Scattering-Free Nature of Intrinsic Anomalous Hall Current

  • Yuki ShiomiEmail author
Part of the Springer Theses book series (Springer Theses)


First, we investigate the intrinsic AHE which is related with Berry-phase. In contrast to the extrinsic mechanisms, an intrinsic AHE induced by the Berry phase is, in principle, not affected by the scattering. Experimentally, the relation that \(\rho _{yx} \propto \rho _{xx}^{\ 2}\) (namely, Hall conductivity \(\sigma _{xy} = \rho _{yx}/\rho _{xx}^{\ 2}\) is independent of \(\rho _{xx}\)) is identified in some materials and is thought to be the evidence of the dissipationless nature of anomalous Hall current (C. Kooi, Phys. Rev. 95, 843 (1954), W-L. Lee, S. Watauchi, V.L. Miller, R.J. Cava, and N.P. Ong, Science 303, 1647 (2004)). Nevertheless, the same \(\rho _{xx}\) dependence of \(\rho _{yx}\) is also expected for the side jump mechanism. In addition, the Hall conductivity may show the nontrivial \(T\)- or doping-dependence because of its high sensitivity to the position of the chemical potential in the electronic band structure. Another way to examine the origin and nature of the AHE is thus highly desired. Here, we take the approach to this problem in terms of the comparative study on the charge and heat anomalous Hall currents. Since the Lorenz ratio for the anomalous Hall current (\(L_{xy}^{A}\)) is sensitive to the inelastic scattering, the scattering-free (dissipationless) nature of the intrinsic anomalous Hall current manifests in the temperature dependence of \(L_{xy}^{A}\). Moreover, we investigate in the second section to what extent the scattering-free nature is robust against the scattering strength by changing the doping concentration in Ni, Fe, or Co.


Anomalous Hall effect Berry phase of electrons Spin-orbit interaction Dissipationless electronic current Itinerant ferromagnet 


  1. 1.
    T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. Nagaosa, Y. Tokura, Phys. Rev. Lett. 99, 086602 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Onose, Y. Shiomi, Y. Tokura, Phys. Rev. Lett. 100, 016601 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Zhang, N.P. Ong, Z.A. Xu, K. Krishana, R. Gagnon, L. Taillefer, Phys. Rev. Lett. 84, 2219 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    S. Onoda, N. Sugimoto, N. Nagaosa, Phys. Rev. Lett. 97, 126602 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    S. Onoda, N. Sugimoto, N. Nagaosa, Phy. Rev. B 77, 165103 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Shiomi, Y. Onose, Y. Tokura, Phys. Rev. B 81, 054414 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    D.A. Goodings, Phys. Rev. 132, 542 (1963), and references thereinGoogle Scholar
  8. 8.
    J.M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, 1972)Google Scholar
  9. 9.
    C. Strohm, G.L.J.A. Rikken, P. Wyder, Phys. Rev. Lett. 95, 155901 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, Y. Tokura, Science 329, 297 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, Y. Tokura, Phys. Rev. B 85, 134411 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    A.H. Wilson, Theory of Metals (University Press, Cambridge, 1965)Google Scholar
  13. 13.
    N.F. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover, New York, 1958)Google Scholar
  14. 14.
    Y. Yao, L. Kleinman, A.H. MacDonald, J. Sinova, T. Jungwirth, D.-S. Wang, E. Wang, Q. Niu, Phys. Rev. Lett. 92, 037204 (2003)ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Department of Applied Physics, Faculty of EngineeringThe University of TokyoTokyoJapan

Personalised recommendations