The other half is in the Shinigami. Also, I don't think the shinigami only takes the yin half, it takes however much the summoner wants taken, for instance, the 3rd never wanted Orochimaru to use seals again, and since he was too weak at that point cause of being stabbed, he had to settle with taking Oro's arms, cutting off that part of Oro's soul. So maybe Minato cut off only the Yin part, sealing it away within the Death God.
What I would like to know, the Death God is a forbidden jutsu. If you summon the god, the you must give up your life to him to take someone's soul. I want to know how Minato managed to cut the fox's soul in half, sealed half in the shinigami then half in Naruto before he died. Can he perform seals/jutsus while using the Shinigami? If he can, maybe he sealed yang in Naruto before taking the yin half with him.