- Email: [email protected]
Fe interface
Journal of Magnetism and Magnetic Materials 118 (1993) 365-372 North-Holland
The Pd polarization H. Nait-Laziz,
S. Bouarab,
at the Pd/Fe
interface
C. Demangeat
IPCMS, lJMR46, Universite Louis Pasteur, 4 rue Blake Pascal, 67070 Strasbourg, France
A. Mokrani Laboratoire de Physique du Solide Thkorique, 2, rue de la Houssini&e, 44072 Nantes, France
and H. Dreysse Laboratoire de Physique des Solides, BP 239, 54506 Vandoeuvre-les-Nancy, France
Received 8 April 1992; in revised form 19 June 1992
The electronic and magnetic properties of the ground state (T = 0 K) at the Pd/Fe(OOl) interface were investigated through the mean-field parameterized tight-binding method. Structurally, the Pd overlayers occupy the fee sites of the substrate, with a few percent expansion of the Pd-Pd distances as compared to the bulk fee Pd. We report results concerning deposition of n Pd layers on semi-infinite Fe. Ferromagnetic polarization of the Pd, layers are obtained up to n = 3. For n = 4, we have obtained ferromagnetic polarization of the nearest neighbour Pd overlayer but negative polarization for the three other planes. For n = 5, all the Pd atoms are polarized ferromagnetically unless the surface which has a quasi-zero magnetic moment. In the case of sandwiches Fe,,, /Pd, /Fe,,, or superlattices (Fe,Pd,), we investigate both ferromagnetic and antiferromagnetic couplings between Fe films through the Pd spacer. For completeness we perform also total energy calculations in order to study the exchange coupling displayed by Celinski and Heinrich [J. Magn. Magn. Mater. 99 (1991) L25]. Similar trends are found: ferromagnetic coupling is shown to be stable until ‘n= 5 for Fe, /Pd, /Fe, sandwiches; antiferromagnetic coupling is however stable for n = 6. We discuss the importance of the interface roughness on this oscillation.
1. Introduction
Recent experiments have revealed that Fe/Pd multilayers show ferromagnetic coupling between Fe layers through Pd spacer up to 12 layers of the non-magnetic compound [1,2]. For a higher number of Pd layers, a marginally small antiferromagnetic coupling is present. As it is well known, Pd Correspondence to: Dr. C. Demangeat, IPCMS, UMR46, Universite Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg, + 33-88-41-61-09; telefax: + 33-88-41-60-88; France. Tel.: email: [email protected]. 0304-8853/93/$06.00
is an incipient ferromagnet: a small percentage of Fe causes ferromagnetism and theoretically a paramagnetic-ferromagnetic (P-F) phase transition occurs in bulk Pd with 6% lattice expansion [3-51. Furthermore, giant moments for Fe impurities in Pd have been observed [6]. Electronic structure calculations based on density functional theory and the Korringa-Kohn-Restocker Green’s function method yield a consistent picture of the behavior of local moments of 3d impurities in Pd [7]. The calculated local impurity moments are in good agreement with experiment. However, less than 30% of the total induced
0 1993 - Elsevier Science Publishers B.V. All rights reserved
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moment is confined to the 42 Pd atoms in the first three shells around Fe. Due to the limited size of the cluster considered, these authors [7] were able to obtain the giant moment only by “fitting the unknown parameter”. Up to now, calculations concerning the Pd/Fe interface have been restricted to the case of a Pd/Fe,/Pd slab [8] or as Fe monolayer on Pd 293. In the spin-polarized self-consistent localized orbitals calculations of Huang et al. [8] the Pd monolayer has a magnetic moment of 0.37~~. The magnetic moment of an adjacent iron atom is 2.74pg, significantly larger than the central plane value of 2.37~~. The d bands of the two metals are found strongly hybridized. B&gel et al. [9] through Full-Potential-Linearized-Plane-Wave (FLAPW) method investigated the entire 3d transition-metal series as monolayer on Pd(001) and concluded