No. A magnet with a single pole cannot exist. North and South poles always occur in pairs.
Test it: take a bar magnet marked N and S, and break it in two.
One magnet: N ——— S
Break it → two magnets: N ——— S and N ——— S
Break each again → four magnets, each still with both poles
However small the piece, it always has a North pole and a South pole.
Why it happens: a magnet is not made of a “north lump” joined to a “south lump”. Every tiny part of the material is itself a complete miniature magnet with two ends, all lined up in the same direction. Cut anywhere and you simply expose the two ends of the smaller stack — so a fresh N and a fresh S appear at the cut.
Did you know? Scientists have searched for a lone magnetic pole (a magnetic monopole) for over a hundred years and have never found one. So far, nature has kept the rule with no exceptions.