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Molecular-Dynamics Simulations of Magnetic Structures in Metallic Systems Ralf Meyer and Laurent J. Lewis D´epartement de Physique, Universit´e de Montr´eal and Groupe de Recherche en Physique et Technologie des Couches Minces (GCM) C.P. 6128 succursale centre-ville, Montr´eal (Qu´ebec) H3C 3J7, Canada

ABSTRACT Recently a method has been proposed which allows the calculation of complex magnetic structures from a simple d-band tight-binding Hamiltonian including Coulomb and exchange interactions with the help of a molecular-dynamics simulations. In this article an improved version of this approach is suggested which retains the rotational symmetry of the simulated system. The improved algorithm is applied to systems with electron numbers in the range 7  nd  8. INTRODUCTION The magnetism of 3d transition metals is a longstanding problem of materials science. Systems like -Fe, Mn and their alloys show complex magnetic structures which until today are not well understood. A new method to investigate such magnetic structures on the basis of a simple tight-binding Hamiltonian with Coulomb and exchange interactions has recently been proposed by Kakehashi and co-workers [1–3]. In their approach the many-body problem is attacked at finite temperature with the help of a molecular-dynamics simulation. Unfortunately, in the original formulation of the method the rotational symmetry of the system is broken in the course of the simulation. In this article an improved version of the simulation method is proposed which avoids this problem.

THEORETICAL FRAMEWORK Our simulations are based on the theoretical background developed by Kakehashi et al. in Ref. [1]. The starting point of their method is the following tight-binding d-band Hamiltonian:

H=

X

tij ayi aj  + 0

ij  0

X

0

i

X X 0i ayi ai + 14 Ui n2i ; 14 Ji m2i :

i

(1)

i

Herein is tij the transfer integral between orbital  at site i and orbital 0 at site j , ayi (ai ) the creation (annihilation) operator of an electron with spin  in orbital  at site i, and 0i the atomic level atP site i. Further denotes Ui (Ji ) the intra-atomic Coulomb (exchange) interaction parameter, P y y ni =  ai ai the occupation number operator, and mi =  ai () ai (with  being the vector of Pauli Spin- 12 matrices) the magnetic moment at site i. In Ref. [1] an approximate expression for the partition function of the system described by the Hamiltonian (1) is derived with the help of functional integral techniques. From this the following 0

0

AA6.3.1

0

0

expression of the local magnetic moment hmi i as an thermal average over local field variables i can be obtained: Z "Y

hmii =

j

dj

#

1 + ~4 2 Jii

Z "Y

j



i e; (fi g)

#

(2)

dj e; (f g) i





X X niwi(fig) ; 14 J~ii2 + 1 ln i2 (fig) = ; 1 ln Tr e; H (f g) ; i i st

Hst (fig) =

X

tij ayi aj  + 0

ij  0

i

X  0i ;  + wi(fig) ayi ai ; 21 J~i i
mi

X

0

i

(3)

(4)

i

Here, = 1=T is the inverse temperature  the chemical potential, and ni the