Many wood turners make spinning tops. Their symmetrical round shape is well suited to the lathe. How small can they go? At least this small it seems: the shaft is about 0.0013″ (0.034mm) in diameter. I tried spinning it, but alas, my fingers are too big for this nano piece of ebony.
Update 22 February: after several more tries and broken shafts, here an even smaller one. The shaft is now 0.001″ (about 0.025 mm) in diameter, and the body 0.008″ (about 0.2 mm) in diameter.
It almost fell through the fiber of the kitchen paper towel. So now I am looking for that playful ant to spin it.