Investigation of ferromagnetism increasing with the temperature in n-type ZnO

We propose a model with a theory to simulate the ferromagnetism increasing with the temperature observed from some ferromagnetic n-type ZnOs. This phenomenon reveals the possible mechanism of ferromagnetism for us to propose that ferromagnetism originates from the electron's spin split in the dopant-induced impurity states by Coulomb excitations. Our theoretical results indicate that the electron-phonon interaction effectively influences ferromagnetism, which can localize the electrons in the impurity states leading to the enhancement of ferromagnetism. At the same time, the electron-phonon interaction suppresses the hybridization coupling between the impurity state and the conduction band, and this hybridization coupling can increase the electron density and ferromagnetism of the impurity state.