Electronic Structure of Magnetic Impurities in Copper

Abstract

A model is presented for dilute iron-series magnetic impurities in copper, which is a generalization of the work of Anderson and the work of Wolff taking into consideration the band structure of copper. The impurity virtual states are treated as bound states pushed out of the 3d bands of copper and broadened into virtual states by admixture with the conduction band. The copper energy bands are represented by an interpolation scheme developed by Hodges and Ehrenreich fit to the energy-band calculation done by Burdick. The equations of motion for the single-particle Green's function of the perturbed lattice are solved in the Hartree-Fock approximation using the Koster-Slater method, and from this Green's function the charge density is calculated and used to solve the equations of motion self-consistently. The bound states at or above the Fermi energy are found to be better than 95% localized to the impurity site, and therefore simplifications result from treating the problem in a hole formalism (i.e., the localized moment is attributed to unoccupied bound states at the impurity site). The effects of crystal-field splitting and spin-orbit coupling on the bound states are discussed. Bohr magneton numbers are calculated and found to be in agreement with experiment in most cases. The net polarization of the conduction bands is also discussed and found to agree semiquantitatively with experiment.

Band Structure, Fermi Surface, and Knight Shift of Indium Metal

“…The cyclotron mass of the £ arms for a magnetic field in the (110) direction has been determined by Brandt and Rayne 6 from the temperature variation of the de Haas-van Alphen oscillations using the relationship m*/fn 0 =(l/w)dA'/dE, (8) dA/dE being the rate of change of cross-sectional area with energy and m 0 the free-electron mass. The experimental value is found to be (w*/^o)ex P =0.19.…”

“…Two other properties which are currently available for indium and which could be used as a test of the accuracy of the wave functions and the model adopted are the anisotropic Knight shift and the nuclear quadrupole coupling constant. 7,8 However, an evaluation of these properties will have to await accurate methods of interpolating wave functions in k space because they require for their interpretation careful integrations throughout the Fermi volume and over the Fermi surface.…”

“…Indium is a particularly suitable metal for such an investigation because of the wealth pf data of both kinds which are currently available for it. 5 " 8 The choice and evaluation of the crystal potential are described in Sec. II.…”

Scattering model for the bound electronic states of an impurity complex in a crystal

“…Much of it is based on the original work of Koster and Slater (KS) [ 5 ] , in which the impurity wave functions are expanded in terms of Wannier functions for the perfect crystal. For detailed applications of the KS method to the theory of the localized states of defects in semiconductors and to the theory of localized magnetic moments in metals, the reader may consult the recent papers by Callaway and Hughes [6] and Sokoloff [7], respectively.…”

“…At negative energies they assume the form t = u + UGU + UGUGU + * . -(7) t;(E) = (-1)'~-'[Rz('> ' u ) , iz(~bu)I/[Rz(E, b a ) , k i ' ) (~b u ) I (expression (24) of (I)). For the positive-energy case see equation (33) of (I).…”