I disagree. OP, YTA.

Correct me if I’m wrong, but there should have been an open dialogue with the cat owner.

I agree that the owner paving their front and back yards and not providing adequate facilities resulted in the cats to defecate in OP’s yard, but I’m missing the “Hey Cat Owner. Your cats are pooping in my yard. Can you prevent that from happening? No, okay. I’ll just invest in ultrasonic device.”

Maybe the owner knew or should have known what was happening and chose to ignore it. But from OP’s part alone, s\he was okay with the occasional poop (personally, I would have confronted neighbor then), and when it got too much, s\he chose to take matters into her hands without first consulting neighbor.