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The d-wave vortex lattice state is studied within the framework ofBogoliubov-de Gennes (BdG) mean field theory. We allow antiferromagnetic (AFM)order to develop self-consistently along with d-wave singlet superconducting(dSC) order in response to an external magnetic field that generates vortices.The resulting AFM order has strong peaks at the vortex centers, and changessign, creating domain walls along lines where $\nabla \times j_s \approx 0$.The length scale for decay of this AFM order is found to be much larger thanthe bare d-wave coherence length, $\xi$. Coexistence of dSC and AFM order inthis system is shown to induce $\pi$-triplet superconducting order. Competitionbetween different orders is found to suppress the local density of states atthe vortex center and comparison to recent experimental findings is discussed.Comment: 10 pages, 7 figure

Competition of superconductivity and antiferromagnetism in ad-wave vortex lattice