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Spin polarization of vanadium overlayers on a semi-infinite tantalum substrate
surface science ELSEVIER
Surface Science 389 (1997) 310-316
Spin polarization of vanadium overlayers on a semi-infinite tantalum substrate T. Khajil, J. Khalifeh * Department of Physics, University of Jordan, Amman, Jordan Received 28 February 1997; accepted for publication 9 June 1997
Abstract
We investigate the substrate bandwidth effect on the onset of magnetism in V overlayers. The local magnetic moments and
magnetic order at the V/Ta interface of ultrathin V films is studied. Different crystallographic directions (001),(011 ) and (111 ) have been considered. The magnetism is described within a real-space tight-binding approach in the unrestricted Hartree-Fock approximation of the Hubbard Hamiltonian. The density of states has been calculated within the recursion technique: The onset of magnetism depends strongly on the faces considered. Magnetism is more pronounced for the (001) surface and is found to decrease when V is allowed to relax in order to recover its bulk volume. The magnetic moments of the surface layers are strongly enhanced by addition of more V layers. A sizeable induced moment appears in the Ta interface layer which decreases by addition of more V layers. The same behavior is shown to occur in the Nb substrate but it is more pronounced as compared to that of Ta. This behavior is expected since the bandwidth of Nb is smaller than that of Ta and their lattice parameters are approximately the same, © 1997 Elsevier Science B.V.
Keywords: Magnetic Order; Overlayers; Tantalum; Vanadium
1. Introduction I n the last two decades m a g n e t i s m o f t w o d i m e n s i o n a l t r a n s i t i o n m e t a l surfaces, o v e r l a y e r s a n d film structures h a s w i t n e s s e d an e n o r m o u s r e s e a r c h activity due to n e w l y a d v a n c e d techniques o f p r e p a r i n g surfaces, which led to b e t t e r u n d e r standing of magnetic properties. Experimental [1,2] a n d t h e o r e t i c a l [3,4] results have focused m a i n l y u p o n the e n h a n c e m e n t o f the t w o - d i m e n sional m a g n e t i s m in the 3d t r a n s i t i o n m e t a l s which are m a g n e t i c in their b u l k f o r m (Cr, M n , Fe, Co, N i ) . I n a d d i t i o n , s o m e o f these results are d e v o t e d to v a n a d i u m systems [5,6]. T h e i d e a o f v a n a d i u m * Corresponding author. Fax: ( + 962) 6 652672. 0039-6028/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S0039-6028 ( 9 7 ) 0 0 4 4 2 - 1
m a g n e t i s m was p r o b a b l y first p u b l i s h e d b y A l l a n [7]~ V w h i c h is a k n o w n p a r a m a g n e t in its b u l k f o r m is f o u n d to exhibit a n t i f e r r o m a g n e t i c ( A F ) b e h a v i o r at e x p a n d e d v o l u m e s [8], a f e r r o m a g n e t i c ( F ) surface p l a n e [9], a n d s t r o n g m a g n e t i s m for V films a n d f r e e - s t a n d i n g clusters f r o m t i g h t - b i n d ing c a l c u l a t i o n s [10-13]. Q u i t e recently, D e Coss p e r f o r m e d c a l c u l a t i o n s b y a similar m e t h o d for V o v e r l a y e r s o n W a n d T a ( 0 0 1 ) to see w h e t h e r the S t o n e r m e c h a n i s m is likely there [14]. A l s o the m a g n e t i s m o f l o w - i n d e x a n d vicinal surfaces o f V has been c o n s i d e r e d [15] a n d the p o l a r i z a t i o n o f the l o w - i n d e x surface a t o m s is q u a l i t a t i v e l y e x p l a i n e d t h r o u g h the c o o r d i n a t i o n n u m b e r rule. O t h e r a u t h o r s h a v e e x t e n d e d their research w o r k to c o v e r the 4d a n d 5d t r a n s i t i o n metals. T h e first
T. Khajil, J. Khalifeh / Surface Science 389 (1997) 310-316
attempts to investigate the possibility of spontaneous magnetization for 4d transition metals were carried out by Gunnarsson [16] and Janak [17]. They found that the Stoner criterion is never satisfied for any 4d metal. The general trend of decreasing localization of valence d wave functions when moving down the periodic table from the 3d to 4d and 5d series indicates that (1) the band width for the d elements increases, (2) the density of states at the Fermi level decreases, and (3) the intra-atomic exchange integral decreases. In view of the above facts, itinerant magnetism in two dimensions is not a priori restricted to those elements which exhibit magnetism in three dimensions. Because of the reduced coordination number in a 2D system the d-band width in 2D is considerably smaller than in 3D and the density of states at the Fermi level becomes larger than in 3D. Consequently the Stoner criterion is satisfied and magnetism appears in some 4d and 5d metals. Results presented by Blt~gel et al. [18,19] of a systematic study based on the full-potential linearized augmented-plane-wave method for 3d, 4d and 5d monolayers o n noble metals and Pd surfaces show that Mn, R u and Ir posses the largest magnetic moments among the 3d, 4d and 5d metals. Recently more attention is devoted to the study of the combined systems of V with other metals. Theoretically, a self-consistent real,space tightbinding approach indicates that magnetism o f V epitaxially grown on Ag(001) exhibits in-plane A F for one monolayer, but layered A F structures for thicker slabs [6], Also, the spin polarization at the F e / V interface was studied by Vega et al. [20]. They f o u n d that the spin polarization of the V atoms at the Fe/V interface is nonzero, with A F coupling between the Fe and V interface atoms. Martin et al. [21] investigated the case of V overlayers on Fe(103) and they have shown that V atoms, are A F coupled with their nearest neighbors and the value of V local moments are smaller than those obtained for V on Fe(001). Experimentally, many experiments .have considered the magnetic properties of V grown on Ag. Electron-capture spectroscopy :[22] and electron-
311
impedance measurements [23] results have been interpreted as due to some magnetic moment in the V layers. The above mentioned survey shows that V systems received considerable investigation and the effects of reduced geometry are taken into account, such as two-dimensional slabs, V surfaces and interfaces with other magnetic materials such as F Fe and A F Cr. However, less attention is devoted to Nb and Ta systems, since 2D slabs of Nb and Ta exhibit no magnetism because their bandwidths are large and their densities of states at E v are small enough so that the Stoner criterion cannot be satisfied. Usually a great deal of research work is devoted to spin polarization at the magnetic/ nonmagnetic interface systems. However, in a very recent work we considered V overlayers on a semiinfinite Nb substrate [24] to investigate the influence of a paramagnetic substrate on the onset of magnetism in vanadium slabs and to estimate the polarization in the substrate interfacial layers. I n this work, we report the results for the magnetic order o f V overlayers on a semi-infinite Ta substrate using a self-consistent real-space method. The structure of the article is as follows. The relevant formalism is developed in Section2, results and discussion are given in Section 3. Finally, the conclusion is presented in Section 4.
