content_image/299762.jpg content_image/299763.jpg content_image/299764.jpg content_image/299761.jpg content_image/299760.jpg
Therefore, if the spin-orbit interaction is treated perturbatively, the wave func- tions ψ$_{d}$ ( − → r − − → R$_{j,m}$ )(cos θ$_{j,m}$ | ↑〉 + e $^{iφ}$sin θ$_{j,m}$ | ↓〉 ) in eqs. (10) will be replaced by 

<img src='content_image/299762.jpg'>

<img src='content_image/299763.jpg'>

<img src='content_image/299764.jpg'>

<img src='content_image/299761.jpg'>

where Δ E$_{cf}$ is the energy difference between cos β | xy 〉 ∓ sin β | x 2 − y $^{2}$〉 in (2) and sin β | xy 〉 ± cos β | x 2 − y $^{2}$〉 . Substituting (13) into eqs. (10), we found that the polarization per unit cell is 

<img src='content_image/299760.jpg'>

