A degenerate gas of spin polarons antiferromagnetic metals

If the spin-polar on model is correct, we must describe the carriers in the antiferromagnetic semimetal formed when the two Hubbard bands overlap as a degenerate gas of spin polarons it should have the following properties. 

A point of some interest is the value of the moment on each atom and the Neel temperature at the metal-insulator transition. Putting B=U in equation (6) of Chapter 3 shows that the moment is reduced by a factor of 1 — (4z) 1 and that the Neel temperature at the transition, since B=U, is given by 

In an ideal case we should expect very high Neel temperatures since for transitional-metal oxides B 1 eV, if 2z = 10 then we expect 1200 K. But in transitional-metal compounds, as we shall see in Chapter 6, the equation that we must use to determine the condition for the transition is 

In real materials the quantity that we have called U/B can be varied in several ways. A decrease in volume will normally increase B. Changing c/a, by altering the overlap between bands, can also affect both parameters (cf. the discussion of V203 in Chapter 6). Alloying can also change the ratio. 

The description given here is appropriate to the case when the atomic orbital is non-degenerate (e.g. ls-states, or the dz2 states in the rutile or carborundum 

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