2. Calculation m e t h o d
A self-consistent real-space tight-binding method in the unrestricted one-electron Hartree Fock approximation of the Hubbard Hamiltonian is used to study the magnetic structure of V overlayers on a semi-infinite Ta substrate.The Hubbard Hamiltonian can be written as i~ ~ i ~ ~j~=,
( 1)
where ~ , ~i~ and ~i~ refer to creation, annihilation and number operators, respectively, of an electron with spin ~ at the orbital e of atomic site i (e-=dxy, dyz, dzx, d~2_y2, d3z2-r~). Our calcula-
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T. Khafil, J. Khalifeh / Surface Science 389 (1997) 310-316
tions in this method are based on the local density of states ( L D O S ) of the d-band. Using the recursion method [25] we can determine n~(e), which is LDOS of the ith site. The spin polarized local density of states (SPLDOS) with spin a of the ith site, nil(e), is determined by using the Hubbard Hamiltonian for d-electrons which proved to be successful for most transition elements, where its spin-dependent diagonal terms, in the case of the V/Ta system, are given by [26]
ei~ =e~
UiANi -- ~ a#(i).
(2)
Here e~ is the center of the d energy level in the paramagnetic solution of the bulk corresponding to either V or Ta. U~ stands for the effective direct intra-atomic coulomb integral, ANz is the ith site charge transfer (the difference between the electronic occupation at site i and the corresponding electronic occupation in the paramagnetic solution), and U~AN~ takes into account the shifts in energy levels due to the intra-atomic direct coulomb interactions and is usually taken from atomic Hartree Slater calculations [27]. The Last term in Eq. (2) stands for the shifts in the energy levels due to the intra-atomic exchange interactions. Here, Jz is the intrasite exchange coulomb integral and #(i) is the local magnetic moment of the site i which is given by
#(i)=NiT --Ni~,
(3)
where Ni~ and N a stand for the majority and minority number of electrons. These quantities are Calculated using the definition
Nz~ =
~
F
ni~(e)de.
(4)
--oo
If we impose local charge neutrality (ANi=0) by considering shifts £21 in the diagonal terms ei~, then the term UiANI in Eq. (2) is replaced by f21. This type of approximation has been successfully applied by Victora and Falicov [28,29]. In this model Hamiltonian, we consider spin-independent hopping integrals, up to next-nearest neighbors, and are assumed to have the canonical values [30] varying as the inverse fifth power of the interatomic
distance R~ between ith and jth neighbor atoms
dd(cr, ~, 6 ) i j - ( 6 , - 4 , 1) x (ddr)b(Ru/RO 5.
(5)
Here Rb is the corresponding distance in the bulk form. They are chosen in order to recover the d-band width of Varma and Wilson [31]. Eq. (2) and Eq. (3) above are solved self-consistently and the procedure is stopped when #(output)-/~(input) is less than 10 -4.
