《纺织复合材料》课程参考文献（Computational Materials Science，From Basic Principles to Material Properties）08 Magnetism, Structure and Interactions at the Atomic Scale

8 Magnetism,Structure and Interactions at the Atomic Scale V.S.Stepanyuk!and W.Hergert2 1 Max Planck Institute of Microstructure Physics,Weinberg 2,06120 Halle, Germany 2 Martin-Luther-University Halle-Wittenberg,Department of Physics, Von-Seckendorff-Platz 1,06120 Halle,Germany Abstract.An efficient scheme is developed to study magnetism and structure as well as interaction between supported particles on the atomic scale.Starting by ab initio calculations of the electronic structure in the framework of density func- tional theory,interaction potentials for molecular dynamics simulations of metallic nanostructures supported on metallic surfaces are carefully optimized. The two methods are shortly explained.Examples for the application of the methods are given.Mainly electronic and structural properties of Co nanostructures on Cu(001)and Cu(111)surfaces are investigated. 8.1 Introduction The essence of nanoscience and technology is the ability to understand and manipulate matter at the atomic level.Structures behave differently when their dimensions are reduced to dimensions between 1 and 100 nm. Such structures show novel physical and chemical properties,due to their nanoscopic size. In the frontier field of nanomagnetism,understanding of the relationship between magnetism and structure plays a central role.During the past few years experimental investigations of metallic nanostructures in the initial stage of heteroepitaxial growth revealed a lot of information which asks for a consistent theoretical explanation.Some important effects experimentally observed recently are: Surface alloying is found also for metals immiscible in bulk form (i.e.Co onCu(001)).[8.1,8.2 Burrowing of Co clusters into Au,Cu and Ag surfaces has been observed. [8.3.8.4 It was observed,that the motion of adatoms on top of islands is not the same as on a fat surface.[8.5 Fast island decay in homoepitaxial growth was observed by Giesen et al. [8.6-8.9] By using STM(scanning tunnelling microscope)adsorbate manipulation techniques,it is possible to construct atomic-scale structures on metal sur- faces and to study artificially confined quantum systems.[8.10] V.S.Stepanyuk and W.Hergert,Magnetism,Structure and Interactions at the Atomic Scale, Lect.Notes Phys.642,159-176(2004) http://www.springerlink.com/ C Springer-Verlag Berlin Heidelberg 2004

8 Magnetism, Structure and Interactions at the Atomic Scale V.S. Stepanyuk1 and W. Hergert2 1 Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany 2 Martin-Luther-University Halle-Wittenberg, Department of Physics, Von-Seckendorff-Platz 1, 06120 Halle, Germany Abstract. An efficient scheme is developed to study magnetism and structure as well as interaction between supported particles on the atomic scale. Starting by ab initio calculations of the electronic structure in the framework of density func￾tional theory, interaction potentials for molecular dynamics simulations of metallic nanostructures supported on metallic surfaces are carefully optimized. The two methods are shortly explained. Examples for the application of the methods are given. Mainly electronic and structural properties of Co nanostructures on Cu(001) and Cu(111) surfaces are investigated. 8.1 Introduction The essence of nanoscience and technology is the ability to understand and manipulate matter at the atomic level. Structures behave differently when their dimensions are reduced to dimensions between 1 and 100 nm. Such structures show novel physical and chemical properties, due to their nanoscopic size. In the frontier field of nanomagnetism, understanding of the relationship between magnetism and structure plays a central role. During the past few years experimental investigations of metallic nanostructures in the initial stage of heteroepitaxial growth revealed a lot of information which asks for a consistent theoretical explanation. Some important effects experimentally observed recently are: – Surface alloying is found also for metals immiscible in bulk form (i.e. Co on Cu(001) ). [8.1, 8.2] – Burrowing of Co clusters into Au, Cu and Ag surfaces has been observed. [8.3, 8.4] – It was observed, that the motion of adatoms on top of islands is not the same as on a flat surface. [8.5] – Fast island decay in homoepitaxial growth was observed by Giesen et al. [8.6–8.9] – By using STM (scanning tunnelling microscope) adsorbate manipulation techniques, it is possible to construct atomic-scale structures on metal sur￾faces and to study artificially confined quantum systems. [8.10] V.S. Stepanyuk and W. Hergert, Magnetism, Structure and Interactions at the Atomic Scale, Lect. Notes Phys. 642, 159–176 (2004) http://www.springerlink.com/
c Springer-Verlag Berlin Heidelberg 2004

