You're basicall looking for a magnetic version of a high dielectric
constant material, I gather. Ordinary materials have small diamagnetic
or paramagnetic responses, but not enough to be useful ordinarily.
Ferromagnetic materials have a large response to magnetic fields, but as
you say, usually exhibit remanent magnetization when the external field
There are specially prepared magnetic materials, such as Permalloy,
Super-Permalloy, and mu-metal, that have very high magnetic permeability
with very low remanent magnetization. The bad news is that they tend to
be very expensive, and their properties depend crucially on their
microcrystalline structure, so that they lose many of their nice
properties if you bend them, hammer them, or even machine them. They
have to be carefully heat-treated after finishing.
Another possibility would be some sort of electromagnet gizmo based on
negative feedback: if you attach a Hall effect magnetic field sensor to
a coil, and servo the coil current to keep the field at zero, it will be
strongly attracted to any magnet in the neighbourhood, but won't do
What do you mean "not turning into a magnet"? If you mean the material does
not have magnetic moment, that is impossible, magnetic moment will always be
induced whatever material you are using. If you mean does not hold the
magnetic moment when field is removed, a lot of options exist, paramagnetic,
soft ferromagnetic, superparamagnetic...
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