I was reading an article, and it said that the total free energy of the system in an external magnetic field H can be written as: F= 0.5 * χe^(-1) * Me^2 + 0.5 * χl^(-1) * Ml^2 - Jeff*Ml*Me - (Ml+Me)H Where Ml and Me denote the magnetization for the local moment and electron subsystem. J_eff is the magnetic exchange coupling between them. H is the applied field and χl and χe the susceptibilty of the system (local moment/electrons) I don't understand where this expression comes from. I start out with U=-M*B, but I cannot seem to get to the right answer. The first two terms of the right hand site of the equation from the paper are mysterious to me, and I would expect a mu_zero to show up somewhere. Can anybody please give it a try? It shouldn't be that hard I would say. Any help would be greatly appreciated! Thanks.