What type of Logia can defeat a Haki user?
There is no such thing as a Devil's Fruit that automatically beats a Haki user. The use of Haki is to be able to make contact with a Logia type fruit user. This allows for a "fair" fight (in the sense that one person isn't inherently untouchable). However, there is no fruit that negates the power of Haki (or at least among the fruits that have been revealed).
From the other perspective, having Haki only allows for Haki user to make contact (or touch) the Logia. It does not give them any anti-Logia super-effective skills.
In other words, any Logia can beat any Haki user, as the fight essentially comes down to better skills (unless we go and look for specific combinations)
The only Logia ability that has a proven record of defeating - nay KO'ing Haki users is the Gas-Gas no Mi, provided it is used with an element of surprise. You would recollect that Ceaser KO'ed both Luffy and Smoker by depriving them of oxygen.
In the future, we could probably see Logia abilities like hot plasma or gamma ray, which could possibly penetrate Haki.
In a sense, Soru Soru no Mi. It's not logia, but paramecia.
Other answer already provide how logia can beat haki user but this devil fruit power can make haki useless against them.
The devil fruit user them self aren't automatically immune to haki but the objects with soul fragments inside them are immune to haki attack. Surely homies (objects and animals that have been anthropomorphized by the Soru Soru no Mi) like King Baum can be cut easily with simple sword attack. But with powerful enough soul like Prometheus, a mass of compressed flames, is completely immune to Luffy's busoshoku haki attack
Powerful as it seems, even Prometheus can get injured by Brook. Supposedly, not because of his haki but because of devil fruit incompatibility. Brook, a soul king, can attack soul directly.