My garden is in a clay area, the top soil is pretty good now, but for some crops, like carrots, they hit the layer of clay underneath and push up out of the soil quite a bit by the end of the season. Standard tiller only gets down about 6 inches. Id really like to break up that layer of clay underneath a bit and get down 10 inches or so, but this would be just about impossible with a shovel. Garden is in fenced yard and is about 30ft x 20ft. Im wondering if anyone has suggestions about how to do this, is there some kind of hook that could be used with a skidsteer or small tractor that would be able to get deeper and bust up that lower layer?

