If you're looking for magnetic field generation rather than something that has energy stored in the form of magnetic field, you should be looking at electromagnets instead of materials that store magnetic fields.

The design that has been able to produce stronger magnetic fields than any other design is the HSMAG electromagnet design.

The HSMAG design uses circular plates with a gap in the center and a radial cut in order to connect down to the next plate, connecting down in helical fashion, separated by an insulator.  In order to disperse the heat generated by dumping so much current through the plates, they often have holes travelling down through the structure and have liquid cooling.

For the sizes they need to be, the most economical (minimize resistance without extravagant costs) are made of highly pure copper.

The record so far was actually done by a hybrid, a HSMAG electromagnet inside of a superconducting magnet.  (Superconducting magnet probably made of Niobium-titanium).  The superconducting magnet is limited to 20T depending on material (Nb-Ti is limited to 15T) thanks to the fundamental physics behind superconductivity, while the electromagnet has no such limit, only the limit of its ability to stay structurally stable while pumping a huge current.

Electromagnets aside and bulk materials aside, I'm going off on a somewhat unrelated tangent here but many, many single-domain magnetic nanoparticles? I'm assuming it would function like fully-magnetized iron. Go ahead and point out any holes in this assumption (pun somewhat intended).

We can make electromagnets with fields far in excess of rare earth magnets. In fact planetary magnetic fields are thought to be a form of electromagnet as the molten iron core rotates.

But for very small magnets we use rare earth magnets, which are quite strong. Palm-sized magnets can't be pulled apart by human strength.

Technically you asked for a material, not a device such as an electromagnet.
That would be neodymium iron boride magnets:
Neodymium magnet

other strong rare-Earth magnets are the samarium-cobalt and 'alnico' (aluminium nickel cobolt) magnets:
Rare-earth magnet