For the field free region, here is an example of using a superconductor to shield modest fields: http://www.sciencedirect.com/science/article/pii/S092145260401083X
The disadvantage here is that one is using a superconductor with a rather low transition temperature. There is work being done in the neutron scattering community to use high temperature superconducting films to do the shielding. There is an alternative technique in which mu-metal is used to try to trap flux from outside fields (the shielding is not as good as with using a superconductor, but it doesn't require cryogens :>). I'm not sure what advantages would be offered by this proposed shield using a FM/SC for these use cases.
Now, there is another neutron scattering measurement which is done called "spin echo" (http://en.wikipedia.org/wiki/Neutron_spin_echo
) in which a polarized neutron interacts with a sample (magnetic or non) and we measure how the precession of the neutron is effected by its interaction with the sample to learn about dynamics in the material. The technique is very sensitive to stray magnetic fields and even cranes moving overhead. The problem is that in the same facility, there are often experiments being run with 11 Tesla magnets--even though the falloff from fringing fields is steep, it is still a problem--so, we have people who have been working on trying to sense and actively cancel those stray fields (it's cheaper than shielding the other instrument)--it sounds to me that this would be the target application of this new shielding technique--if our active cancellation weren't perfect, we could use this to shield the remaining stray fields--but again, what the advantage would be over just using a superconductor or mu metal is not clear. You could also imagine using it when you wanted say for example shield magnetic materials from being detected...
Now, these are static applications--suppose you had a dynamic field (for example in a radio wave), could you shield the magnetic component of the wave? Would there be any use in doing so?