Validity of the force theorem for magnetocrystalline anisotropy

Xindong Wang*, Ding Sheng Wang, Wu Ruqian, A. J. Freeman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


The validity of the so-called force theorem is critical for the computational/theoretical determination of the magnetocrystalline anisotropy (MCA) in the framework of local density theory. This theorem states that the spin-orbit coupling induced MCA energy is given by the difference in the fully relativistic band energies between two magnetization directions calculated with the same self-consistent scalar-relativistic potential. We show that the charge-and spin-density variations caused by spin-orbit coupling vanish to first order in the spin-orbit coupling strength. By the stationary property of the total energy functional, we establish rigorously the validity of the force theorem for surface/interface MCA. We show that our arguments also apply to a variant of the MCA force theorem and discuss problems of applying the force theorem for MCA in bulk systems with cubic crystalline symmetry.

Original languageEnglish (US)
Pages (from-to)337-341
Number of pages5
JournalJournal of Magnetism and Magnetic Materials
Issue number3
StatePublished - Jul 1996

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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