160 V.S.Stepanyuk and W.Hergert To discuss all the effects from theoretical point of view,to get a deep under- standing of the underlying physics,it is absolutely necessary to investigate the real structure of the system as well as the electronic and magnetic struc- ture of the nanosystems,because these aspects are strongly interconnected on the atomic scale. Our combination of the Korringa-Kohn-Rostoker (KKR)Green's func- tion(GF)method with a molecular dynamics(MD)scheme allows us to study the effects mentioned above in detail. We will discuss the methods briefly.The magnetic properties of metallic nanostructures are discussed.We start from an ideal lattice structure and take into account step by step imperfections,mixing and relaxations.The effect of quantum interference and the implications for long-range interactions and self-organization are discussed next.Finally,we introduce the new concept of mesoscopic misfit and discuss the consequences for strain fields,adatom motion and island decay. 8.2 Theoretical Methods 8.2.1 Calculation of Electronic Structure Our calculations are based on the density functional theory and multiple- scattering approach using the Korringa-Kohn-Rostoker Green's function method for low-dimensional systems [8.11].The basic idea of the method is a hierarchical scheme for the construction of the Green's function of adatoms on a metal surface by means of successive applications of Dyson's equation. We treat the surface as an infinite two-dimensional perturbation of the bulk. fcc(001) Fig.8.1.Structure to calculate the surface Green's function for the (001)surface of the fcc-structure (blue -decoupled half-crystals,brown-vacuum layers). For the construction of the ideal surface the nuclear charges of several monolayers are removed,thus creating two half crystals being practically

160 V.S. Stepanyuk and W. Hergert To discuss all the effects from theoretical point of view, to get a deep under￾standing of the underlying physics, it is absolutely necessary to investigate the real structure of the system as well as the electronic and magnetic struc￾ture of the nanosystems, because these aspects are strongly interconnected on the atomic scale. Our combination of the Korringa-Kohn-Rostoker (KKR) Green’s func￾tion(GF) method with a molecular dynamics (MD) scheme allows us to study the effects mentioned above in detail. We will discuss the methods briefly. The magnetic properties of metallic nanostructures are discussed. We start from an ideal lattice structure and take into account step by step imperfections, mixing and relaxations. The effect of quantum interference and the implications for long-range interactions and self-organization are discussed next. Finally, we introduce the new concept of mesoscopic misfit and discuss the consequences for strain fields, adatom motion and island decay. 8.2 Theoretical Methods 8.2.1 Calculation of Electronic Structure Our calculations are based on the density functional theory and multiple￾scattering approach using the Korringa-Kohn-Rostoker Green’s function method for low-dimensional systems [8.11]. The basic idea of the method is a hierarchical scheme for the construction of the Green’s function of adatoms on a metal surface by means of successive applications of Dyson’s equation. We treat the surface as an infinite two-dimensional perturbation of the bulk. Fig. 8.1. Structure to calculate the surface Green’s function for the (001) surface of the fcc-structure (blue -decoupled half-crystals, brown - vacuum layers). For the construction of the ideal surface the nuclear charges of several monolayers are removed, thus creating two half crystals being practically

