  Motivated by emergent $SU(2)$ symmetry in the spin orbit coupled system, we
study the spin helix driven insulating phase in two dimensional lattice. When
both Rashba and Dresselhaus spin orbit couplings are present, the perfect Fermi
surface nesting occurs at a special condition depending on the lattice
geometry. In this case, the energies of spin up at any wave vector $\vec{k}$
are equivalent to the ones of spin down at $\vec{k}\!+\!\vec{Q}$ with so-called
the \textit{shifting wave vector} $\vec{Q}$. Thus, the system stabilizes
magnetic insulator with spiral like magnetic ordering even in the presence of
tiny electron-electron interaction where the magnetic ordering wave vector is
proportional to $\vec{Q}$. We first show the condition for existence of the
\textit{shifting wave vector} in general lattice model and emergent $SU(2)$
symmetry in the spin orbit coupled system. Then, we exemplify this in square
lattice at half filling and discuss the insulating phase with (non-) coplanar
spin density wave and charge order. Our study emphasizes possible new types of
two dimensional magnetic materials and can be applicable to various van-der
Waals materials and their heterostructures with the control of electric field,
strain and pressure.
