Theory of Magnetic Field Induced Spin Density Wave in High Temperature Superconductors

The induction of spin density wave (SDW) and charge density wave (CDW) orderings in the mixed state of high $T_c$ superconductors (HTS) is investigated by using the self-consistent Bogoliubov-de Gennes equations based upon an effective model Hamiltonian with competing SDW and d-wave superconductivity interactions. The modulation of the induced SDW is determined by the vortex lattice and it oscillates with the same wave length in x and y directions, and the associated CDW has a period just half that of the SDW along y-direction and is quasi-one dimensional like. From the calculation of the local density of states, we found that the majority of the quasi-particles inside the vortex core are localized. All these results are in good agreement with several recent experiments on HTS.