Combined analysis of ferromagnetic materials using the Heisenberg Green functions and Ising EFT methods

• EFT presents a simple tool to get exchange parameters J of ferromagnetic systems.
• Percolation is introduced to model diluted ferromagnetic materials.
• At high spin, ratio of critical temperature to J is independent of transverse fields.
• Large anisotropic effects do not affect high spin systems of various geometries.
• Results are useful to extract interaction parameters between Jahn–Teller centres.

Ferromagnetic phase diagrams were, for a long time, unsuccessfully determined theoretically, despite the important Callen's 1963 [21] theoretical model. A great variety of experimental data for the magnetization over the entire range of temperature defining the ordered phase compared well with an empirical formula recently determined by Kuz'min (2005) [22]. Nonetheless, the Ising effective field theory (EFT), which can be of enormous support to both methods, was never given attention. The present work intends to show how the Ising EFT technique, when combined with the Green functions in Callen's work, is able to reconcile theoretical work with experimental data. The ratio kTc/JZS(S+1)kTc/JZS(S+1) plays an important role in finding values for the exchange parameter J, whose first-principles calculation, often depending on the package used, is not properly done. J can be determined for a variety of ferromagnetic materials represented by general spin systems S with a number of nearest neighbours Z and critical temperature Tc, even for models including a percolative feature, characteristic of diluted interactive systems. We demonstrate that EFT is capable of estimating a value of J, which can substitute the use of more complex theoretical models or the performance of ab initio/DFT calculations.