# An electronic model for amorphous systems

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752 AN ELECTRONIC MODEL FOR AMORPHOUS SYSTEMS J. SCHREIBER Joint institute for Nuclear Research, Head Post office, P.O. Box 79, 101000 Moscow, USSR Linearly coupled diagonal and off-diagonal randomness are considered using a "cluster-effective-lattice" method where the potential parameters in the cluster are assumed to fluctuate according to a Lorentzian distribution. The density of states, the magnetic properties within a Stoner-like theory, and the localization of electrons are studied. In amorphous or liquid systems diagonal disorder and, first of all, off-diagonal random- ness (ODR) appear [1,2] whereas in general both kinds of disorder are coupled. Hence we use the following tight binding model for a system of N identical atoms forming an amor- phous structure. Instead of the total Hamiltonian we only consider the projection onto the sub- space spanned by the atomic orbitals IP~). Using a second quantization representation the ap- proximated hamiltonian may be written as [2] i jo io (1) Because of the non-orthogonality of ]p~) we have [ai~, ci~+~.] = (S-~)~i, where S is the matrix of overlap integrals. The second term in eq. (1) represents only the Hubbard-like part of elec- tron correlation. We restrict our discussion to cases where (i) the atomic orbitals are well enough localized and (ii) the amorphous struc- ture has a well established short range order. Therefore we can suppose that Vii and S o are different from zero only for i= j and for nearest-neighbours (NN). Considering s-like states IPi), e~ = Vii, Vii, and S o are functions of the atomic distances. Therefore the structure fluctuations of these quantities are coupled so that really only one random variable exists. In a first approximation, expanding ei, V~j, and Sij linearly in the variations of the distances l i - Jl and neglecting three centre integrals, the fol- lowing simple relations can be obtained: ei = A ~ (Vii - Vo) + B, Sir = C(V~i - Vo) + D, (2) where V0 belongs to the averaged atomic posi- tions. The density of states is given by the relation (cf. [2]) p(E) = - 1 /wN~ S,j Im Go(E + i0 +) i,j = I lN~ pi(E), i (3) where Gij is the Zubarev-Green function. We find that Gij obeys the equation (ES i t - Vit)Gij = 8ij. (4) I The structure averaging for p(E) is performed by a self-consistent "cluster-effective-lattice" method. Thereby it is required that the averaged local density of states pi(E) for an atom sur- rounded by its Z NN and embedded in an effective medium- characterized by an effective lattice (the Be lattice or regular one with equivalent short range order) and a coherent hopping integral Vc- is equal to the cor- responding quantity for the effective medium. Numerical computations become easy if we as- sume that in the cluster the Vii fluctuate statis- tically independent according to a Lorentzian distribution with mean value V0 and width F (cf. [2]). Results are shown for a Ni-like effective structure (fig. 1) [3, 4]. Switching on ODR, an asymmetrical change of p(E) is obtained, where the sign of the coupling between e~ and V~i influences the results qualitatively. We note that the case AVo< 0 is the physically realistic one since the ei-level will be lowered if Iv01 becomes greater. The consideration of random overlap integrals (Ca 0) leads also to an asymmetrical change of p(E). Now we investigate the amorphous mag- netism within the Hartree-Fock approximation (HF) for the model (1) (cf. [3, 4]). Assuming that U~ is only determined by the sort of atoms, and incorporating the results for p(E), the Stoner- Physica 86-88B (1977) 752-754 North-Holland 753 0 ferromag- netism (FM) is monotonously weakened in- creasing F. In contrast to that for the "physical" case (AV0754 U[Vo and F will be lowered if pressure is ap- pl ied to amorphous non-metal l ic systems. Then we meet the poss ib i l i ty of real izat ion of a non- meta l -meta l transit ion. This transit ion is a mixed one of the Mott and Anderson type where the dominant mechanism is due to elec- tron correlat ion. The author is very grateful to Dr. W. John and Mr. J. R ichter for valuable d iscuss ions. References [1] G.W. Wright, Amorphous Transition Metal Films, 7th Int. Colloquium on Magnetic Thin Films, Regensburg (1975). [2] J. Schreiber, in: Proc. of VII-th Autumn School on Magnetism, Gaussig (1975). [3] J. Kanemori, J. de Physique C4 (Suppl.) (1974) 131. [4] J. Richter, J. Schreiber and K. Handrich, Phys. Status Solidi (b) 74 (1976) K125.

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