In this paper we present a method for reducing the three dimensional Schrödinger equation to study confined metallic states, such as quantum well states, in a multilayer film geometry. While discussing some approximations that are employed when dealing with the three dimensionality of the problem, we derive a one dimensional equation suitable for studying such states using an envelope function approach. Some applications to the Cu/Co multilayer system with regard to spin tunneling/rotations and angle resolved photoemission experiments are discussed. Recent experimental studies of spin dependent, hot electron transmission such as those described in Ref. 4 and resonant tunneling through two discrete states (Ref. 5), have raised a number of interesting issues related to the ferromagnetic and insulating materials used, the nature of the electronic states that are involved in transmission and enhancements in spin filtering effects. Apart from the first principles based attempts which can be quite tedious, most theoretical studies of these spin dependent effects have used free electron band structures and other simplifications in the metallic as well as in the insulating regions. Our work, though motivated by free electron approaches such as those introduced by Slonczewski 6 , is an attempt to bring out a more realistic lateral dependence of the electronic states under consideration.This paper is organized as follows. First, starting from the three dimensional Schrödinger equation, we proceed to derive an envelope function approach suitable for multilayered films.This procedure will go beyond the free electron methods that have been commonly used in the past, making use of more realistic wave functions, but avoiding a full pledged ab-initio calculation when studying such systems. We introduce an approach which incorporates the two dimensional Bloch wave vector k || and show that the associated parallel band structure characteristic of the material being used, plays a major role in perpendicular transmission.Second, We will study spin tunneling and rotation effects (to be defined later) in a multilayer system with two ferromagnetic layers separated by a nonmagnetic metal such as Co/Cu/Co. We will also address some issues related to angle resolved photoemission and inverse photoemission experiments focused on confined states in metallic multilayers.

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Ab initio computational studies were performed for CdSe nanocrystals over a wide range of sizes and topologies. Substantial relaxations and coordination of surface atoms were found to play a crucial role in determining the nanocrystal stability and optical properties. While optimally ͑threefold͒ coordinated surface atoms resulted in stable closed-shell structures with large optical gaps, suboptimal coordination gave rise to lower stability and negligible optical gaps. These computations are in qualitative agreement with recent chemical etching experiments suggesting that closed-shell nanocrystals contribute strongly to photoluminescence quantum yield while clusters with nonoptimal surface coordination do not.

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We have determined theoretically both the orbital and the spin contribution to the magnetic moment on the (001) surfaces of fcc Mn, bcc and fcc Fe, hcp Co, and fcc Ni. We used a surface geometry that corresponds to the bulk crystal structure (except for Mn) with no relaxation of the surface. In addition to enhanced spin moments at the surface we find that the orbital moment for surface states is greatly enhanced (sometimes by more than 100%). We also present calculations for different spin configurations in fcc Fe, and we find that two competing spin configurations exists. fcc Mn is found to have a surface spin moment slightly larger than the surface moment of bcc Fe. Detailed information from the calculations is presented, i.e. , density of states, charge-density contour plots, and orbital-projected spin moments.

The valence-band structure of nickel aluminum was measured by use of angle-resolved photoemission with synchrotron radiation and calculated using the local-density approximation. The overall agreement between theory and experiment is remarkably goodmuch better than for pure nickel. This means that the "self-energy" corrections are significantly less in NiA1 than in pure nickel. The core-level binding energies in NiAl are compared experimentally and theoretically with the equivalent levels in Ni and Al. Surprisingly, the Ni core shifts to higher binding energy and the Al to lower as if charge were transferred from Ni to Alopposite to the direction predicted from electronegativity. These observations are discussed in terms of bonding in NiA1. 42 1582 1990 The American Physical Society 42 ELECTRONIC STRUCTURE OF NiAl 1583 from Ni to Al), leading to a net transfer from nickel to aluminum.This is consistent with the observed corelevel shifts, which are in the direction of larger binding energy for the nickel and smaller binding energy for the aluminum. Shifts to the lower binding energy are usually attributed to an increase in electron number at a site which increases the Coulomb repulsion with the cores and reduces the binding energy.

An exact study of charge-spin separation, pairing fluctuations and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T ), magnetic field (h), on-site interaction (U ) and chemical potential (µ). Our results, near the average number of electrons N ≈ 3, strongly suggest the existence of a critical parameter Uc(T ) for the localization of electrons and a particle-hole binding (positive) gap ∆ e−h (T ) > 0 at U > Uc(T ), with a zero temperature quantum critical point, Uc(0) = 4.584. For U < Uc(T ), particle-particle pair binding is found with a (positive) pairing gap ∆ P (T ) > 0. The ground state degeneracy is lifted at U > Uc(T ) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers (1 ≤ N ≤ 8) of electrons. In contrast, for U ≤ Uc(T ), we find an electron pair binding instability at finite temperature near N ≈ 3, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin-spin pairing, (spin) pseudogap and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich ( N = 2), hole-poor ( N = 4) and magnetic ( N = 3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high Tc cuprates.

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