Is that a Cub Cadet? We have one; I call it "the bumble bee," due to the coloring. A front end loader bucket... Oh, my... Be still, my heart!
I just copied a picture from a Google search. I believe those front end loaders are made to fit on any number of different brand riding mowers. From what I have seen, you can get a front end loader with manual levers the raise/lower the bucket and another for dumping the bucket. That is less expensive than front end loaders that use some kind of cable hoist system. Unfortunately, nobody sells either type of front end loader where I live, so I don't know anything more than the YouTube videos I have watched.
Of course, those front end loaders for a riding lawn mower are not as big as the ones made for a tractor. I don't have the exact specs, but it looks like maybe half the load in the riding mower buckets. Makes sense because a riding mower is much lighter than a tractor. If the bucket was too big and too heavy for a riding mower, it would just do a nose dive and the back wheels would lift up off the ground.
Despite the limitations, I watched a YouTube video of a guy who bought one of those front end loaders for his riding mower to move gravel from a large pile on to his long driveway. Not only did he end up saving money from a tractor rental, but now he has a front end loader on his riding mower for any future projects. Yes, a rental tractor would have done the job faster, but it would have cost more and he was more than happy to put that rental money into something that he would have forever.
In my case, I have mentioned that I turned my entire chicken run into a chicken run composting system. About twice a year, I go into the run and load up Gorilla carts, many times, full of compost that I take over to my cement mixer compost sifter. It certainly would be easier for me to open up a panel on the run and take a riding mower in there with a front end bucket. But I still do OK with the carts, so I'm not complaining.

As I get older, there may come a day when I can't use the walk behind snow blower to clear our driveway. At that point, I have considered getting something with a plow or shovel to move the snow. Depending on the winter, snow removal service can be a major expense if you have to pay someone else to do the job. That's one job I think a front end loader on the riding machine could do and may justify the investment for me.