  We use a real-space recursion method to calculate the local density of states
(LDOS) within a model that contains both d-wave superconducting and
antiferromagnetic order. We focus on the LDOS in the superconducting phase near
single vortices with either normal or antiferromagnetic cores. Furthermore, we
study the low-energy quasiparticle structure when magnetic vortices operate as
pinning centers for surrounding unidirectional spin density waves (stripes). We
calculate the Fourier transformed LDOS and show how the energy dependence of
relevant Fourier components can be used to determine the nature of the magnetic
field-induced order, and predict field-induced LDOS features that can be tested
by future scanning tunneling microscopy (STM) experiments.
