(6), p. 1098.
[37] M. Rahm and R. Ho¨llinger. In?uence of point defects on magnetic vortex structures. Journal ofApplied Physics, June 2004, vol. 95(11), p. 6708.
[38] R. Ribo′, M.A. de Riera Pasenau, and E. Escolano. GiD home page, international center fornumerical methods in engineering (CIMNE). Available from http://gid.cimne.upc.es, 2002.
[39] R. Hertel and J. Kirschner. Resonant modes of vortex structures in soft-magnetic nanodiscs.Journal of Magnetism and Magnetic Materials, 2004, vol. 272-276, pp. 655–656.