3. Results and discussion
The magnetic moments of the ground state for V overtayers on a Ta semi-infinite substrate are calculated in the (001), (011 ) and ( 111 ) directions through a self-consistent real-space tight-binding method in the unrestricted Hartree Fock approximation of the Hubbard Hamiltonian. In a recent publication we have investigated the magnetic structure of V overlayers on a semi-infinite Nb substrate using the above-mentioned technique [24]. In this type of calculation, the exchange integrals which link the local magnetic moment and the band splitting of the local density of states, play a major role. Vanadium and tantalum in their bulk form are known to be non-magnetic, therefore their exchange integral values Jv and JTa cannot be calculated by fitting them to the magnetic moment values of the elements in their bulk form. This in fact is also the case for elements that are not magnetic in their bulk form because one could fit the exchange parameter to a surface or to a different system. In addition, there is uncertainty about the exact values of the exchange integrals due to the different approaches and approximations employed for such calculations. However, through the linear muffin-tin orbital ( L M T O ) method, Christensen et al. [32] have obtained values of J for all the transition metal elements, J r = 0 . 6 0 eV and JTa=0.56 eV. But according to Stollhoff et al. [33], using a Hubbard-type Hamiltonian, this value is overestimated by 10-20% due to the partial neglect of spin correlations in the local density approximation (LDA). This is why the value of 0.50 eV is proposed for both elements. The number of d-type electrons for
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T. Khajil, J. Khalifeh / Surface Science 389 (1997) 310-316
V and Ta is taken equal to four in order to recover the correct position of the Fermi level. V and Ta have bcc structure with lattice parameters 5.71 and 6.24a.u., respectively. The Slater-Koster parameters of Ta substrate and V overlayers have been adjusted in order to satisfy their band widths (Wv=7.48 eV, wTa= 11.42 eV). Since the Ta lattice parameter is larger than that of V, the hopping integrals of V are scaled to those of the substrate assuming that when V is evaporated on the Ta substrate its atoms occupy the same positions as those of Ta keeping the same geometry in the direction parallel to the surface. Furthermore, f e w V overlayers are expected to adopt the substrate's interatomic distance in the plane parallel to the surface of the semi-infinite Ta substrate, but for a large number of V overlayers 2D periodicity is unexpected. The lattice parameter of V in the direction perpendicular to the surface is taken either as the s a m e as the bulk (nonrelaxed case) or relaxed towards the Ta substrate in order to recover a constant V volume as the bulk. In Fig. 1 we d i s p l a y the m a g n e t i c moments of V and Ta interfacial layers for the case of o n e V overlayer on Ta(001) i n dependence of the intraatomic V exchange integral. A second order phase
,~
transition from the paramagnetic state to the ferromagnetic state is found. The magnetic moments of V in the relaxed form are smaller than those of the nonrelaxed case for the same value of the exchange integral. This sort of behavior is reasonable as the distances between V and Ta decrease due to relaxation and consequently the hopping integrals increase. The induced magnetic moments of the Ta interface are sizable and found proportional to those of the V interface. As mentioned in the introduction, in a recent work [24] a similar result for V , / N b ( 0 0 1 ) is obtained (Fig. 2) which gives roughly the same trend as that of V , / T a but with slightly larger values of magnetic moments a s WTa>WNb(WNb=9.84eV). Figs. 1 and 2 are quite similar, however, slight differences could be observed. In particular the onset of magnetism for V/Ta(001 ) takes place at Jv = 0.42 eV whereas tha~ of V/Nb(001) occurs at J r = 0 . 4 0 eV. The local density of states ( L D O S ) of the relaxed V monolayer on the Ta substrate for the different crystallographic directions is shown in Fig. 3. The effect of the crystallographic face on the onset of magnetism is considerable. A peak is present at the Fermi level of the V(001 ~ overlayer L D O S while this is no longer the case for the
2.2
2.2 V O0
1.2
0
1.2
.2 O~
0.2
0.2
-0.8
i 0.0
0.2
i
0.4
0.6
-0.8
i 0.8
1.0
J Fig. l. Magnetic moments (in Bohr magnetons) of V/Ta(001) interfacial layers for one overlayer as a function of the intraatomic V exchange integral (eV). The squares (~) refer to the nonrelaxed case and the triangles (A) refer to the relaxed case.
i 0.0
0.2
0.4
0.6
0.8
I .0
Jr(w) Fig. 2. Magnetic moments (in Bohr magnetons) of V/Nb (001 ) interfacial layers for one overlayer as a function of the intraatomic V exchange integral (eV). The squares (E]) refer to the nonrelaxed case and the triangles (A) refer to the relaxed case.
7". Khajil, J. Khalifeh / Surface Science 389 (1997) 310 316
314 5.0
t
Table 3 Magnetic moments (in Bohr magnetons) of nonrelaxed V , / T a ( l l l ) for n = l to 3
/I
I;'
IIA
4.0
n 3.0
.,o
210
o
].0
0.0 -6.0
1 2 3
-4.0
-2.0
0.0
4.0
2.0
6.0
E(eV) Fig. 3. Local density of states (LDOS) of a V monolayer o n the Ta substrate. Full line: (001), dotted line: ( 111 ) and dashed line: (011 ) directions.
(011) and (111) directions. The Stoner criterion is satisfied for the (001) and (011 ) directions but this is not exactly the case for the (111) direction. Qualitatively speaking, a similar result has been found in the case of V slabs [6]. The magnetic moments for different crystallographic directions are calculated as given in Tables 1, 2 and 3. In Table 1 we display the magTable 1 Magnetic moments (in Bohr magnetons) of nonrelaxed V,/Ta(001) for n = l to 3 n
1 2 3
Ta
V
I--1
I
1
I+1
1+2
0.00 0.04 0.01
-0.28 0.06 --0.02
1.80 --0.77 0.21
2.49 --0.99
2.52
Table 2 Magnetic moments (in Bohr magnetons) of relaxed V,/Ta(001 ) for n = 1 to 3 n
1
2 3
Ta
V
I--1
I
1
0.01 0.02 0.00
--0.19 0.01 0.00
1.22 --0.14 0.00
I+1
1+2
-
0.56 --0.06
0.16
Ta
V
I-- 1
I
I
I+ 1
I+ 2
0.01 --0.03 0.02
--0.24 0.05 --0.07
1.25 -0.80 0.20
2.42 --1.10
2.49
netic moments of V,/Ta nonrelaxed overlayers for n = l to 3 in the (001) direction. For the case of one V overlayer the magnetic moment of V is equal to 1.80 #~ and that of Ta is - 0 . 2 8 #B. The addition of a second V layer is found to increase the surface magnetic moment to 2.49 #B and gives A F coupling between the V surface and the layer just below. A similar behavior has been found for 3- and 1 l-layer free-standing V slabs in the (001) crystallographic face [5, 6 ]. Layered antiferromagnetic structures (LAS) have been observed for values of J smaller than those necessary for the onset of ferromagnetic ( F ) solutions. A small value of magnetic moment (0.06 #B) is induced in the Ta interface. A slight increase in the magnetic moment at the surface is obtained by addition of a third V layer. A saturation behavior is expected to occur for more V layers as the surface layers become less affected by the substrate on the one hand, and the V film becomes thicker and tends towards its bulk extreme on the other. The same sort of A F magnetic coupling appears between V overlayers with less influence on the Ta substrate. This trend has been observed in recent studies on V overlayers on a Nb substrate [24]. Now when V overlayers were allowed to relax in order to recover their bulk volume, magnetism decreased. For one V overlayer, the magnetic moment on the surface is found to be 1.22 #B and that of the induced moment is - 0 . 1 9 #B (see Table 2). As the number of V overlayers increased to two the magnetic moments decrease appreciably. This behavior is justified as the distances between atoms in the (001) direction decrease due to relaxation. Other crystallographic planes are considered such as the (111 ) and (011 ) directions. The results
T. Khajil, J. Khalifeh / Surface Science 389 (1997) 310-316
for the magnetic moments of nonrelaxed (111) direction are given in Table 3, they are found to be comparable to those of the (001) nonrelaxed case. It is well known that the main factors which play a major role in such results are the interatomic distances and the coordination number. For the (011 ) direction, the system is totally paramagnetic due to the fact that V free standing slabs in this particular direction do not show magnetism except for large values of Jv. Following Bouarab et al. [6,10,34], the onset of magnetism takes place for values of Jv >0.71 eV whereas the exchange integral value used in this calculation is Jr--0.50 eV. Therefore, the only remaining possibility for surface magnetism of V is some kind of A F coupling between layers.
