A Tight-Binding Study of Very Thin Transition Metal Film Magnetic Anisotropy
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A TIGHT-BINDING STUDY OF VERY THIN TRANSITION METAL FILM MAGNETIC ANISOTROPY
PICK I and H. DREYSSE 2 J. Heyrovskj Institute of Physical Chemistry and Electrochemistry, Academy of Sciences of the Czech Republic, CS-182 23 Prague 8, Czech Republic 2 Laboratoire de Physique du Solide, B.P. 239, 54506 Vandoeuvre-les-Nancy, France 1
ABSTRACT We discuss shortly some problems that have been met in recent systematic calculations of the magnetic anisotropy energy ( MAE ) performed by the present authors as well as in studies of other investigators. As an example, we present MAE for ferromagnetic (001) bilayers with antiferromagnetic interplane coupling and for an antiferromagnetic (001) monolayer. It appears that antiferromagnetism can invoke specific effects and under certain conditions, both MAE and magnetic orbital moment are strongly enhanced. Due to the symmetry lowering at transition metal surfaces and in films, the magnetic (magnetocrystalline) anisotropy energy (MAE) is enhanced with respect to its bulk value. It is, nevertheless, small enough ( 10-4 - 10-3eV) to make its evaluation difficult. Recently, the present authors completed an extensive semi-empirical study 1,2 of MAE in transition metal mono- and bilayers, respectively. Into the common tight-binding d-band Hamiltonian for magnetic films the spin-orbit coupling (SOC) operator was introduced to account for the magnetic anisotropy and the relevant quantities were evaluated by using the recursion method. The model parameters were fitted to reproduce the data for the iron overlayer at the Au(001) surface (large exchange splitting case) or for the free-standing Ni(001) monolayer (small exchange splitting). With the above parameters, MAE has been calculated for a number thin films as a function of the d-electron occupation Nd . Simultaneously a formal analysis of the Hamiltonian moments Mk= TrH* has been performed. By using a mathematical theorem we have shown that MAE changes its sign four-times at least as Nd varies from 0 to 10. It appears, however, that a number of oscillatory features are imposed on the MAE curve that in some cases mask completely the "canonical" form suggested by the moment analysis. Presently, there are strong indications 1-4 showing that the irregular features on the MAE curve originate from the energy-band crossings at the Fermi level EF removed by the SOC. According to ref. 4 such contributions to MAE are of order ý • A where ý is the SOC parameter and A is the area in the 2-dim Brillouin zone where the quasidegenerate perturbation theory is valid. Since for the band crossing in an isolated point generally A _ ý2 the authors of ref. 4 conclude that the contribution is small in comparison with the 2nd order perturbation theory terms and the irregular features come from numerical errors. Let us stress, nevertheless, that our calculations are free
Mat. Res. Soc. Symp. Proc. Vol. 313. @1993 Materials Research Society
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from the possible sources (special integration grid and EF independent of ý ) of numerical inaccuracy listed in ref
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