Field induced d_x^2-y^2+id_xy state in d-density-wave metals

We argue that the d_{xy} component of the order parameter can be generated to form the d_x^2-y^2+id_xy-density wave state by the external magnetic field. The driving force for this transition is the coupling of the magnetic field with the orbital magnetism. The fully gapped particle spectrum and the magnetically active collective mode of the condensate are discussed as a possible signature of the d+id’ density wave state.