Cauchy-Born rule and spin density wave for the spin-polarized Thomas-Fermi-Dirac-von Weizsacker model

The electronic structure (electron charges and spins) of a perfect crystal under external magnetic field is analyzed using the spin-polarized Thomas-Fermi-Dirac-von Weizsacker model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density wave and spin density wave. A Landau-Lifschitz type micromagnetic energy functional is derived.