According to the hits of google search "come to mind" is most often used and "come down to mind" is least used.
What difference have these three phrases?
Should I only use the "come to mind" that is most used?
Learn English – How different are “come up to mind”, “come down to mind” and “come to mind”
word-difference
Best Answer
Come down to mind and come up to mind are extremely rare, at least in the United States. In fact, I've never heard anyone write or say either of those phrases.
Come to mind is pretty common, though. It is defined in The Free Dictionary:
Another definition is the following:
I would say, feel free to use come to mind.
But come down to mind or come up to mind wouldn't make much sense to people.