Magnetic core transfer loops (logic)
You can buy vintage bare 45,000 cores here for $US49.00, with free international shipping from Bulgaria. Find 9 other friends interested in sharing and you have 4,500 each for $5.

One bit core memory project - liable to be of high interest. Use a suitable ferrite bead if needs be. Drive levels etc need looking at. 

This vintage core memory board costs $400  on ebay BUT I have bought similar here for about nothing and while they are rarer than way back then they are probably still available for looking as electronic junk.

Almost any small ferrites with a hole in them will do - including RF decoupling beads. Or you could wrap a coil around a stick core etc. You can also just use iron or steel with due attention to characteristics. A steel nail with a suitable amp-turns pulse will be magnetised. Not the most efficint core memory but doable.

How to drive one

Very useful 

Useful

Old discussion -2010 - may be some use