  We have developed a method to systematically compute the form of Rashba- and
Dresselhaus-like contributions to the spin Hamiltonian of heterostructures to
an arbitrary order in the wavevector k. This is achieved by using the double
group representations to construct general symmetry-allowed Hamiltonians with
full spin-orbit effects within the tight-binding formalism. We have computed
full-zone spin Hamiltonians for [001]-, [110]- and [111]-grown zinc blende
heterostructures (D_{2d},C_{4v},C_{2v},C_{3v} point group symmetries), which
are commonly used in spintronics. After an expansion of the Hamiltonian up to
third order in k, we are able to obtain additional terms not found previously.
The present method also provides the matrix elements for bulk zinc blendes
(T_d) in the anion/cation and effective bond orbital model (EBOM) basis sets
with full spin-orbit effects.
