Magnetic polaron effects

The intrinsic electrical conductivity of LiFeP04 is of a polaronic type, as in many ionic compounds. The polaron in the present case is linked to the existence of Fe ions that maintain the charge neutrality in presence of lithium vacancies. According to the Mott formula, the conductivity a(T) is [116]  

In the conduction process, an electron jumps from a Fe site to a neighboring 

Fe site. This electron is the igj, 3d-electron of Fe since it is in the high spin multi-electronic state while the state of lowest energy for Fe is the 

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Zaghib K, Mauger A, Goodenough JB, Gendron F, Julien CM (2007) Electronic, optical, and magnetic properties of LiFePOa small magnetic polaron effects. Chem Mater 19 3740-3747... 

Diet T, Spalek J (1982) Effect of Fluctuations of Magnetization on the Bound Magnetic Polaron - Comparison with Experiment. Phys Rev Lett 48 355-358... 

As a result we have obtained the effective Hamiltonian with the two types of interaction of neighboring segments. The competition between these types of interactions leads to the formation of a magnetic polaron similar to the anisotropic one band U=oo Hubbard model. 

In thick ( 300 pm) crystals of GaN electronic excitons of shallow dopants have been observed in far infrared absorption at 215 cm 1 [44], Interpreted as the ls-2p transition of a residual shallow donor, its binding energy was calculated to be (35.5 0.5) meV. Further modes at 149 and 242 cm 1 have been observed in mixed phase GaN/GaAs in Raman scattering and have been associated with electronic excitations of shallow donors in cubic and sphalerite GaN, respectively [45] see also [46], Far infared absorption at 23.2 cm 1 in magnetic fields has been used to determine the effective electron mass in GaN, m = 0.20 0.005 m, (corrected for polaron effects) in cyclotron resonance [47]. 

Kugel KI., and Khomskii D.L., (1980). Polaron effects and exchange interaction in magnetic insulators with Jahn-Teller ions. Zh. Eksp. Teor. Fiz. 79 987-1005 [Sov. Phys. JETP 52 501-515],... 

Fig. 12 Complexity of the problem of marginal metallicity (adapted from ref. 27). The oxides discussed in this article fall somewhere in the three-dimensional space indicated here. The other factors include electron-lattice interaction, magnetic polaron and finite temperature effects.

While we have been calling the broadening effect as phonon broadening, it must be pointed out that the PAM likewise predicts a broadening of PES features with temperature, but not associated with phonons. Experimentally there is no way to distinguish between phonons and the magnetic polaron interactions inherent in the PAM. Suffice it to say that the temperature effects observed in PES measurements are not inconsistent with the PAM predictions. 

Dietl, T. and Spalek, J. (1982) Effect of fluctuations of magnetization on the bound magnetic polaron comparison with experiment. Physical Review Letters, 48, 355. 

The model of a degenerate gas of spin polarons suggests that if the direct or RKKY interaction between moments is weak and EF too great to allow ferromagnetism then the moments might all resonate between their various orientations. This would mean that it is possible in principle to have a heavily doped magnetic semiconductor or rare-earth metal in which there is no magnetic order, even at absolute zero. This possibility is discussed further in Section 8 in connection with the Kondo effect. 

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