Microscopic theory of spin toroidization in periodic crystals

Yang Gao, David Vanderbilt, Di Xiao

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Using the semiclassical theory of electron dynamics, we derive a gauge-invariant expression for the spin toroidization in a periodical crystal. We show that the spin toroidization is comprised of two contributions: One is due to the configuration of a classical spin array, while the other comes from the coordinate shift of the electron as spin carrier in response to the inhomogeneous magnetic field. We then establish a direct and elegant relation between our spin toroidization and the antisymmetric magnetoelectric polarizability in insulators. Finally, we demonstrate our spin toroidization in a tight-binding model and show that it is a genuine bulk quantity.

Original languageEnglish (US)
Article number134423
JournalPhysical Review B
Issue number13
StatePublished - Apr 23 2018

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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