Magnetic moments on 3D-impurities in Cu-based alloys

Formalism is developed to evaluate spin-dependent conduction electron density Δnσ(r) where σ denotes the spin. Mixed band scheme is used in which 3d-electrons of the impurity are represented in the simple tight binding approximation and the host metal in the free-electron approximation. The total Δnσ(r) is found to be the sum of free electron and d-electron contributions. The free electron contribution exhibits the usual 1/r³ radial dependence but the d-electron contribution exhibits R_d(r)/r² and R_d(r)/r³ radial dependence where R_d(r) is the radial part of 3d-wave function. The formalism is applied to calculate spin density distribution Δn_spin^(r) and magnetic moments on V, Cr and Fe impurities in Cu metal. It is found that within the Wigner-Seitz (WS) cell it is the d-electron contribution, which dominates Δn_σ(r) and Δn_spin(r) in all the alloys but outside the WS cell it approaches zero and such a behaviour is due to the quasilocalized nature of d-electrons. In the asymptotic limit both Δn_σ(r) and Δn_spin(r) exhibit Friedel oscillations. Further, the calculated local and total magnetic moments on all the three impurities exhibit reasonable agreement with the experimental values. So the present formalism explains well the existence of magnetic moments on 3d-impurities in Cu metal and can also be extended to f-electron impurities in metallic systems.