*6.3. Berry Curvatures*

Finally, we calculate the Berry curvature, <sup>Π</sup>−*n*<sup>ˆ</sup>(*<sup>α</sup>*R, *<sup>α</sup>*D) for the spin in the state |−*n*<sup>ˆ</sup> as shown in the left of Figure 6. Obviously, the Berry curvature becomes large at around (*<sup>α</sup>*R, *<sup>α</sup>*D)=( *π*2 , <sup>0</sup>),(0, *π*2 ). The other spin state is not much pumped as shown in the right of Figure 6.

**Figure 6.** (**Left**) Contour plot of the Berry curvature for |−*n*<sup>ˆ</sup> with *β* = *π*/5 and *ν* = *π*/2. We set *φ* = *π*/3,  *k* = <sup>−</sup>*j*, *J*0*b* = *Jb*1 = *J*<sup>0</sup>*c* = *Jc*1 = *j* and 0 = 1 =  *b* =  *c* = 0.9*j*. (**Right**) Berry curvatures for two spin directions with *α*D = 0.1 with the same parameter with the left panel.