8 Magnetism,Structure and Interactions at the Atomic Scale 161 uncoupled.Taking into account the 2D periodicity of the ideal surface,we calculate the structural Green's function by solving a Dyson equation self- consistently: ()(+)(E)G EX8.1) j"L Here G is the structural Green's function of the bulk in a k-layer representa- tion(j,j-layer indices).The k wave vector belongs to the 2D Brillouin zone. △t,(E)is the perturbation of the t matrix to angular momentum L=(亿，m) in the j-th layer. The consideration of adsorbate atoms on the surface destroys the trans- lation symmetry.Therefore the Green's function of the adsorbate adatom on the surface has to be calculated in a real space formulation.The structural Green's function of the ideal surface in real space representation is then used as the reference Green's function for the calculation of the adatom-surface system from an algebraic Dyson equation: G(E)=Gt(E)+∑G2(E)4t%(E)G院(E, (8.2) n"Eu where G(E)is the energy-dependent structural Green's function matrix onn and GLL(E)the corresponding matrix for the ideal surface,serving as a reference system.At(E)describes the difference in the scattering properties at site n induced by the existence of the adsorbate atom. Exchange and correlation effects are included in the local density approx- imation.The full charge density and the full potential approximation can be used in the calculations.Details of the method and several of its applications can be found elsewhere [8.11]. 8.2.2 Molecular Dynamics Simulations In the last years we developed a method which connects the ab initio elec- tronic structure calculations with large scale molecular dynamics simulations. Our approach is based on fitting of the interaction parameters of potentials for molecular dynamic simulations to accurate first-principle calculations of selected cluster-substrate properties,bulk properties and forces acting on adatoms of the system under investigation.8.12 To describe metallic clusters on noble metal substrates,many body poten- tials in the second moment tight-binding approximation are used.[8.13,8.14] The cohesive energy Ecoh is the sum of the band energy EB and the repulsive part ER

8 Magnetism, Structure and Interactions at the Atomic Scale 161 uncoupled. Taking into account the 2D periodicity of the ideal surface, we calculate the structural Green’s function by solving a Dyson equation self￾consistently: Gjj
LL
(k , E) = G˚jj
LL
(k , E) +  j

L

G˚jj

LL

(k , E)∆tj

L

(E)Gj

j
L

L
(k , E)(8.1) . Here G is the structural Green’s function of the bulk in a ˚ k -layer representa￾tion (j, j - layer indices). The k wave vector belongs to the 2D Brillouin zone. ∆tj L(E) is the perturbation of the t matrix to angular momentum L = (l, m) in the j-th layer. The consideration of adsorbate atoms on the surface destroys the trans￾lation symmetry. Therefore the Green’s function of the adsorbate adatom on the surface has to be calculated in a real space formulation. The structural Green’s function of the ideal surface in real space representation is then used as the reference Green’s function for the calculation of the adatom-surface system from an algebraic Dyson equation: Gnn
LL
(E) = G˚nn
LL
(E) +  n

L

G˚nn

LL

(E)∆tn

L

(E)Gn

n
L

L
(E), (8.2) where Gnn
LL
(E) is the energy-dependent structural Green’s function matrix and G˚nn

LL

(E) the corresponding matrix for the ideal surface, serving as a reference system. ∆tn L(E) describes the difference in the scattering properties at site n induced by the existence of the adsorbate atom. Exchange and correlation effects are included in the local density approx￾imation. The full charge density and the full potential approximation can be used in the calculations. Details of the method and several of its applications can be found elsewhere [8.11]. 8.2.2 Molecular Dynamics Simulations In the last years we developed a method which connects the ab initio elec￾tronic structure calculations with large scale molecular dynamics simulations. Our approach is based on fitting of the interaction parameters of potentials for molecular dynamic simulations to accurate first-principle calculations of selected cluster-substrate properties, bulk properties and forces acting on adatoms of the system under investigation. [8.12] To describe metallic clusters on noble metal substrates, many body poten￾tials in the second moment tight-binding approximation are used. [8.13, 8.14] The cohesive energy Ecoh is the sum of the band energy EB and the repulsive part ER

162 V.S.Stepanyuk and W.Hergert Eoh=∑(E路+R) (8.3) 1/2 -2aa/-l (8.4) E=∑(（Aier/r88-1)+4A8a)ep(-pas(r/n6-10 (8.5) whererij represents the distance between the atoms i and j,and ro is the first-neighbour distance in the a,B lattice structure,while it is just an adjustable parameter in the case of the cross interaction.is an effective hopping integral and depends on the material and gos and pas describe the dependence of the interaction strength on the relative interatomic distance. Table 8.1.Data used for the fitting of the potential together with the values calculated with the optimized potential.(cohesive energy Ec,bulk modulus B,elas- tic constants C from Cleri et al.[8.13],first and second neighbour interaction energies Efgc,Eco from Hoshino et al.8.15]solution energy Eon Cu from Drittler etal 816]and binding energies of small CoclustersE)E E2x2island oncu(oo)are calculated using the KKR Green's function method. quantity data fitted value Cu aCu 3.615A 3.614A (fcc) e 3.544eV 3.545eV 1.42 Mbar 1.42 Mbar C11 1.76 Mbar 1.76 Mbar C12 1.25 Mbar 1.25 Mbar C44 0.82 Mbar 0.82 Mbar Co aC 2.507A 2.515A Ee 4.386eV 4.395eV B 1.948 Mbar 1.989 Mbar C1 3.195 Mbar3.337 Mbar C12 1.661 Mbar 1.426 Mbar C13 1.021 Mbar 1.178 Mbar C33 3.736 Mbar 3.665 Mbar C44 0.824 Mbar 0.646 Mbar ●o-Cu Eso in Cu 0.4eV 0.38eV -0.12eV -0.18eV 0.03eV -0.05eV ECu(001) -1.04eV -1.04eV ECn Cu -0.26eV -0.35eV -2.06eV -1.96eV -3.84eV -3.86eV

