Skip to main content
SpringerLink
Log in

Influence of normal and shear strain on magnetic anisotropy energy of hcp cobalt: An ab initio study

  • Articles
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The magnetic anisotropy energy (MAE) of the bulk hcp Co under mechanical deformation is calculated by ab initio density functional theory (DFT) calculations based on the projector augmented wave method. We present a thorough investigation with respect to the choice of exchange-correlation functionals. The generalized gradient approximation (GGA) succeeds in predicting the easy axis of magnetization but underestimates the MAE in comparison to the experimental value, whereas the local density approximation gives a wrong magnetic easy axis. The DFT+ U method offers an alternative to increase the MAE value. Unfortunately, as the MAE reaches the experimental value, strong distortions of the lattice parameters are observed. Our results with GGA suggest that a simultaneous reduction of the c/a ratio and increase of the lateral lattice parameter a will strongly enhance the MAE of the material, as observed experimentally. We also found that the MAE in hcp Co is reduced by shear strain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Table I
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. D. Weller and A. Moser: Thermal effect limits in ultrahigh-density magnetic recording. IEEE Trans. Magn. 35, 4423 (1999).

    Article  CAS  Google Scholar 

  2. C.H. Lee, H. He, F.J. Lamelas, W. Vavra, C. Uher, and R. Clarke: Magnetic anisotropy in epitaxial Co superlattices. Phys. Rev. B 42, 1066 (1990).

    Article  CAS  Google Scholar 

  3. N. Inaba, A. Nakamura, T. Yamamoto, Y. Hosoe, and M. Futamoto: Magnetic and crystallographic properties of CoCrPt thin films formed on Cr–Ti single crystalline under layers. J. Appl. Phys. 79, 5354 (1996).

    Article  CAS  Google Scholar 

  4. M. Futamoto, N. Inaba, A. Nakamura, and Y. Honda: Microstructures and basic magnetic properties of co-based epitaxial magnetic thin films. Acta Mater. 46, 3777 (1998).

    Article  CAS  Google Scholar 

  5. T. Shimatsu, Y. Okazaki, H. Sato, O. Kitakami, S. Okamoto, H. Aoi, H. Muraoka, and Y. Nakamura: Large uniaxial magnetic anisotropy of Co–Pt perpendicular films induced by lattice deformation. IEEE Trans. Magn. 43, 2995 (2007).

    Article  CAS  Google Scholar 

  6. G. Andersson and B. Hjörvarsson: Effects of strain on magnetic anisotropy in Fe-and Co-based heterostructures. Phase Transitions 81, 679 (2008).

    Article  CAS  Google Scholar 

  7. T. Shimatsu, Y. Okazaki, H. Sato, H. Muraoka, H. Aoi, T. Sakurai, S. Okamoto, O. Kitakami, S. Tanii, and A. Sakuma: Uniaxial magnetic anisotropy in Co and Co–Pt based perpendicular films in relation to lattice deformation. J. Appl. Phys. 103, 07F524 (2008).

    Article  CAS  Google Scholar 

  8. J-J. Wang, T. Sakurai, K. Oikawa, K. Ishida, N. Kikuchi, S. Okamoto, H. Sato, T. Shimatsu, and O. Kitakami: Magnetic anisotropy of epitaxially grown Co and its alloy thin films. J. Phys. Condens. Matter 21, 185008 (2009).

    Article  CAS  Google Scholar 

  9. D.M. Paige, B. Szpunar, and B.K. Tanner: The magnetocrystalline anisotropy of cobalt. J. Magn. Magn. Mater. 44, 239 (1984).

    Article  CAS  Google Scholar 

  10. G.H.O. Daalderop, P.J. Kelly, and M.F.H. Schuurmans: First-principles calculation of the magnetocrystalline anisotropy energy of iron, cobalt, and nickel. Phys. Rev. B 41, 11919 (1990).