4. Conclusion
The calculations of the local magnetic moments and magnetic order of V,/Ta systems, for n = 1, 2 and 3, with different crystallographic directions were performed using a self-consistent real-space tight-binding approach. The ground state electronic structure of the system has been described within the unrestricted Hartree-Fock scheme of the Hubbard Hamiltonian. In this work we have shown that: (i) The presence of the Ta substrate did not kill the two-dimensional magnetism in V overlayers as V free-standing film is known to be magnetic [6]. This behavior has been demonstrated in the case of V,/Nb [24]. (ii) The induced magnetic moment in the Ta interface is sizable (0.28 PR) for the (001) surface and (0.24 #B) for the (111 ) surface; and decreases by addition of more V layers as the coordination number increases. This magnetic state of Ta is due to strong hybridization effects at the interface with the V film which is known to be magnetic in two dimensions. For the (011) case, magnetism is unlikely because the Jv value necessary to develop it is large as has been established by others for V slabs [5,6,10]. A F coupling between V and Ta interface layers is found and the AF coupling between V layers is observed to include the Ta
315
substrate. The same trend has been found in V,/Nb overlayers [24]. (iii) Magnetism in the V interface decreases by relaxation towards the substrate and consequently, the induced magnetic moment in the Ta interface decreases because it is proportional to that of V. (iv) The onset of magnetism in a paramagnetic/paramagnetic system depends on the crystallographic faces considered. The (011 ) orientation is less favorable for the onset of magnetism since the effective coordination number of this surface is larger than for the (00t) and ( 111 ) faces. (v) Qualitatively, the above behavior has been shown to occur in the Nb substrate but it is more pronounced as compared to that of Ta as the bandwidth of Nb is smaller than that of Ta while their lattice parameters are approximately the same. (vi) The exchange integral is chosen with care according to other calculations [32,33], however, the absolute values for the magnetic moments depend strongly on the value of J (see Fig. 1 and Fig. 2). A complete discussion concerning the effective coordination number rule for a bcc structure is given by Tomanek et al. [35]. In addition, the onset of magnetism can be explained through a simple model of rectangular bands according to Friedel [36]. Finally, as far as we are aware, for comparative purposes experimental results for this particular system are not available in the literature with but our results are qualitatively in agreement with the general trend. These results compare favorably well with the experimental observations [22,23] and calculations [6,24,37] for analogous systems.
References [1] C. Krembel, M.C. Hanf, J.C. Peruchetti, D. Bolmont, G. Gewinner, Phys Rev. B 44 ( 1991 ) 11427. [2] P. Schieffer, C. Krembel0 M.C. Hanf, D. Bolmont, G. Gewinner, 15th European Conference on Surface Science, Lille, France, 4-8th Sept (1995) to be published. [3] C.L. Fu, A.J. Freeman, T. Oguchi, Phys. Rev. Lett. 54 (1985) 2700. [4] A.J. Freeman, C.L. Fu, S. Ohnishi, M. Weinert, in: R. Feder (Ed.), Polarized Electron in Surface Physics,
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Advanced Series in Surface Physics, Vol. 1, World Scientific, Singapore, 1985. [5] A. Mokrani, C. Demangeat, H. Dreyss6, Phys. Rev. B 42 (1990) 10319. [6] S. Bouarab, H. Nait-Laziz, C. Demangeat, A. Mokrani, H. Dreyss6, Phys. Rev. B 46 (1992) 889. [7] G. Allan, Phys. Rev. B 19 (1979) 4774. [8] V. Morruzi, P. Marcus, Phys. Rev. B 42 (1990) 8361. [9] H. Akoh, A. Tasaki, J. Phys. Soc. Jpn. 42 (1977) 791. [10] S. Bouarab, H. Nait:Laziz, C. Demangeat, A. Mokrani, H. DreyssG J. Magn. Magn. Mater; 104 (1991) 233. [ 11 ] F. Liu, S.N. Khanna, P. Jena, Phys. Rev. B 43 ( 1991 ) 8179. [12] J. Dorantes-Dfivila, H. Dreyss6, Phys. Rev. B 47 (1993) 3857. [13] D. Homouz, J. Khalifeh, J. Magn. Magn. Mater. 153 (1996) 355. [14] R. De Coss, Surf. Rev. Lett. 3 (1996) 1505~ [15] H. Dreyss6, A. Vega, C. Demangeat, L.C. BalbAs, Europhys. Lett. 27 (2) (1994) 165. [16] O. Gunnarsson, J. Phys. F 6 (1976) 587. [17] J.F. Janak, Phys. Rev. B 16 (1977) 255. [18] S. Bltigel, Phys. Rev. Lett. 68 (1992) 851. [19] S. Bltigel, Europhys. Lett. 18 (1992) 257. [20] A. Vega, L. Balbfis, H. Nait-Laziz, C. Demangeat, H. Dreyss6, Phys. Rev. B 48 (1993) 985. [21] P. Martin, A. Vega, C. Demangeat, H. Dreyss6, J. Magn. Magn. Mater. 148 (1996) 177. [22] C. Rau, G. Xing, C. Liu, M. Robert, Phys. Lett. A 135 (1989) 227.
