In ferromagnetic or antiferromagnetic material a vortex can be moved to generate bits for information storage and recognition, corresponding, e.g., to changes of the quantum number n. But although the magnetization has the usual azimuthal direction, and although one has vorticity quantization as in superfluids, as long as the circular integration lines surround the central axis at far enough perpendicular distance, this apparent vortex magnetization will change with the distance from an azimuthal direction to an upward or downward one, as soon as the vortex center is approached.