    Article  CAS  Google Scholar 

  11. J. Trygg, B. Johansson, O. Eriksson, and J.M. Wills: Total energy calculation of the magnetocrystalline anisotropy energy in the ferromagnetic 3d metals. Phys. Rev. Lett. 75, 2871 (1995).

    Article  CAS  Google Scholar 

  12. M.S.S. Brooks: Calculated ground state properties of light actinide metals and their compounds. Physica B & C 130, 6 (1985).

    Article  CAS  Google Scholar 

  13. O. Eriksson, M.S.S. Brooks, and B. Johansson: Orbital polarization in narrow-band systems: Application to volume collapses in light lanthanides. Phys. Rev. B 41, R7311 (1990).

    Article  Google Scholar 

  14. S.V. Beiden, W.M. Temmerman, Z. Szotek, G.A. Gehring, G.M. Stocks, Y. Wang, D.M.C. Nicholson, W.A. Shelton, and H. Ebert: Real-space approach to the calculation of magnetocrystalline anisotropy in metals. Phys. Rev. B 57, 14247 (1998).

    Article  CAS  Google Scholar 

  15. M.D. Stiles, S.V. Halilov, R.A. Hyman, and A. Zangwill: Spin-other-orbit interaction and magnetocrystalline anisotropy. Phys. Rev. B 64, 104430 (2001).

    Article  CAS  Google Scholar 

  16. Y. Xie and J.A. Blackman: Magnetocrystalline anisotropy and orbital polarization in ferromagnetic transition metals. Phys. Rev. B 69, 172407 (2004).

    Article  CAS  Google Scholar 

  17. T. Burkert, O. Eriksson, P. James, S.I. Simak, B. Johansson, and L. Nordström: Calculation of uniaxial magnetic anisotropy energy of tetragonal and trigonal Fe, Co, and Ni. Phys. Rev. B 69, 104426 (2004).

    Article  CAS  Google Scholar 

  18. F. Ono and H. Maeta: Determination of lattice parameters in hcp cobalt by using x-ray bond’s method. J. Phys. Colloq. 49, 8 (1988).

    Google Scholar 

  19. G. Kresse and J. Hafner: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).

    Article  CAS  Google Scholar 

  20. G. Kresse and J. Furthmüller: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

    Article  CAS  Google Scholar 

  21. P.E. Blöchl: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

    Article  Google Scholar 

  22. J.P. Perdew and Y. Wang: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244 (1992).

    Article  CAS  Google Scholar 

  23. J.P. Perdew, K. Burke, and M. Ernzerhof: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  CAS  Google Scholar 

  24. H.J. Monkhorst and J.D. Pack: Special points for brillouin-zone integrations. Phys. Rev. B 13, 5188, (1976).

    Article  Google Scholar 

  25. S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, and A.P. Sutton: Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study. Phys. Rev. B 57, 1505 (1998).

    Article  CAS  Google Scholar 

  26. A.E. Mattsson, R. Armiento, P.A. Schultz, and T.R. Mattsson: Nonequivalence of the generalized gradient approximations PBE and PW91. Phys. Rev. B 73, 195123 (2006).

    Article  CAS  Google Scholar 

  27. I. Yang, S.Y. Savrasov, and G. Kotliar: Importance of correlation effects on magnetic anisotropy in Fe and Ni. Phys. Rev. Lett. 87, 216405 (2001).

    Article  CAS  Google Scholar 

  28. R. Wu and A.J. Freeman: Spin–orbit induced magnetic phenomena in bulk metals and their surfaces and interfaces. J. Magn. Magn. Mater. 200, 498 (1999).

    Article  CAS  Google Scholar 

  29. M.M. Steiner, R.C. Albers, and L.J. Sham: Quasiparticle properties of Fe, Co, and Ni. Phys. Rev. B 45, 13272 (1992).

    Article  CAS  Google Scholar 

  30. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671 (1992).

    Article  CAS  Google Scholar 

  31. H.J.F. Jansen: Origin of orbital momentum and magnetic anisotropy in transition metals. J. Appl. Phys. 67, 4555 (1990).