162 V.S. Stepanyuk and W. Hergert Ecoh =  i Ei B + Ei R  (8.3) Ei B = −   j ξ2 αβ exp(−2qαβ(rij/rαβ 0 − 1))   1/2 (8.4) Ei R =  j  A1 αβ(rij/rαβ 0 − 1)) + A0 αβ exp(−pαβ(rij/rαβ 0 − 1)) (8.5) where rij represents the distance between the atoms i and j, and r αβ 0 is the first-neighbour distance in the α, β lattice structure, while it is just an adjustable parameter in the case of the cross interaction. ξ is an effective hopping integral and depends on the material and qαβ and pαβ describe the dependence of the interaction strength on the relative interatomic distance. Table 8.1. Data used for the fitting of the potential together with the values calculated with the optimized potential. (cohesive energy Ec, bulk modulus B, elas￾tic constants Cij from Cleri et al. [8.13], first and second neighbour interaction energies ECo-Co 1,b , ECo-Co 2,b from Hoshino et al. [8.15] solution energy ECo in Cu S from Drittler et al. [8.16] and binding energies of small Co clusters ECo-Co 1,on Cu(001), ECo-Co 1,in Cu, Etrimer on Cu(100), E2×2island on Cu(100) are calculated using the KKR Green’s function method. quantity data fitted value Cu aCu 3.615 ˚A 3.614 ˚A (fcc) Ec 3.544 eV 3.545 eV B 1.42 Mbar 1.42 Mbar C11 1.76 Mbar 1.76 Mbar C12 1.25 Mbar 1.25 Mbar C44 0.82 Mbar 0.82 Mbar Co aCo 2.507 ˚A 2.515 ˚A Ec 4.386 eV 4.395 eV B 1.948 Mbar 1.989 Mbar C11 3.195 Mbar 3.337 Mbar C12 1.661 Mbar 1.426 Mbar C13 1.021 Mbar 1.178 Mbar C33 3.736 Mbar 3.665 Mbar C44 0.824 Mbar 0.646 Mbar Co-Cu ECo in Cu S 0.4 eV 0.38 eV ECo-Co 1,b -0.12 eV -0.18 eV ECo-Co 2,b 0.03 eV -0.05 eV ECo-Co 1,on Cu(001) -1.04 eV -1.04 eV ECo-Co 1,in Cu -0.26 eV -0.35 eV Etrimer on Cu(100) -2.06 eV -1.96 eV E2×2 island on Cu(100) -3.84 eV -3.86 eV