[23] S. Moodera, R. Meservey, Phys. Rev. B 40 (1989) 8541. [24] J. Khalifeh, J. Magn. Magn. Mater. 166 (1997) to be published. [25] R. Haydock, in: Solid State Physics, vol. 35, Academic, New York, 1980. [26] G~ Pastor, J. Dorantes-Davila, K. Benneman, Physica B 149 (1988) 22. [27] T. Bandyopadhyay, D.D. Sharma, Phys. Rev. B 39 (1989) 3517. [28] R. Victora, L. Falicov, Phys. Rev. B 31 (1985) 7335. [29] R. Vietora, L. Falicov, S. Ishida, Phys. Rev. B 30 (1984) 3896. [30] D.G. Pettifor, J. Phys. F: Met. Phys. 7 (1977) 613. [31] C.M. Varma, A.J. Wilson, Phys. Rev. B 22 (1980) 3795. [32] N.E. Christensen, O. Gunnarsson, O. Jepsen, O.K. Andersen, J. Phys. (Paris) Colloq. 49 (1988) C8-17. [33] G. Stollhoff, A.M. Oles, V. Heine, Phys. Rev. B 41 (1990) 7028. [34] S. Bouarab, H. Nait-Laziz, C. Demangeat, A. Mokrani, H. Dreyss6, Surf. Sci. 269 (1992) 643. [35] D. Tomanek, S. Muklerjee, K. Bennemann, Phys. Rev. B 28 (1983) 665. [36] J. Friedel, in: J. Ziman (Ed.), The Physics of Metals, Cambridge University Press, Cambridge, 1969, p. 340. [37] S. Bouarab, Ph.D. thesis, Louis Pasteur University, Strasbourg, 1993.
Surface Science 389 (1997) 310-316
Spin polarization of vanadium overlayers on a semi-infinite tantalum substrate T. Khajil, J. Khalifeh * Department of Physics, University of Jordan, Amman, Jordan Received 28 February 1997; accepted for publication 9 June 1997
Abstract
We investigate the substrate bandwidth effect on the onset of magnetism in V overlayers. The local magnetic moments and
magnetic order at the V/Ta interface of ultrathin V films is studied. Different crystallographic directions (001),(011 ) and (111 ) have been considered. The magnetism is described within a real-space tight-binding approach in the unrestricted Hartree-Fock approximation of the Hubbard Hamiltonian. The density of states has been calculated within the recursion technique: The onset of magnetism depends strongly on the faces considered. Magnetism is more pronounced for the (001) surface and is found to decrease when V is allowed to relax in order to recover its bulk volume. The magnetic moments of the surface layers are strongly enhanced by addition of more V layers. A sizeable induced moment appears in the Ta interface layer which decreases by addition of more V layers. The same behavior is shown to occur in the Nb substrate but it is more pronounced as compared to that of Ta. This behavior is expected since the bandwidth of Nb is smaller than that of Ta and their lattice parameters are approximately the same, © 1997 Elsevier Science B.V.
Keywords: Magnetic Order; Overlayers; Tantalum; Vanadium
1. Introduction I n the last two decades m a g n e t i s m o f t w o d i m e n s i o n a l t r a n s i t i o n m e t a l surfaces, o v e r l a y e r s a n d film structures h a s w i t n e s s e d an e n o r m o u s r e s e a r c h activity due to n e w l y a d v a n c e d techniques o f p r e p a r i n g surfaces, which led to b e t t e r u n d e r standing of magnetic properties. Experimental [1,2] a n d t h e o r e t i c a l [3,4] results have focused m a i n l y u p o n the e n h a n c e m e n t o f the t w o - d i m e n sional m a g n e t i s m in the 3d t r a n s i t i o n m e t a l s which are m a g n e t i c in their b u l k f o r m (Cr, M n , Fe, Co, N i ) . I n a d d i t i o n , s o m e o f these results are d e v o t e d to v a n a d i u m systems [5,6]. T h e i d e a o f v a n a d i u m * Corresponding author. Fax: ( + 962) 6 652672. 0039-6028/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S0039-6028 ( 9 7 ) 0 0 4 4 2 - 1
m a g n e t i s m was p r o b a b l y first p u b l i s h e d b y A l l a n [7]~ V w h i c h is a k n o w n p a r a m a g n e t in its b u l k f o r m is f o u n d to exhibit a n t i f e r r o m a g n e t i c ( A F ) b e h a v i o r at e x p a n d e d v o l u m e s [8], a f e r r o m a g n e t i c ( F ) surface p l a n e [9], a n d s t r o n g m a g n e t i s m for V films a n d f r e e - s t a n d i n g clusters f r o m t i g h t - b i n d ing c a l c u l a t i o n s [10-13]. Q u i t e recently, D e Coss p e r f o r m e d c a l c u l a t i o n s b y a similar m e t h o d for V o v e r l a y e r s o n W a n d T a ( 0 0 1 ) to see w h e t h e r the S t o n e r m e c h a n i s m is likely there [14]. A l s o the m a g n e t i s m o f l o w - i n d e x a n d vicinal surfaces o f V has been c o n s i d e r e d [15] a n d the p o l a r i z a t i o n o f the l o w - i n d e x surface a t o m s is q u a l i t a t i v e l y e x p l a i n e d t h r o u g h the c o o r d i n a t i o n n u m b e r rule. O t h e r a u t h o r s h a v e e x t e n d e d their research w o r k to c o v e r the 4d a n d 5d t r a n s i t i o n metals. T h e first