    Article  CAS  Google Scholar 

  32. J. Wang, J-M. Albina, and Y. Umeno. Ab initio calculation of strain effect on the magnetic properties of the thiogermanate [(CH3)4N]2FeGe4S10. J. Phys. Condens. Matter. 24, 245501 (2012).

    Article  CAS  Google Scholar 

  33. M. Cerný, J. Pokluda, M. Šob, M. Friák, and P. Šandera: Ab initio calculations of elastic and magnetic properties of Fe, Co, Ni, and Cr crystals under isotropic deformation. Phys. Rev. B 67, 035116 (2003).

    Article  CAS  Google Scholar 

  34. S. Ogata, Y. Umeno, and M. Kohyama: First-principles approaches to intrinsic strength and deformation of materials: Perfect crystals, nano-structures, surfaces and interfaces. Modell. Simul. Mater. Sci. Eng. 17, 013001 (2009).

    Article  CAS  Google Scholar 

  35. M. Friák, M. Šob, and V. Vitek: Ab initio calculation of phase boundaries in iron along the bcc-fcc transformation path and magnetism of iron overlayers. Phys. Rev. B 63, 052405 (2001).

    Article  CAS  Google Scholar 

  36. T. Shimada, Y. Ishii, and T. Kitamura: Ab initio study of magnetism at iron surfaces under epitaxial in-plane strain. Phys. Rev. B 81, 134420 (2010).

    Article  CAS  Google Scholar 

  37. E.G. Moroni, G. Kresse, J. Hafner, and J. Furthmüller: Ultrasoft pseudopotentials applied to magnetic Fe, Co, and Ni: From atoms to solids. Phys. Rev. B 56, 15629 (1997).

    Article  CAS  Google Scholar 

  38. D. Bagayoko and J. Callaway: Lattice-parameter dependence of ferromagnetism in bcc and fcc iron. Phys. Rev. B 28, 5419 (1983).

    Article  CAS  Google Scholar 

  39. Y. Honda, H. Funamono, S. Hasegawa, T. Kawasaki, F. Kugiya, M. Koizumi, K. Yoshida, and A. Tonomura: Recorded magnetization patterns of highly c-axis oriented Co-Cr film observed by electron holography. J. Phys. Colloq. 49, C8–C1969 (1988).

    Google Scholar 

  40. J.P.C. Bernards, C.P.G. Schrauwen, and S.B. Luitjens: Single-layer and multilayered films for perpendicular recording based on a Co-Cr alloy. Appl. Phys. A 49, 491 (1989).

    Article  Google Scholar 

  41. J. Xu, M. Furukawa, A. Nakamura, and M. Honda: Mechanical demagnetization at head disk interface of perpendicular recording. IEEE Trans. Magn. 45, 893 (2009).

    Article  Google Scholar 

Download references

Acknowledgments

The present work was partly supported by the GMSI (Global Center of Excellence for Mechanical Systems Innovation) program at the University of Tokyo: A GCOE (Global Center of Excellence) program by Ministry of Education, Culture, Sport, Science and Technology (MEXT). J.W. gratefully acknowledges the MEXT scholarship program.

Author information

Authors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan

    Juan Wang, Jan-Michael Albina, Tomio Iwasaki & Yoshitaka Umeno

  2. Department of Mechanical Engineering, The University of Tokyo, Tokyo, 113-8656, Japan

    Juan Wang

  3. Advanced Simulation Department, Hitachi Research Laboratory, Hitachi, Ltd., Hitachinaka, Ibaraki, 312-0034, Japan

    Hiroshi Moriya

Authors
  1. Juan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan-Michael Albina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomio Iwasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroshi Moriya
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yoshitaka Umeno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Albina, JM., Iwasaki, T. et al. Influence of normal and shear strain on magnetic anisotropy energy of hcp cobalt: An ab initio study. Journal of Materials Research 28, 1559–1566 (2013). https://doi.org/10.1557/jmr.2013.149

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2013.149

Search

Navigation