High permeabilty materials and megnetic fields

We are all familiar with the classic presentation of a solenoid with an iron
core, in which the high permeability core magnifies the strength of the
inducted filed. What about a situation with a permanent magnet? If I
bring a high permeability material into contact with a very strong permanent
magnet (e.g. neodymium magnet), do I get a similar field strengthening? My
specific question regards the coupling of a neodymium magnet and a piece of
“Mu” metal. This is a metal that supposedly has a permeability 25,000 times
that of free space at 0.002 Tesla. Does this mean that I will get a field of
25,000 Tesla within the Mu metal if I place it in contact with a Neodymium
magnet with a surface field strength of 1 Tesla ? This hardly seems possible.


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