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attempts to investigate the possibility of spontaneous magnetization for 4d transition metals were carried out by Gunnarsson [16] and Janak [17]. They found that the Stoner criterion is never satisfied for any 4d metal. The general trend of decreasing localization of valence d wave functions when moving down the periodic table from the 3d to 4d and 5d series indicates that (1) the band width for the d elements increases, (2) the density of states at the Fermi level decreases, and (3) the intra-atomic exchange integral decreases. In view of the above facts, itinerant magnetism in two dimensions is not a priori restricted to those elements which exhibit magnetism in three dimensions. Because of the reduced coordination number in a 2D system the d-band width in 2D is considerably smaller than in 3D and the density of states at the Fermi level becomes larger than in 3D. Consequently the Stoner criterion is satisfied and magnetism appears in some 4d and 5d metals. Results presented by Blt~gel et al. [18,19] of a systematic study based on the full-potential linearized augmented-plane-wave method for 3d, 4d and 5d monolayers o n noble metals and Pd surfaces show that Mn, R u and Ir posses the largest magnetic moments among the 3d, 4d and 5d metals. Recently more attention is devoted to the study of the combined systems of V with other metals. Theoretically, a self-consistent real,space tightbinding approach indicates that magnetism o f V epitaxially grown on Ag(001) exhibits in-plane A F for one monolayer, but layered A F structures for thicker slabs [6], Also, the spin polarization at the F e / V interface was studied by Vega et al. [20]. They f o u n d that the spin polarization of the V atoms at the Fe/V interface is nonzero, with A F coupling between the Fe and V interface atoms. Martin et al. [21] investigated the case of V overlayers on Fe(103) and they have shown that V atoms, are A F coupled with their nearest neighbors and the value of V local moments are smaller than those obtained for V on Fe(001). Experimentally, many experiments .have considered the magnetic properties of V grown on Ag. Electron-capture spectroscopy :[22] and electron-
311
impedance measurements [23] results have been interpreted as due to some magnetic moment in the V layers. The above mentioned survey shows that V systems received considerable investigation and the effects of reduced geometry are taken into account, such as two-dimensional slabs, V surfaces and interfaces with other magnetic materials such as F Fe and A F Cr. However, less attention is devoted to Nb and Ta systems, since 2D slabs of Nb and Ta exhibit no magnetism because their bandwidths are large and their densities of states at E v are small enough so that the Stoner criterion cannot be satisfied. Usually a great deal of research work is devoted to spin polarization at the magnetic/ nonmagnetic interface systems. However, in a very recent work we considered V overlayers on a semiinfinite Nb substrate [24] to investigate the influence of a paramagnetic substrate on the onset of magnetism in vanadium slabs and to estimate the polarization in the substrate interfacial layers. I n this work, we report the results for the magnetic order o f V overlayers on a semi-infinite Ta substrate using a self-consistent real-space method. The structure of the article is as follows. The relevant formalism is developed in Section2, results and discussion are given in Section 3. Finally, the conclusion is presented in Section 4.
2. Calculation m e t h o d
A self-consistent real-space tight-binding method in the unrestricted one-electron Hartree Fock approximation of the Hubbard Hamiltonian is used to study the magnetic structure of V overlayers on a semi-infinite Ta substrate.The Hubbard Hamiltonian can be written as i~ ~ i ~ ~j~=,
( 1)
where ~ , ~i~ and ~i~ refer to creation, annihilation and number operators, respectively, of an electron with spin ~ at the orbital e of atomic site i (e-=dxy, dyz, dzx, d~2_y2, d3z2-r~). Our calcula-
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T. Khafil, J. Khalifeh / Surface Science 389 (1997) 310-316
tions in this method are based on the local density of states ( L D O S ) of the d-band. Using the recursion method [25] we can determine n~(e), which is LDOS of the ith site. The spin polarized local density of states (SPLDOS) with spin a of the ith site, nil(e), is determined by using the Hubbard Hamiltonian for d-electrons which proved to be successful for most transition elements, where its spin-dependent diagonal terms, in the case of the V/Ta system, are given by [26]
ei~ =e~
UiANi -- ~ a#(i).
(2)
Here e~ is the center of the d energy level in the paramagnetic solution of the bulk corresponding to either V or Ta. U~ stands for the effective direct intra-atomic coulomb integral, ANz is the ith site charge transfer (the difference between the electronic occupation at site i and the corresponding electronic occupation in the paramagnetic solution), and U~AN~ takes into account the shifts in energy levels due to the intra-atomic direct coulomb interactions and is usually taken from atomic Hartree Slater calculations [27]. The Last term in Eq. (2) stands for the shifts in the energy levels due to the intra-atomic exchange interactions. Here, Jz is the intrasite exchange coulomb integral and #(i) is the local magnetic moment of the site i which is given by
#(i)=NiT --Ni~,
(3)
where Ni~ and N a stand for the majority and minority number of electrons. These quantities are Calculated using the definition
Nz~ =
~
F
ni~(e)de.
(4)
--oo
If we impose local charge neutrality (ANi=0) by considering shifts £21 in the diagonal terms ei~, then the term UiANI in Eq. (2) is replaced by f21. This type of approximation has been successfully applied by Victora and Falicov [28,29]. In this model Hamiltonian, we consider spin-independent hopping integrals, up to next-nearest neighbors, and are assumed to have the canonical values [30] varying as the inverse fifth power of the interatomic
distance R~ between ith and jth neighbor atoms
dd(cr, ~, 6 ) i j - ( 6 , - 4 , 1) x (ddr)b(Ru/RO 5.
