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Local moments, electron correlation and density functional theory
Author(s) -
Stoddart J. C.,
March N. H.,
Wiid D.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560050883
Subject(s) - magnetic moment , wave function , chemistry , density functional theory , electron , magnetism , physics , condensed matter physics , density matrix , atomic orbital , atomic physics , spin (aerodynamics) , ground state , spins , wannier function , quantum mechanics , thermodynamics , quantum
In earlier work, the magnetism of pure metals has been discussed in terms of the total energy E as a functional of the densities ρ ± ( r ) of electrons with upward and downward spins. In the present paper, the problem of local moment formation when a magnetic impurity such as Fe or Co is added to a non‐magnetic metallic matrix such as Cu or Al is considered. It is shown that at the heart of the theory is a one‐body spin‐dependent potential V σ( r ) which can be divided into four parts V σ( r ) = V̄ ( r ) + V ( r ) + V c ( r ) + V σ( r ). Here V̄ is the potential generating the bands of the matrix metal, with dispersion relation ε( k ) and Wannier function w ( r ). V ( r ) generates the impurity state, with energy ε d and wave function ϕ d , while V c (r) denotes the coupling between this d ‐state and the bands. Finally, and most importantly, V σ( r ) represents the effects of electron correlations on the impurity site. Using this one‐body potential, the density ρσ( r ) can be calculated, in principle exactly, by summing the squares of the occupied orbitals of the potential V σ( r ). This spin density has three components. The first involves the square of the Wannier function w , with weight determined by parameters n σ. The second involves the product of ϕ d and w , with weight m σ while the third comes from ϕ 2 d , with weight l σ. The total energy E [ρ +, ρ‐] becomes a function of l σ, m σ and n σ. It is shown that the Hartree‐Fock solution of Anderson is readily regained solely from the dependence of the energy on l σ. The present work shows how the dependence of the total energy on m and n can be formally incorporated into the theory. The main effects can be described by changes in the self‐energy in the Anderson solution, this becoming now spin‐dependent. If, eventually, spin and charge densities could be measured around impurities having local moments, it is pointed out that the one‐body potentials V σ( r ) could be obtained. Matrix elements of the one‐body potential with respect to ϕ d and w ( r ) then give direct information on electron correlation. A brief discussion of the relation of the present approach to the calculation of Schrieffer and coworkers of the many‐body partition function is given.