8 Magnetism,Structure and Interactions at the Atomic Scale 163 We will explain the method for the system Co/Cu(001).Co and Cu are not miscible in bulk form.Therefore the determination of the cross interac- tion is a problem.A careful fitting to accurate first-principles calculations of selected cluster substrate properties solves the problem.The result is a manageable and inexpensive scheme able to account for structural relaxation and including implicitly magnetic effects,crucial for a realistic determination of interatomic interactions in systems having a magnetic nature.After de- termination of the Cu-Cu parameters,which are fitted to experimental data only 8.14,the Co-Co and Co-Cu parameters are optimized simultaneously by including in the fit the results of first-principles KKR calculations.To this purpose,we have taken the solution energy of a single Co impurity in bulk Cu ESo in Cu [8.16],energies of interaction of two Co impurities in Cu bulk 815]EoEand binding energies of small supported Co clusters oCu(100)E2x2 island on Cu(001)-E)E(terrace position),E on Cu(100) The set of data used to define the potential and the corresponding values cal- culated by means of the optimized potential are given in Table 8.1.The bulk and surface properties are well reproduced. The method,discussed so far has been further improved.We are able to calculate forces on atoms above the surface on the ab initio level.The forces are also included in the fitting procedure.This gives a further improvement of the potentials used in the MD simulations.It should be mentioned that our method allows also to use only ab initio bulk properties from KKR cal- culations.Therefore,we can construct ab initio based many-body potentials. 8.3 Magnetic Properties of Nanostructures on Metallic Surfaces Using the KKR Green's function method we have studied the properties of 3d,4d and 5d adatoms on Ag(001),Pd(001)and Pt(001)systematically. 8.17,8.18 One central point of investigation was the study of imperfect nanostructures.We have investigated the influence of Ag impurities on the magnetism on small Rh and Ru clusters on the Ag(001)surface.[8.19]The change of the magnetic moments could be explained in the framework of a tight-binding model.Nevertheless it was observed that the magnetism of Rh nanostructures shows some unusual effects.8.20]An anomalous increase in the magnetic moments of Rh adatoms on the Ag(001)surface with decreasing interatomic distance between atoms was observed,whereas for dimers of other transition metals the opposite behaviour is found. In this chapter we will discuss some selected results for the real,electronic and magnetic structure of metal nanostructures on noble metal surfaces.We will concentrate our discussion on one special system:Co nanostructures on Cu surfaces.Although a special system is investigated general conclusions can be drawn

8 Magnetism, Structure and Interactions at the Atomic Scale 163 We will explain the method for the system Co/Cu(001). Co and Cu are not miscible in bulk form. Therefore the determination of the cross interac￾tion is a problem. A careful fitting to accurate first-principles calculations of selected cluster substrate properties solves the problem. The result is a manageable and inexpensive scheme able to account for structural relaxation and including implicitly magnetic effects, crucial for a realistic determination of interatomic interactions in systems having a magnetic nature. After de￾termination of the Cu-Cu parameters, which are fitted to experimental data only [8.14], the Co-Co and Co-Cu parameters are optimized simultaneously by including in the fit the results of first-principles KKR calculations. To this purpose, we have taken the solution energy of a single Co impurity in bulk Cu ECo in Cu S [8.16], energies of interaction of two Co impurities in Cu bulk [8.15] ECo-Co 1,b , ECo-Co 2,b and binding energies of small supported Co clusters on Cu(001) - ECo-Co 1,on Cu(001), ECo-Co 1,in Cu (terrace position), Etrimer on Cu(100), E2×2 island on Cu(100). The set of data used to define the potential and the corresponding values cal￾culated by means of the optimized potential are given in Table 8.1. The bulk and surface properties are well reproduced. The method, discussed so far has been further improved. We are able to calculate forces on atoms above the surface on the ab initio level. The forces are also included in the fitting procedure. This gives a further improvement of the potentials used in the MD simulations. It should be mentioned that our method allows also to use only ab initio bulk properties from KKR cal￾culations. Therefore, we can construct ab initio based many-body potentials. 8.3 Magnetic Properties of Nanostructures on Metallic Surfaces Using the KKR Green’s function method we have studied the properties of 3d, 4d and 5d adatoms on Ag(001), Pd(001) and Pt(001) systematically. [8.17, 8.18] One central point of investigation was the study of imperfect nanostructures. We have investigated the influence of Ag impurities on the magnetism on small Rh and Ru clusters on the Ag(001) surface. [8.19] The change of the magnetic moments could be explained in the framework of a tight-binding model. Nevertheless it was observed that the magnetism of Rh nanostructures shows some unusual effects. [8.20] An anomalous increase in the magnetic moments of Rh adatoms on the Ag(001) surface with decreasing interatomic distance between atoms was observed, whereas for dimers of other transition metals the opposite behaviour is found. In this chapter we will discuss some selected results for the real, electronic and magnetic structure of metal nanostructures on noble metal surfaces. We will concentrate our discussion on one special system: Co nanostructures on Cu surfaces. Although a special system is investigated general conclusions can be drawn