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