  Toroidal order, given by a composite of electric and magnetic orders,
manifests itself not only in the peculiar magnetism but also in anomalous
transport and magnetoelectric effect. We report our theoretical results on the
influence and stability of a 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 the atomic spin-orbit coupling,
off-site hybridizations between orbitals with different parities, and
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 the toroidal ordered state with a vortex-like
magnetic structure. The ferroic order of the microscopic toroidal moments acts
as an effective gauge field for electrons, which modulates the electronic band
structure with a shift of the band bottom in the momentum space. In addition,
the site-dependent antisymmetric spin-orbit coupling gives rise to highly
anisotropic Hall responses. The most salient feature is two different types of
magnetoelectric responses: one is a magnetic order with net toroidal
magnetization induced by an electric current perpendicular to the planes, and
the other is a uniform transverse magnetization induced by an electric current
within the planes. We examine the ground state of the effective model by the
mean-field approximation, and show that the toroidal order is stabilized by
strong electron correlations at low electron density. We also discuss the
temperature dependence of the magnetoelectric effects associated with
spontaneous toroidal ordering. Implications to experiments are also presented.
