A magnetoresistive read head is capable of reading cross-track magnetizations in a magnetic recording disk drive that has the magnetized regions or magnetizations in the magnetic recording layer of the disk oriented in the cross-track direction. The magnetic recording disk has the magnetizations in the concentric data tracks oriented in the radial or cross-track direction. The read head has its free-layer magnetization direction perpendicular to the disk surface and its pinned-layer magnetization direction parallel to the disk surface and orthogonal to the free-layer magnetization direction. The read head may have magnetic side shields spaced from it in the cross-track direction to prevent magnetic flux from adjacent data tracks from reaching the read head.