Hi Jens,
That's something I think.  I'm having fun contemplating magnetism in blades for a couple of reasons:
1. It exists.
2.  It exists in folded blades,
3.  It exists in tempered blades.
1. is self-evident (and I'm enjoying reading these accounts).  As for 2., well, if a sheet of magnetized steel is folded over itself, doesn't it cancel out?  What about if it's folded over itself a bunch of times?  3., What happens to magnetization when a blade is differentially heat treated?  Since the crystal structure is getting deformed, I'm still puzzling out whether this would affect a magnetic field.  Basically, I don't see a straight route from magnetite to a blade without remagnetizing the blade after it's manufactured.
Balanced against all this skepticism are the observations people are reporting here.  Perhaps there's a way for a hunk of magnetite to retain its magnetism after it's been folded, tempered, heat treated (and possibly alloyed).  Personally, I think the magnetic field came later.  As Nechesh points out, it's quite easy to do.  As to where those asymmetric fields up and down blades came from, I think that an experiment with some magnets and a  non-magnetized sword are in order  
 
Fearn (not Fern, thanks!)