Mounting a hook on a tree in my back yard

I have a nice tall sweetgum tree (about 2 feet in diameter) in my back yard, optimal distance from a corner fencepost to put up a hammock in warmer months.

For the past several years I have been been running a few loops of sturdy rope around the tree and tying a hook to that.
I would like to mount the hook permanently to the tree. How can I do this in a way that is not harmful to the tree and will still resist years of hammock use?

You can pretty much drill directly into the tree trunk and not worry. a single hole of smallish diameter won’t make any appreciable effect on the flow of water and nutrients up through the living sections under the bark. Just try to keep the hole neat to avoid giving insects or fungi an entry into the tree past the protective layer of bark.

Also check with someone who knows a lot about trees to see which metals are safe.
I know copper for instance will kill a tree if left in it.