  Stimulated by recent studies of quantum phases with broken local inversion
symmetry, we study the magnetoelectric effect in locally noncentrosymmetric
metals. We consider three-dimensional (3D) coupled zigzag chains and
demonstrate that the antiferromagnetic moment is induced by the electric
current through a staggered antisymmetric spin-orbit coupling. This
current-induced magnetism is much larger than that in globally
noncentrosymmetric metals. We provide an intuitive understanding of the
current-induced antiferromagnetic moment by showing the inverse magnetoelectric
effect, that is, the ferroic p-wave charge nematic order accompanied by the
asymmetric band structure in the antiferromagnetic state. We also examine
conduction electrons coupled to localized spins via Kondo exchange coupling and
demonstrate a significant enhancement of the magnetoelectric effect. A possible
experimental observation of the magnetoelectric effect in metals is discussed,
with focus on LnM_2Al_10 compounds, such as NdRu_Al_10 and TbRu_2Al_10.
