Zener pairs

All Np states belonging to the Pth sub-space interact strongly with each other in the sense that each pair of consecutive states have at least one point where they form a Landau-Zener type interaction. In other words, all j = I,... At/> — I form at least at one point in configuration space, a conical (parabolical) intersection. 

Recently it was pointed out by Zener7 that the atomic moments, in parallel orientation, might react with the electrons in the conduction band in such a way as to uncouple some of the pairs, producing a set of conduction electrons occupying individual orbitals, and with spins parallel to the spins of the atomic electrons. Zener assumed that the conduction band for the transition metals is formed by the 4.s orbitals of the atoms, and that there is somewhat less than one conduction electron per atom in iron, cobalt, and nickel. Like Slater, he attributed the atomic magnetic moments to the partially filled 3d subshell. 

Zener appears to have been the first to consider this problem to some depth in his theoretical work on ferromagnetic crystals of the type l.a. Ca.MnO, (Zener 1951). For x = 0 one has LainMnin03 but for x > 0 some of the Mn will be 4+, and so we have the structure I. a " / a " Mn "(Mn CL in which some Mn-Mn pairs will be mixed valence, that is, MiF Mnj) or MnJ) Mn . Mnm is 3d4 (S = 2) and MnIV is 3d3 (S = 3/2), and Zener proposed that the excess electron (also called itinerant electron or Zener electron) on Mn111 can travel to the MnIV via a doubly-occupied p-orbital of... 

In order to account for an observed global ferromagnetism, Zener (1951) had to make the further assumption that these pairs do not require an activation energy to diffuse through the lattice. This model leads to a charge-carrier mobility... 

The pair of levels 21s - (16,3) is exactly analogous to the extreme blue and red Na Stark states of n and + 1. The fact that only one has a permanent dipole moment is of no consequence it is only the difference in the permanent moments which is significant. Based on the single cycle Landau-Zener description of microwave ionization we expect that if atoms in the 18s state are exposed to a microwave field of amplitude equal to the crossing field, Eq = 753 V/cm, they would make transitions to the (16,3) state. On the other hand, if a static field is present as well as the microwave field it should be possible to see resonant microwave multiphoton transitions between these two bound states, and seeing the connection between these processes is part of our objective. 

Above Tc, the conductivity of the O phase fits the adiabatic small-polaron model a - (A/T) exp(-Ea/kT) over the entire doping range [162]. As already discussed, an electron tunnels from an Mn(III) to either an Mn(IV) ion or a Zener Mn(III)—O—Mn(IV) pair in a time Zh > where is the period of the locally cooperative oxygen displacements that, for x < 0.5, dress the mobile holes as Mn(IV) ions or as Mn(III)—O—Mn(IV) pairs. Fast electron transfer (zh < occurs within a Zener polaron. 

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