It has been shown that the traditional matching of wavefunctions between regions of different effective mass (matching {psi} and (1/m*)partial{psi}/partialx) is not correct, but that one should match (1/surdm*){psi} and (1/surdm*)partial{psi}/partial
x. It has not been clear how serious is the error in using the traditional formula. We apply the two sets of conditions to a simple, but rather general, example and find that the traditional matching is not even qualitatively correct.
A uniform distribution of La and Sr in lanthanum-strontium manganites would lead to charged crystal planes, a charged surface, and arbitrarily large surface energy for a bulk crystal. This divergent energy can be eliminated by depleting the La concen
tration near the surface. Assuming an exponential form for segregation suggested by experiment, the total electrostatic energy is calculated, depending only upon the decay length and on an effective charge Z* associated with the La ion. It is found to be lower in energy than neutralization of the surface by changing Mn charge states, previously expected, and lower than simply readjusting the La concentration in the surface plane. The actual decay length obtained by minimizing this electrostatic energy is shorter than that observed. The extension of this mechanism to segregation near the surface in other systems is discussed.
A localized description, rather than energy bands, is appropriate for the manganite substrate. Empty substrate levels lower in energy than occupied oxygen levels indicate need for further terms beyond the Local Density Approximation. So also does van
-der-Waals interaction between the two. Methods to include both are suggested by related, exactly soluble, two-electron problems. The descriptions of the electronic structure of the molecule and a LaSrMnO3 (LSM) substrate are greatly simplified to allow incorporation of these effects and to treat a range of problems involving the interactions between oxygen atoms, or oxygen molecules, and such a substrate. These include elastic impacts, impacts with electronic transitions, and impacts with phonon excitation. They provide for capture of the atoms or molecules by the surface, leaving the neutral molecule strongly bound over a Mn(4+) site. It is found that oxygen vacancies in LSM diffuse as a neutral species, and can appear at the surface. Bound molecules tend to avoid sites next to vacancies but, if there, should drop one atom into the vacancy leaving the remaining triplet oxygen atom bound to the resulting ideal surface, with no need for spin flips nor successive ionization steps.
An earlier analysis of manganese oxides in various charge states indicated that free-atom term values and universal coupling gave a reasonable account of the cohesion. This approach is here extended to LaxSr(1-x)MnO3 in a perovskite structure, and a
wide range of properties, with comparable success, including the cohesion, as a function of x. Magnetic and electronic properties are treated in terms of the same parameters and the cluster orbitals used for cohesion. This includes an estimate of the Neel and Curie-Weiss temperatures for SrMnO3, an antiferromagnetic insulator, and the magnitude of a Jahn-Teller distortion in LaMnO3 which makes it also insulating with (100) ferromagnetic planes (due to a novel double-exchange for the distorted state), antiferromagnetically stacked, as observed. We estimate the Neel temperature and its volume dependence, and the ferromagnetic Curie-Weiss temperature which applies between the Neel and Jahn-Teller temperatures. We expect hopping conductivity when there is doping (0<x<1) and estimate it in the context of small-polaron theory. It is in accord with experiment between the Neel and Jahn-Teller temperatures, but below the Neel temperature the conduction appears to be band-like, for which we estimate a hole mass as enhanced in large-polaron theory. We see that above the Jahn-Teller temperature LaMnO3 should be metallic as observed, and paramagnetic with a ferromagnetic Curie-Weiss constant which we estimate. Many of these predictions are not so accurate, but are sufficiently close to provide a clear understanding of all of these properties in terms of a simple theory and parameters known at the outset. We provide also these parameters for Fe, Co, and Ca so that formulae for the properties can readily be evaluated for similar systems.
The electronic structure is found to be understandable in terms of free-atom term values and universal interorbital coupling parameters, since self-consistent tight-binding calculations indicate that Coulomb shifts of the d-state energies are small.
Special-point averages over the bands are seen to be equivalent to treatment of local octahedral clusters. The cohesive energy per manganese for MnO, Mn2O3, and MnO2, in which manganese exists in valence states Mn2+, Mn3+, and Mn4+, is very nearly the same and dominated by the transfer of manganese s electrons to oxygen p states. There are small corrections, one eV per Mn in all cases, from couplings of minority-spin states. Transferring one majority-spin electron from an upper cluster state to a nonbonding oxygen state adds 1.67 eV to the cohesion for Mn2O3, and two transfers adds twice that for MnO2 . The electronic and magnetic properties are consistent with this description and appear to be understandable in terms of the same parameters.
