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We study magnetoelectric (magneto-current) effects in a diamond structureunder antiferro quadrupole (AFQ) orders. The AFQ orders break the spacialinversion symmetry and cause the current-induced magnetization. Thecurrent-induced magnetization strongly depends on the types of the orderparameters and the direction of the current. This gives a way to theexperimental identification of AFQ order parameters. We also discuss thecurrent-induced magnetization under the AFQ orders in the diamond structure canbe intuitively understood in terms of charge-imbalanced solenoids.

Magnetoelectric Effects and Charge-Imbalanced Solenoids: Antiferro Quadrupole Orders in a Diamond Structure