Journal of Magnetism and Magnetic Materials 29 (1982) 147-150 147 North-Holland Publishing Company MODIFIED CPA THEORY AS THE METHOD FOR CALCULATION OF THE DENSITY OF STATES FOR MATERIALS HAVING COMPLEX CRYSTAL STRUCTURES Barbara SZPUNAR * Department of Solid State Physics, Academy of Mining and Metallurgy, Krakrw, Poland In the theory presented the structure of crystalline or amorphous materials is described by the number and position of nearest neighbours and by an average medium. CPA theory is modified to the first four moments which makes possible the calculation of the magnetic moments of constituents in different sites. Extension of CPA theory, using the energy dependent potential in CPA equations, provides the possibility of extending previous calculations for any arbitrary shape of the density of states of the average medium. The method presented for calculation of the density of states in alloys can be used for any crystalline and amorphous material. 1. Introduction The CPA theory modified to the first four moments of Green function has been used previ- ously [1,2] for calculating the density of states. In the first paper it was demonstrated that there is a strong influence of the first four moments of the Green function on the density of states and thus the shape of the density of states depends strongly on the crystal structures. In the next paper [2] this method was used to calculate the spin contribution of the Co atoms in two different sites in YCo 5. The calculations agreed well with experimental results. In all previous calculations the contribution from the average medium of farther neighbours has been calculated using CPA theory and assum- ing the elliptic density of states of components. Under this assumption the CPA equations can be solved analytically. Such a possibility is essentially important because the selfconsistent computer calculation of the magnetic moment is time con- suming. In a recently proposed CPPA theory [3] a new solution was presented. The assumption is made that the reference crystal has an elliptic density of states, and the constituents may have * Present address: Physics Department, University of Durham, South Road, Durham DH1 3LE, UK. any arbitrary density. In this work we generalise the method described in the previous paper [2] by introducing the real density of states of the con- stituents of the average medium. Also an accurate calculation of the contribution of the second neighbours for bcc structure is made. 2. Proposed model We consider a model consisting of localised spins, for example coming from the f electrons, and of the narrow band formed i.e. from the s-d hybridised band. The corresponding Hamiltonian has the form: n=~ci, nis+ ~ Tijci+ cj,. (1) is i vajs We introduce the Hartree-Fock approximations for intra-atomic Coulomb repulsion. An assump- tion is made that at zero temperature the spin fluctuation can be neglected, thus we can include the interaction between the localised spin and band electrons into the Cis. We obtain [4]: cis = "i + Ui(ni-s) -- lpiSi°Js X sqn[(<n,s > -- <ni_s))I], (2) where ~i represents the atomic energy levels, U~ the 0304-8853/82/0000-0000/$02.75 © 1982 North-Holland