An alfalfa plant over 1/2 or 1 year old will be putting toxins in the soil that usually kill any new alfalfa seed trying to sprout that is within 18-24 inches of the old plant.
So you cannot plant new alfalfa seed into a field that has old alfalfa plants growing in it.
After 3 moths of good growing weather and _no_ living alfalfa plants, those toxins go away. But most folks feel better waiting a full year of some other crop befroe replanting alfalfa - it is difficult to kill off every old alfalfa plant quickly.
Both alfalfa and soybeans are legume plants, in the same family. So you use some of the same herbicides, and they are subject to a few of the same diseases/ insects. Both beans and alfalfa use up P and somewhat K, and produce excess N, so they are the same, not complementary on fertilizer use.
If corn is a good crop in your area, like I said below, it would be grass crop, easier to control weeds, insects, and diseases, uses the build up N you have in the ground, and in most places, it pays off better than beans - tho yes it does take more money to get it growing.
Don't know where you are located so don't know which crop is right for you, but in most situations corn is a much better crop behind 4 year old alfalfa than beans would be.