# an electronic model for amorphous systems

Post on 21-Jun-2016

215 views

Embed Size (px)

TRANSCRIPT

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 (AV0

754

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.

Recommended