  Thermodynamic flunctuations in BaFe2As2 is addressed with a first-principles
formulation of the Helmholtz energy by accounting for the mixture of various
electronic states each distinguished by different spin orientation
distributions. We find that it is the spin exchange coupling in the inter-plane
c direction that dictates the spin density wave ordering. We quantitatively
predicted the pressure dependence of the spin density wave ordering, the
Schottky anomaly, and the temperature dependence of thermal populations of spin
structures, all in agreement with available experimental data.