(5)
Here Rb is the corresponding distance in the bulk form. They are chosen in order to recover the d-band width of Varma and Wilson [31]. Eq. (2) and Eq. (3) above are solved self-consistently and the procedure is stopped when #(output)-/~(input) is less than 10 -4.
3. Results and discussion
The magnetic moments of the ground state for V overtayers on a Ta semi-infinite substrate are calculated in the (001), (011 ) and ( 111 ) directions through a self-consistent real-space tight-binding method in the unrestricted Hartree Fock approximation of the Hubbard Hamiltonian. In a recent publication we have investigated the magnetic structure of V overlayers on a semi-infinite Nb substrate using the above-mentioned technique [24]. In this type of calculation, the exchange integrals which link the local magnetic moment and the band splitting of the local density of states, play a major role. Vanadium and tantalum in their bulk form are known to be non-magnetic, therefore their exchange integral values Jv and JTa cannot be calculated by fitting them to the magnetic moment values of the elements in their bulk form. This in fact is also the case for elements that are not magnetic in their bulk form because one could fit the exchange parameter to a surface or to a different system. In addition, there is uncertainty about the exact values of the exchange integrals due to the different approaches and approximations employed for such calculations. However, through the linear muffin-tin orbital ( L M T O ) method, Christensen et al. [32] have obtained values of J for all the transition metal elements, J r = 0 . 6 0 eV and JTa=0.56 eV. But according to Stollhoff et al. [33], using a Hubbard-type Hamiltonian, this value is overestimated by 10-20% due to the partial neglect of spin correlations in the local density approximation (LDA). This is why the value of 0.50 eV is proposed for both elements. The number of d-type electrons for
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T. Khajil, J. Khalifeh / Surface Science 389 (1997) 310-316
V and Ta is taken equal to four in order to recover the correct position of the Fermi level. V and Ta have bcc structure with lattice parameters 5.71 and 6.24a.u., respectively. The Slater-Koster parameters of Ta substrate and V overlayers have been adjusted in order to satisfy their band widths (Wv=7.48 eV, wTa= 11.42 eV). Since the Ta lattice parameter is larger than that of V, the hopping integrals of V are scaled to those of the substrate assuming that when V is evaporated on the Ta substrate its atoms occupy the same positions as those of Ta keeping the same geometry in the direction parallel to the surface. Furthermore, f e w V overlayers are expected to adopt the substrate's interatomic distance in the plane parallel to the surface of the semi-infinite Ta substrate, but for a large number of V overlayers 2D periodicity is unexpected. The lattice parameter of V in the direction perpendicular to the surface is taken either as the s a m e as the bulk (nonrelaxed case) or relaxed towards the Ta substrate in order to recover a constant V volume as the bulk. In Fig. 1 we d i s p l a y the m a g n e t i c moments of V and Ta interfacial layers for the case of o n e V overlayer on Ta(001) i n dependence of the intraatomic V exchange integral. A second order phase
,~
transition from the paramagnetic state to the ferromagnetic state is found. The magnetic moments of V in the relaxed form are smaller than those of the nonrelaxed case for the same value of the exchange integral. This sort of behavior is reasonable as the distances between V and Ta decrease due to relaxation and consequently the hopping integrals increase. The induced magnetic moments of the Ta interface are sizable and found proportional to those of the V interface. As mentioned in the introduction, in a recent work [24] a similar result for V , / N b ( 0 0 1 ) is obtained (Fig. 2) which gives roughly the same trend as that of V , / T a but with slightly larger values of magnetic moments a s WTa>WNb(WNb=9.84eV). Figs. 1 and 2 are quite similar, however, slight differences could be observed. In particular the onset of magnetism for V/Ta(001 ) takes place at Jv = 0.42 eV whereas tha~ of V/Nb(001) occurs at J r = 0 . 4 0 eV. The local density of states ( L D O S ) of the relaxed V monolayer on the Ta substrate for the different crystallographic directions is shown in Fig. 3. The effect of the crystallographic face on the onset of magnetism is considerable. A peak is present at the Fermi level of the V(001 ~ overlayer L D O S while this is no longer the case for the
2.2
2.2 V O0
1.2
0
1.2
.2 O~
0.2
0.2
-0.8
i 0.0
0.2
i
0.4
0.6
-0.8
i 0.8
1.0
J Fig. l. Magnetic moments (in Bohr magnetons) of V/Ta(001) interfacial layers for one overlayer as a function of the intraatomic V exchange integral (eV). The squares (~) refer to the nonrelaxed case and the triangles (A) refer to the relaxed case.
i 0.0
0.2
0.4
0.6
0.8
I .0
Jr(w) Fig. 2. Magnetic moments (in Bohr magnetons) of V/Nb (001 ) interfacial layers for one overlayer as a function of the intraatomic V exchange integral (eV). The squares (E]) refer to the nonrelaxed case and the triangles (A) refer to the relaxed case.
7". Khajil, J. Khalifeh / Surface Science 389 (1997) 310 316
314 5.0
t
Table 3 Magnetic moments (in Bohr magnetons) of nonrelaxed V , / T a ( l l l ) for n = l to 3
/I
I;'
IIA
4.0
n 3.0
.,o
210
o
].0
0.0 -6.0
1 2 3
-4.0
-2.0
0.0
4.0
2.0
6.0
E(eV) Fig. 3. Local density of states (LDOS) of a V monolayer o n the Ta substrate. Full line: (001), dotted line: ( 111 ) and dashed line: (011 ) directions.
