content_image/345003.jpg content_image/345002.jpg content_image/345001.jpg
same way the transitions D − → D + are also suppressed. Thus the resistance increases as a result of application of external magnetic field. 

In our case of p-type structures the situation appears, again, more complicated due to more complex structure of A + centers. However, in general, the considerations given in [9], [10] still hold. Basing on the calculations similar to given in [10] one obtains for weak field limit µgH < T the following estimate: 

where C ∼ 1 / 3, 

<img src='content_image/345003.jpg'>

<img src='content_image/345002.jpg'>

while g$_{l}$ , g$_{u}$ are the densities of states of the lower and upper Hubbard bands. Note that for the low concentration of dopants g$_{u}$ is controlled by the concentration of A + centers while g$_{l}$ - by the concentration of A − centers and thus g$_{l}$ = g$_{u}$ . At stronger magnetic fields when µgH > T , the corresponding contribution to magnetoresistance still increases with magnetic field increase until µgH reaches the value ξT and then saturates [9], [10]. 

One notes that at low enough temperatures the positive magnetoresistance of the spin nature suggested in [9] can exceed the wave shrinkage magnetoresistance. At the same time this contribution at relatively weak fields when µgH < T is expected to be comparable to the spin magnetoresistance resulting from interference term discussed above. Summarizing the both spin contributions to quadratic magnetoresistance we estimate the coefficient k resulting from the similar parametrization of the positive quadratic and linear negative magnetoresistance as was done above: 

<img src='content_image/345001.jpg'>

Thus, as it is seen, for the Mott case at T → 0 k ∝ T 1 / 3 while for the ES case it is ∝ T 1 / $^{4}$. 

Note that in our calculations we assumed that the value of H$_{min}$ still corresponds to linear behavior of negative magnetoresistance which means that the magnetic flux through the interference area is much less than magnetic flux quantum Φ$_{0}$. The critical field H$_{sat}$ 

