We study theoretically the resistance at the interface between the two planar systems with different lattice constants a and b. The resistance and the effect of the magnetic field depends sensitively on the ratio a/b. The size of the enlarged unit cell λ=nAa=nBb (nA, nB: integers) is the crucial quantity, and the magnetic flux penetrating this enlarged unit cell determines the oscillation of the resistance. Therefore, the magnetoresistance is very much enhanced at (nearly) incommensurate relation between a and b.
@article{arxiv.1302.7108,
title = {Theory of giant magnetoresistance at misfit interfaces},
author = {Daichi Asahi and Naoto Nagaosa},
journal= {arXiv preprint arXiv:1302.7108},
year = {2013}
}