Polaronic ferromagnet

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Figure 9.5 Schematic representation of a bound magnetic polaron (a) one bound magnetic polaron located on a charged defect and (b) overlapping bound magnetic polarons leading to ferromagnetic alignment of magnetic ions.

Co0.04Zn0.96O is a ferromagnetic semiconductor, (a) Estimate the radius of a bound magnetic polaron in this material, (b) If the Co2+ ions are uniformly... 

Very direct evidence for the existence of bound spin polarons is provided by the work of Torrance et al (1972) on the metal-insulator transition in Eu-rich EuO At low temperatures, when the moments on the Eu ions are ferromagnetically aligned, the electrons in the oxygen vacancies cannot form spin polarons and are present in sufficient concentration to give metallic conduction. Above the Curie temperature the conductivity drops by a factor of order 10 , because the electrons now polarize the surrounding moments, forming spin polarons with higher effective mass. 

The susceptibility should also increase if the coupling between spin polarons is ferromagnetic—or in other words because of the Zener coupling. The condition for ferromagnetism is that... 

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. 

For the size determination of spin polarons from the field-dependent magnetization data (SQUID results in Fig. 6) we first employed a fitting based on the Brillouin function /3(./), which is justified since the respective temperatures around T]T are sufficiently above the ferromagnetic transition. The paramagnetic magnetization as a function of field is given by... 

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