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Toroidal order, given by a composite of electric and magnetic orders, manifests itself not only in unusual magnetism but also in anomalous transport and magnetoelectric effects. We report our theoretical results on the influence and stability of toroidal order in metals on the basis of a microscopic model. We consider an effective single-band Hubbard-type model with a site-dependent antisymmetric spin-orbit coupling, which is derived from a four-band tight-binding model including atomic spin-orbit coupling, off-site hybridization between orbitals with different parities, and an odd-parity crystalline electric field. For this single-band model on a layered honeycomb lattice, we investigate the electronic structure, magnetotransport, and magnetoelectric effect in a toroidal ordered state with a vortexlike magnetic structure. The ferroic order of the microscopic toroidal moments acts as an effective gauge field for electrons, which …