Tree Cut In My Neighbor's Yard And Fell Into My Yard. Who Is Responsible For Removing It? (located In Georgia)

Hi all. I'm facing a situation with a felled tree in my backyard and am curious which party (myself or my neighbor) is responsible for removing the tree. The stump is located on my neighbor's side of the fence. The tree has been cut (about 5' above the ground) by my neighbor and either fell or was pushed to fall onto my side of the fence. A wedge was cut out from the trunk before a horizontal cut was made, proof that the tree was deliberately cut and didn't fall naturally. The lower felled portion of the tree is still barely attached to the stump, so the fence between our properties is undamaged. Additionally, there are several limbs and a large branch from another tree, also originating from my neighbor's side of the fence, that have clearly been cut and discarded into my backyard. I first noticed the tree and tree debris about a month ago, but didn't take action as I was leaving town for the holidays.

I have never spoken to my neighbor, and I have yet to be approached by them about the tree and debris. I've called the local sheriff's department seeking advice, and was told to take the neighbor to small claims court. I'm not looking to escalate the situation that far (yet), more so just looking to go have a conversation with the neighbor about when they plan on handling the removal. Before that happens, am I correct to assume that they are legally responsible for removing the tree and limbs/branches?

For context: I'm renting the home and have contacted the landlord about the issue. She said "that wasn't very nice" and we (my partner and I) can remove the tree ourselves. We are young professionals, and even if we scraped together enough disposable income for a tree removal service or a chainsaw, it's more about the principle of the matter and not tolerating disrespect from neighbors.

I'm happy to provide more context in the comments, and I appreciate any help!