(011) and (111) directions. The Stoner criterion is satisfied for the (001) and (011 ) directions but this is not exactly the case for the (111) direction. Qualitatively speaking, a similar result has been found in the case of V slabs [6]. The magnetic moments for different crystallographic directions are calculated as given in Tables 1, 2 and 3. In Table 1 we display the magTable 1 Magnetic moments (in Bohr magnetons) of nonrelaxed V,/Ta(001) for n = l to 3 n
1 2 3
Ta
V
I--1
I
1
I+1
1+2
0.00 0.04 0.01
-0.28 0.06 --0.02
1.80 --0.77 0.21
2.49 --0.99
2.52
Table 2 Magnetic moments (in Bohr magnetons) of relaxed V,/Ta(001 ) for n = 1 to 3 n
1
2 3
Ta
V
I--1
I
1
0.01 0.02 0.00
--0.19 0.01 0.00
1.22 --0.14 0.00
I+1
1+2
-
0.56 --0.06
0.16
Ta
V
I-- 1
I
I
I+ 1
I+ 2
0.01 --0.03 0.02
--0.24 0.05 --0.07
1.25 -0.80 0.20
2.42 --1.10
2.49
netic moments of V,/Ta nonrelaxed overlayers for n = l to 3 in the (001) direction. For the case of one V overlayer the magnetic moment of V is equal to 1.80 #~ and that of Ta is - 0 . 2 8 #B. The addition of a second V layer is found to increase the surface magnetic moment to 2.49 #B and gives A F coupling between the V surface and the layer just below. A similar behavior has been found for 3- and 1 l-layer free-standing V slabs in the (001) crystallographic face [5, 6 ]. Layered antiferromagnetic structures (LAS) have been observed for values of J smaller than those necessary for the onset of ferromagnetic ( F ) solutions. A small value of magnetic moment (0.06 #B) is induced in the Ta interface. A slight increase in the magnetic moment at the surface is obtained by addition of a third V layer. A saturation behavior is expected to occur for more V layers as the surface layers become less affected by the substrate on the one hand, and the V film becomes thicker and tends towards its bulk extreme on the other. The same sort of A F magnetic coupling appears between V overlayers with less influence on the Ta substrate. This trend has been observed in recent studies on V overlayers on a Nb substrate [24]. Now when V overlayers were allowed to relax in order to recover their bulk volume, magnetism decreased. For one V overlayer, the magnetic moment on the surface is found to be 1.22 #B and that of the induced moment is - 0 . 1 9 #B (see Table 2). As the number of V overlayers increased to two the magnetic moments decrease appreciably. This behavior is justified as the distances between atoms in the (001) direction decrease due to relaxation. Other crystallographic planes are considered such as the (111 ) and (011 ) directions. The results
T. Khajil, J. Khalifeh / Surface Science 389 (1997) 310-316
for the magnetic moments of nonrelaxed (111) direction are given in Table 3, they are found to be comparable to those of the (001) nonrelaxed case. It is well known that the main factors which play a major role in such results are the interatomic distances and the coordination number. For the (011 ) direction, the system is totally paramagnetic due to the fact that V free standing slabs in this particular direction do not show magnetism except for large values of Jv. Following Bouarab et al. [6,10,34], the onset of magnetism takes place for values of Jv >0.71 eV whereas the exchange integral value used in this calculation is Jr--0.50 eV. Therefore, the only remaining possibility for surface magnetism of V is some kind of A F coupling between layers.
4. Conclusion
The calculations of the local magnetic moments and magnetic order of V,/Ta systems, for n = 1, 2 and 3, with different crystallographic directions were performed using a self-consistent real-space tight-binding approach. The ground state electronic structure of the system has been described within the unrestricted Hartree-Fock scheme of the Hubbard Hamiltonian. In this work we have shown that: (i) The presence of the Ta substrate did not kill the two-dimensional magnetism in V overlayers as V free-standing film is known to be magnetic [6]. This behavior has been demonstrated in the case of V,/Nb [24]. (ii) The induced magnetic moment in the Ta interface is sizable (0.28 PR) for the (001) surface and (0.24 #B) for the (111 ) surface; and decreases by addition of more V layers as the coordination number increases. This magnetic state of Ta is due to strong hybridization effects at the interface with the V film which is known to be magnetic in two dimensions. For the (011) case, magnetism is unlikely because the Jv value necessary to develop it is large as has been established by others for V slabs [5,6,10]. A F coupling between V and Ta interface layers is found and the AF coupling between V layers is observed to include the Ta
315
substrate. The same trend has been found in V,/Nb overlayers [24]. (iii) Magnetism in the V interface decreases by relaxation towards the substrate and consequently, the induced magnetic moment in the Ta interface decreases because it is proportional to that of V. (iv) The onset of magnetism in a paramagnetic/paramagnetic system depends on the crystallographic faces considered. The (011 ) orientation is less favorable for the onset of magnetism since the effective coordination number of this surface is larger than for the (00t) and ( 111 ) faces. (v) Qualitatively, the above behavior has been shown to occur in the Nb substrate but it is more pronounced as compared to that of Ta as the bandwidth of Nb is smaller than that of Ta while their lattice parameters are approximately the same. (vi) The exchange integral is chosen with care according to other calculations [32,33], however, the absolute values for the magnetic moments depend strongly on the value of J (see Fig. 1 and Fig. 2). A complete discussion concerning the effective coordination number rule for a bcc structure is given by Tomanek et al. [35]. In addition, the onset of magnetism can be explained through a simple model of rectangular bands according to Friedel [36]. Finally, as far as we are aware, for comparative purposes experimental results for this particular system are not available in the literature with but our results are qualitatively in agreement with the general trend. These results compare favorably well with the experimental observations [22,23] and calculations [6,24,37] for analogous systems.
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