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Magneto-Electric Effect in Three-dimensional Coupled Zigzag Chains

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.