Skyrmions in Magnetic Materials by Shinichiro Seki & Masahito Mochizuki

Author:Shinichiro Seki & Masahito Mochizuki
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.1)

where the Pauli matrix denotes the conduction-electron spin and the unit vector represents the direction of local magnetisation. The magnetisation vector is given in polar coordinates as

(3.2)

Here, a quantisation axis is selected to be parallel to the z axis. When a ferromagnetic (anti-ferromagnetic) coupling J sd or the Hund’s rule coupling J H is sufficiently strong, the conduction-electron spin always points parallel (anti-parallel) to localised magnetisation as it flows and follows the spatial and temporal variations of . On the basis of this assumption, we rotate the local quantisation axis from the fixed axis to the axis parallel to at a given by introducing

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