reader with the MF potential, we first review its appearance in spin 1/2 SOI systems without any additional discrete degrees of freedom. The Hamiltonian for a homogenous 2DEG with SOI and an electric field $E_x$ in the $x$ direction can be generically written as $$H = \frac{p^2}{2m} + \vec{B}(\vec{k})\cdot\vec{\sigma} + E_x x$$ where the $\vec{B}(\vec{k})$ represents a momentum dependent spin orbit interaction. We define a unitary transformation $U(\vec{k})$ which diagonalizes $\vec{B}.\vec{\sigma}$ in spin space so that after the unitary transformation, we have $$UHU^\dagger = \frac{p^2}{2m} + |\vec{B}|\sigma_z + E_x (x - i U \partial_{k_x} U^\dagger).$$

Mathematically, the effect of $U$ can be interpreted as rotating the spin space coordinates so that in the rotated frame, the spin $z$ axis points in the direction of the SOI field $\vec{B}(\vec{k})$. The non commutation between $x$ and the momentum dependent $U$ results in the appearance of the $-i E_x (U \partial_{k_x} U^\dagger)$ term which acts as an effective magnetization $M'_i \tilde{\sigma}_i$ in the rotated frame where the tilde on the $\tilde{\sigma}_i$ indicates that the index $i$ refers to the $i$th spin direction in the rotated frame. To determine what *lab* frame direction this effective magnetization points in, we perform the inverse unitary transformation 