The invention uses an upper and lower magnetic layer of a laminated magnetic layer structure that includes an AF spacer layer that results in weak antiferromagnetic coupling of the magnetic layers that is insufficient to cause either of the layers to switch so that the magnetic orientations of the two ferromagnetic layers remain parallel. An advantage of the invention is that the AF-coupling tends to anti-correlate the noise in the two layers. The weak AF coupling according to the invention is believed to act at the transition boundaries in the media to cause some of the noise domains to be oriented antiparallel and the noise to be less correlated than would be the case without the AF coupling and thereby to achieve improved SNR.