If you're looking for music made freely available by the artist I don't really have a suggestion. If you're looking for hit songs and stars, music that most people pay for, we can't discuss those as downloading those tracks for free is theft.
Quick note, if you're interested -- what those "free" music download apps and services do is check many open servers around the world for music tracks uploaded by other users, then provide them to you. Some of those tracks may have been uploaded by users intended for their own use only, but there are many that were also uploaded with the intention of piracy. In order to skirt copyright law, these "free" music services say in their fine print that the music you download is for "research" only, and that after your "research" is over, you must delete the music from your device. If you don't, then you're knowingly violating copyright law, and you could be held liable.