Just a remark for clarification of the question. The Gibbs free energy/particle (chemical potential) is continuous both at first (kink in the thermodynamic potential) and second order phase transitions (kink in the derivative of the potential). I would argue (in zero applied magnetic field) a meaningful difference can only be defined between two different temperatures above and below the transition. Of course the difference in the potential will depended on the difference of the selected temperatures. In this sense there is not a unique answer to the question before it is more specified.
I think he means the change in free energy. He could perform some DSC on his sample in zero magnetic field and employ the second law of thermodynamics to compute what he's after.
You could also consider the total possible entropy change generated by a magnetic species using dSmag = R*ln(2J+1)
I'm am really just looking for an order of magnitude? I have Antiferromagnetic and Ferromagnetic structure of the same TMO calculated by a DFT code and I just wanted to make sure they make sense in terms of an energy difference. In actuality this difference in energy is just the internal energy, but I was hoping by asking for the free energy, it would open the question up to more values (experimental or theoretical) to compare and rationalize. I guess I should have asked my question more directly, I apologize.