Journal of Magnetism and Magnetic Materials 54-57 (1986) 279-280

ELECTRONIC STRUCTURE AND MAGNETISM IN AMORPHOUS ALLOYS LOCAL ICOSAHEDRAL ORDER

M.E. McHENRY, M.E. EBERHART, R.C. O’HANDLEY and K.H. JOHNSON

Department of Materials Science and Engineering, MIT, Cambridge, MA 02139, USA

279

EXHIBITING

The influence of icosahedral short range order on electronic structure has been investigated. We have calculated and compared the electronic structure for 13 atom Co clusters in I, and 0, symmetry. The two clusters have state densities and magnetic moments which are essentially similar and closely resemble bulk properties.

There is increasing evidence for the existence of icosahedral order in many amorphous and other meta- stable non-crystalline materials [l]. We have chosen to examine the implications of local icosahedral order on electronic structure using self-consistent-field Xa scattered wave (SCF-X&SW) molecular orbital cluster calculations. This work is motivated by the assumed role of icosahedral local order in amorphous metallic

alloys and particularly its possible involvement in a lst-order displacive transformation inferred from mag- netic properties anomalies in Co-rich metallic glasses

[21. We have calculated electronic structure of Co,, clus-

ters in both octahedral (0,) symmetry typical of crys- talline fee cobalt and in icosahedral symmetry (Ih), in both the spin-degenerate and spin-unrestricted modes so as to model magnetic properties, also. Whereas icosahedral symmetry has been found to dramatically influence has electronic structure of free-electron-like Al alloys [3], the effect on cobalt electronic structure is more subtle. Strong similarities between the electronic density of states (DOS) of the I, and 0, Co,, clusters will be shown, lending credence to the assertion that Co behaves similarly in the glassy and crystalline phases. Co is known to show little difference in moment be- tween its cubic and hexagonal close packed phases [4,5].

For the purpose of comparison with band structure calculations it is convenient to define a cluster density of states (CDOS). This CDOS is obtained through an arbitrary Gaussian broadening of the molecular orbital (MO) eigenvalues. Fig. 1 compares CDOS for 13-atom Co clusters, in octahedral and icosahedral symmetry, respectively, with the density of a states (DOS) arrived at from a band structure calculation [6] (all for spin-de- generate (unpolarized) Co). The similarities between these three electronic structures are striking. Fig. la shows the DOS for bulk, fee Co to be characterized by five distinct peaks. These features are mirrored in the Co,, cluster with I,, symmetry, while for the 0, cluster a sixth peak is observed due to the splitting of peak 3. Peak 1 represents the large DOS at the Fermi level ( EF)

typical of ferromagnetic transition metals. Consistent with similar calculations of Fe [7] and Ni [8] clusters,

the peak in the CDOS at E, for both Co,, clusters is dominated by MOs of primarily antibonding character.

The narrower energy range occupied by peaks 2-5 in the clusters compared with that in the bulk band struc- ture is primarily a cluster size effect and is broadened for calculations on larger clusters (see results for a Co,, cluster [9]). Peak 3 is characterized for both Co,, CDOS by d-states of bonding character. The absence of second neighbors in these small clusters leaves non-bonding orbitals at higher energies helping to explain the split- ting of peak 3 for the 0, cluster. In the I, cluster, all d states are symmetrically equivalent and therefore peak 3 remains unsplit. Peak 4 in both CDOS is characterized

(bi ~0,~

I, Cluster

5 I1 I I-

(C) co,,

0, Cluster

5 1 I 1 IN

-0 -6 -4 -2 0

ENERGY CeV)

Fig. 1. (a) DOS for crystalline fee Co adapted from ref. [6]; (b) CDOS from Co,, cluster in I,, symmetry; (c) CDOS for Co,, cluster in 0, symmetry.

0304-8853/86/$03.50 0 Elsevier Science Publishers B.V.

by spd hybrid bonding states. Peak 5 is derived from a quantitative agreement with the band structure results MO of a, symmetry of predominately sp character. for fee cobalt).

In order to evaluate the magnetic properties of our model clusters. MO energy eigenvalues were recalcu- lated in a spin unrestricted fashion yielding both a majority spin and minority spin CDOS. Fig. 2 shows the resulting CDOS for the Co,, icosahedral cluster. This CDOS shows many features which are in general qualitative agreement with features of the DOS for bulk fee Co. The spin polarization of the Co,, I, cluster yields a magnetic moment of 1.61p, corresponding to a net excess of 21 electrons in the spin up levels. This value compares well with the calculated values of 1.56~” for bulk crystalline fee Co [5,6] and the measured 3d orbital spin moment contribution of 1.56pr,, per Co atom [9]. Also consistent is the fully occupied majority- spin band. While detailed differences in exchange split- ting are calculated from level to level, the majority and minority spin bands of I, Co,, are fairly well described 3s being rigidly split by approximately 1.5 eV (in good

Cluster values of magnetic moment and exchange splitting agree well between I, and 0, symmetry and with band theory. A slight difference in the cluster moments may possibly be attributable to a faster con- vergence of icosahedral clusters to bulk-like properties. The magnetic moment is sensitive to local coordination and in the case of the icosahedral cluster each Co atom on the surface of the cluster is coordinated by six other Co atoms, while for an octahedral 13-atom cluster this surface coordination number is five. The average mag- netic moment is seen to increase from 1.46 to 1.52~~ on going from a 13-atom to a 19-atom cluster in 0, sym- metry [lo] consistent with the higher average coordina- tion of the latter.

These calculations indicate that from the standpoint of magnetic and electronic properties, local icosahedral and octahedral order are essentially similar. Given the

rather small energy differences between the two struc- tures. it is possible that transformations between the two local symmetries could be activated with small thermal energies. It therefore remains quite plausible that these two local symmetries are involved in the I St-order displacive phase transformation observed [3] and modelled [lo] in Co-rich metallic glasses. This

transformation has been characterized as occurring be- tween states with similar magnetic moments at satura- tion but differing in their magnetic anisotropy. The similar magnetic moments of the 1, and 0,, clusters are consistent with this observation. Further, the difference in symmetry between the I, and 0, point groups could account for the observed difference in magnetic ani-

I I I I I I I I

t MAJORITY SPIN

MINORITY SPIN

J

I-

:

I I

I 1 I I

I I I I I I I I 7 6 5 4 3 2 I 0

- E(eV)

Fig. 2. M~JWIIY spin (a) and minority spin (h) CDOS for Co, 1 cluster in I, symmetry.

sotropy.

This work is supported by grant the National Science Foundation.

DMR 8318829 from

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