How to say thank you to references - via letter, email, or text?

I recently got a job offer and they talked to my references over the phone. I want to say thank you in a meaningful way.

I need to get their addresses.

Would it be too much to send a physical thank you letter in the mail?

If I decide on the snail mail route, should I first send them a text thanking them and then asking them for a good mailing address? Should I specify why I want their address? Would it be repetitive sending them the note through mail?

Or should I stick to just email or text? Text is how I primarily communicate with them.

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