 Electric-field coupling to nematic order

The leading scalar coupling of an electric field to the nematic order parameter is quadratic in the field and linear in the tensor. For uniaxial nematic order, it is $-3\chi \lambda E^2({\cos }^2\vartheta -1/3)/2$. When $\chi \lambda >0$, minimization aligns the nematic director with the field axis and adds $-\chi E^2\lambda$ to the scalar Landau free energy.