Journal of Magnetics

The Korean Magnetics Society (한국자기학회)
권호 표지
DOI QR코드

DOI QR Code

Hysteresis Loops, Critical Fields and Energy Products for Exchange-spring Hard/soft/hard Trilayers

  • Chen, B.Z. (Traffic and Transportation School, Dalian Jiaotong University) ;
  • Yan, S. (Traffic and Transportation School, Dalian Jiaotong University) ;
  • Ju, Y.Z. (Traffic and Transportation School, Dalian Jiaotong University) ;
  • Zhao, G.P. (College of Physics and Electronic Engineering, Sichuan Normal University) ;
  • Zhang, X.C. (College of Physics and Electronic Engineering, Sichuan Normal University) ;
  • Yue, M. (College of Materials Science and Engineering, Beijing University of Technology) ;
  • Xia, J. (College of Physics and Electronic Engineering, Sichuan Normal University)
  • Received : 2014.04.01
  • Accepted : 2015.03.10
  • Published : 2015.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by a three-dimensional (3D) model for exchange-coupled Sm-Co/${\alpha}-Fe$/Sm-Co trilayers with in-plane collinear easy axes. These results are carefully compared with the popular one-dimensional (1D) micromagnetic models and recent experimental data. It is found that the results obtained from the two methods match very well, especially for the remanence and coercivity, justifying the calculations. Both nucleation and coercive fields decrease monotonically as the soft layer thickness $L^s$ increases while the largest maximum energy product (roughly 50 MGOe) occurs when the thicknesses of hard and soft layers are 5 nm and 15 nm, respectively. Moreover, the calculated angular distributions in the thickness direction for the magnetic moments are similar. Nevertheless, the calculated nucleation and pinning fields as well as the energy products by 3D OOMMF are systematically smaller than those given by the 1D model, due mainly to the stray fields at the corners of the films. These demagnetization fields help the magnetic moments at the corners to deviate from the previous saturation state and facilitate the nucleation. Such an effect enhances as $L^s$ increases. When the thicknesses of hard and soft layers are 10 nm and 20 nm, respectively, the pinning field difference is as large as 30%, while the nucleation fields have opposite signs.

Keywords

References

  1. E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). https://doi.org/10.1109/20.102931
  2. E. E. Fullerton, J. S. Jiang, M. Grimsditch, C. H. Sowers, and S. D. Bader, Phys. Rev. B 58, 12193 (1998). https://doi.org/10.1103/PhysRevB.58.12193
  3. M. Shindo, M. Ishizone, A. Sakuma, H. Kato, and T. Miyazaki, J. Appl. Phys. 81, 4444 (1997). https://doi.org/10.1063/1.364970
  4. R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993). https://doi.org/10.1103/PhysRevB.48.15812
  5. S. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser, Science 287 1989 (2000). https://doi.org/10.1126/science.287.5460.1989
  6. H. Zeng, J. Li, J. P. Liu, Z. L. Wang, and S. Sun, Nature 420 395 (2002). https://doi.org/10.1038/nature01208
  7. D. J. Sellmyer, Nature 420, 374 (2002). https://doi.org/10.1038/420374a
  8. B. Balasubramanian, R. Skomski, X.-Zh. Li, Sh. R. Valloppilly, J. E. Shield, G. C. Hadjipanayis, and D. J. Sellmyer, Nano Lett. 11, 1747 (2011). https://doi.org/10.1021/nl200311w
  9. W. B. Cui, Y. K. Takahashi, and K. Hono, Adv. Mater. 24, 6530 (2012). https://doi.org/10.1002/adma.201202328
  10. G. P. Zhao and X. L. Wang, Phys. Rev. B 74, 012409 (2006). https://doi.org/10.1103/PhysRevB.74.012409
  11. J. Xia, G. P. Zhao, H. W. Zhang, Z. H. Cheng, Y. P. Feng, J. Ding, and H. T. Yang, J. Appl. Phys. 112, 013918 (2012). https://doi.org/10.1063/1.4736438
  12. E. Goto, N. Hayashi, T. Miyashita, and K. Nakagava, J. Appl. Phys. 36, 2951 (1965). https://doi.org/10.1063/1.1714613
  13. T. Leineweber and H. Kronmuller, J. Magn. Magn. Mater. 176, 145 (1997). https://doi.org/10.1016/S0304-8853(97)00601-X
  14. E. E. Fullerton, J. S. Jiang, and S. D. Bader, J. Magn. Magn. Mater. 200, 392 (1999). https://doi.org/10.1016/S0304-8853(99)00376-5
  15. G. Asti, M. Solzi, M. Ghidini, and F. M. Neri, Phys. Rev. B 69, 174401 (2004). https://doi.org/10.1103/PhysRevB.69.174401
  16. R. Pellicelli, M. Solzi, C. Pernechele, and M. Ghidini, Phys. Rev. B 83, 054434 (2011). https://doi.org/10.1103/PhysRevB.83.054434
  17. R. Pellicelli, M. Solzi, V. Neu, K. Hafner, C. Pernechele, and A. M. Ghidini, Phys. Rev. B 81, 184430 (2010). https://doi.org/10.1103/PhysRevB.81.184430
  18. G. P. Zhao, M. G. Zhao, H. S. Lim, Y. P. Feng, and C. K. Ong, Appl. Phys. Lett. 87, 162513 (2005). https://doi.org/10.1063/1.2108120
  19. I. A. Al-Omari and D. J. Sellmyer, Phys. Rev. B 52, 3441 (1995). https://doi.org/10.1103/PhysRevB.52.3441
  20. Z. H. Cheng, J. X. Zhang, and H. Kronmuller, Phys. Rev. B 68, 144417 (2003). https://doi.org/10.1103/PhysRevB.68.144417
  21. V. Neu, K. Hafner, A. K. Patra, and L. Schultz, J. Phys. D: Appl. Phys. 39, 5116 (2006). https://doi.org/10.1088/0022-3727/39/24/003
  22. X. B. Liu and Z. Altounian, J. Appl. Phys. 111, 07B526 (2012). https://doi.org/10.1063/1.3677656
  23. Y. Choi, J. S. Jiang, J. E. Pearson, S. D. Bader, J. J. Kavich, J. W. Freeland, and J. P. Liu, Appl. Phys. Lett. 91, 072509 (2007). https://doi.org/10.1063/1.2769755
  24. S. Sawatzki, R. Heller, C. Mickel, M. Seifert, L. Schultz, and V. Neu, J. Appl. Phys. 109, 123922 (2011). https://doi.org/10.1063/1.3596756
  25. M. J. Donahue and D. G. Porter, OOMMF user's guide, version 1.0. NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD (1999).
  26. W. F. Brown, Jr., Rev. Mod. Phys. 17, 15 (1945). https://doi.org/10.1103/RevModPhys.17.15
  27. W. F. Brown, Micromagnetics (Interscience Publishers, New York, 1963).
  28. Y. Deng, G. P. Zhao, and H. W. Zhang, J. Magn. Magn. Mater 323, 535-538 (2011). https://doi.org/10.1016/j.jmmm.2010.10.005
  29. G. Asti, M. Ghidini, R. Pellicelli, C. Pernechele, and M. Solzi, Phys. Rev. B 73, 094406 (2006). https://doi.org/10.1103/PhysRevB.73.094406
  30. E. C. Stoner and E. P. Wohlfarth, Phil. Trans. R. Soc. 240, 599 (1948). https://doi.org/10.1098/rsta.1948.0007