Microscopic theory of spin toroidization in periodic crystals

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...

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Bibliographic Details
Published in:Physical review. B 2018-04, Vol.97 (13), Article 134423
Main Authors: Gao, Yang, Vanderbilt, David, Xiao, Di
Format: Article
Language:English
Subjects:
Electron spin
Insulators
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Summary: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.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.97.134423