We report magnetoresistance data in magnetic semiconductor multilayers, which exhibit a clear step-wise behavior as a function of external field. We attribute this highly non-trivial step-wise behavior to next-nearest-neighbor interlayer exchange coupling. Our microscopic calculation suggests that this next-nearest-neighbor coupling can be as large as 24% of the nearest-neighbor coupling. It is argued that such unusually long-range interaction is made possible by the quasi-one-dimensional nature of the system and by the long Fermi wavelength characteristic of magnetic semiconductors.
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