Magneto-resistivity model and ionization energy approximation for ferromagnets

The evolution of resistivity versus temperature ($\rho(T)$) curve for different doping elements, and in the presence of various defects and clustering are explained for both diluted magnetic semiconductors (DMS) and manganites. Here, we provide unambiguous evidence that the concept of ionization energy ($E_I$), which is explicitly associated with the atomic energy levels, can be related quantitatively to transport measurements. The proposed ionization energy model is used to understand how the valence states of ions affect the evolution of $\rho(T)$ curves for different doping elements. We also explain how the $\rho(T)$ curves evolve in the presence of, and in the absence of defects and clustering. The model also complements the results obtained from first-principles calculations.