Effective Interatomic Interactions VIA The TB-LMTO Method
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INTERACTIONS METHOD
VIA
THE TB-LMTO
V. DRCHALa"b, J. KUDRNOVSKYa,b, A. PASTURELC, I. TUREK'd, P. WEINBERGERb, A. GONISe, and P.E.A. TURCHIe aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-180 40 Praha 8, Czech Republic blnstitute for Technical Electrochemistry, Technical University of Vienna, Getreidemarkt 9, A-1060 Vienna, Austria cExperimentation Numdrique, Maison des Magist~res, CNRS, BP 166, 38042 Grenoble Cedex, France dlnstitute of Physics of Materials, Academy of Sciences of the Czech Republic, Zi~kova 22, CZ-616 62 Brno, Czech Republic eLawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A.
ABSTRACT The energetics of metallic alloys, their surfaces or interfaces, and magnetic multilayers is studied in terms of effective interatomic (or interlayer) interactions that are determined from ab initio electronic structure calculations using the TB-LMTO method combined with the coherent potential approximation and the method of surface Green functions. First the theoretical background (force theorem, Lloyd formula, generalized perturbation method for bulk and surfaces, vertex cancellation theorem, method of infinitesimal rotations) is discussed, and then the applications to the phase stability of bulk alloys, surface segregation in disordered alloys, magnetism-induced ordering in two- and three-dimensional systems, phase diagram of two-dimensional alloys, interlayer exchange coupling in metallic multilayers, and the construction of Heisenberg-like Hamiltonians for magnetic systems are presented. INTRODUCTION The thermodynamical properties of various systems such as alloys, their surfaces, magnetic multilayers, and ferromagnets can be predicted on an ab initio level. First, the internal energy and its dependence on the configuration of the system is expressed in terms of an effective Hamiltonian. The parameters of this Hamiltonian (which are often called effective cluster interactions (ECIs)) are determined from first principles electronic structure calculations. In the second step, the thermodynamical properties of the system are studied by the methods of statistical mechanics. By using an effective Ising-type Hamiltonian the configurational dependence of the total energy of a disordered binary alloy A, BI_ can be expressed as 1 HI=E0 + ZDR rR± +
VRR' • rR, ÷ ....
(1)
2R
R
The parameters entering (1) are the configurationally independent part of the total energy Eo, the on-site energies DR, the interatomic pair nteractions VRrt,, and generally, the interatomic interactions of higher order. A particular configuration of the alloy is determined by a set of occupation indices rta, where rtR 1 if the site R is occupied by an atom of the type A, and rjR 0 otherwise. By using an effective (classical) Heisenberg-type Hamiltonian the total energy of a ferromagnet can be expressed as HH =Eo -
Z
JaR, eR"eR,
RR'
65
... ,
(2)
where eR
m=R/1maj is the unit vector in the direction of a magnetic dipole mR at site R.
THEORY The tight-binding linear muffin-tin orbi
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