Extended Data Fig. 11: Effect of spin Berry phase.
From: Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet

a, The spin Berry phase Ωijk is equal to half the solid angle formed by spins Si, Sj and Sk. b, An electron hopping in the chiral spin background is equivalent to hopping in the presence of a gauge flux Ω. c, Band structures in the presence of both λand chiral flux Ω, when the magnetic field and the magnetization are along the x–y plane (Mab) and the z direction (Mc).