I recall that early crystal radios sometimes used wide loop antennas (like a hula hoop, or a several-feet square diamond, or octagon. Or basket-weave coils many inches in diameter.) Look up: crystal radio loop antenna.
In early internet days some guy had a ferrite antenna, using a collection of inch-thick ferrite rods, in series segments totalling several feet long! (Also, I see a reference to "ferrite sleeve" antennas, so that might be another possibility.)
Hobbyist VLF antennas aren't possible? Since they're fifty miles wide? Nah, just build a tuned, short antenna, where the Electrical Aperture EA is far, far wider than the physical parts. Those antennas act as "wave-funnels," where they may be electrically a quarter-wave wide, even though they're physically only .0001-wave in width. Essentially, if you build any large VLF radio antenna project, it can also be tuned for AM band. Look for DIY groups doing "natural radio" or "diy vlf antenna," or perhaps "vlf antenna tutorial."
For small antennas like this, the Q-factor becomes critical, and the wire in the coil needs to be fairly thick (or use heavy copper tape, or litz wire found on eBay, or even some 1/8" copper fridge-tubing.)