magnetic materials will produce magnetic field near it
All magnets are made up of small magnet type atoms which are known as domains
These all atoms will align itself so that they all produce strong magnetic field along the axis
this magnetic field will become more strong as more number of atoms are aligned.
Now if we break the magnet into small piece then the magnetic field strength will start decreasing and at the end when only one atom will remain then the magnetic field strength will reduce to the field of one atom only.