that Fe/Pd(OOl) is ferromagnetic with Fe inducing moments of 0.32 and 0.17~~ in the first and second Pd layers respectively. However, from this calculation which uses a nine-layer (001) films containing seven layers of Pd and one 3d monolayer on each surface, only polarization up to second Pd layer are reported. It has also been argued recently that a few monolayers of Pd on Ag(OO1) may present magnetism [lo]. This experiment based on ElectronCapture-Spectroscopy (ECS) has suggested the existence of ferromagnetism in thin epitaxial films of Pd grown on Ag(001). However, experiments utilizing the Surface-Magneto-Optic-Kerr-Effect (SMOKE) fail to detect magnetism of Pd on Ag(OOl)/ll/ or Pd on Au(OO1) [12]. Recent calculations by Eriksson et al. [13] and Zhu et al. [14] do not display any onset of magnetism for an overlayer of Pd on Ag(OO1) or Au(OO1). We have recently argued [15,161, using tight-binding calculations, that the onset of ferromagnetism versus the exchange integral J, in the case of Pd films or overlayer on Ag(OOl), is obtained for a J smaller than the one necessary to get ferroniagnetism in the bulk. In the case of free-standing monolayer, we do not find any magnetism contrary to the calculation by. Zhu et al. [14]. This absence of magnetism is related to the small Density-ofStates (DOS) at the Fermi level of the monolayer. Our result is however in full agreement with
at the Pd /Fe interface
recent Linearized-Muffin-Tin-Orbital (LMTO) calculations showing no magnetism in the Pd monolayer range [17], for bulk lattice-parameter. Magnetism may however be obtained by changing the lattice parameter [8]. But, by increasing the number of Pd layers in the slab, magnetism appears more readily than in the bulk case. A thickness effect of the onset of magnetism may be present [15,18]. Free-standing Pd slabs, with bulk lattice-parameter are however only a “theoretician” model so that we have also performed calculation of n Pd layers epitaxially grown on Ag(OO1) [161. The results obtained are qualitatively similar with those of free-standing slabs i.e. our results display a strong thickness dependence of the onset of magnetism versus J. Therefore, these results can give an explanation concerning those obtained on Pd overlayer on Ag(OO1) through SMOKE [ll] and on thicker slab by ECS [lo]. Such thickness dependence has been already observed by Moodera and Meservey [193 in the case of V epitaxially grown on Ag(OO1). Polarization of Pd at the Fe/Pd interface is confirmed through SMOKE experiments [20], Angle-Resolved-Photoemission-Spectroscopy (ARPES) [21], Mijssbauer-spectroscopy [22], spin-resolved and spin-integrated photoemission 1231. In the case of Pd/Fe(OOl) interfaces, the films grow pseudomorphically [1,2,20,21] but, whereas Fe on Pd(001) is body-centered-tetragonal, Pd on Fe(001) expands its lattice parameter in order to accomodate for pseudomorphic growth [1,2]. Epitaxial growth of Pd(ll1) films on Fe(ll0) [231 or Fe(llO)/Pd(lll) superlattices [22], because of the considerable lattice mismatch, does require a special analysis. In this paper, using a mean-field parametrized tight-binding method, we present electronic and magnetic properties for an IZlayers Pd film grown on semi-infinite Fe(OOl), for Fe,/Pd,/Fe,, sandwiches and (Fe,/Pd,), superlattices. In all cases, the structural approach is an adjustment of the Pd lattice to that of Fe. In this “ideal” case, the lattice parameter of Pd is equal to that of Fe times fi. This expansion is however too small to induce magnetism in the bulk case [3-51. Magnetism is therefore obtained through the combined effect of strong hybridization between the
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367
d orbitals of Fe and Pd, and the lattice expansion. In section 2, the methodology and computational details are given. The results concerning the polarization of n layers of Pd on semi-infinite Fe(001) are presented in section 3. Section 4 is devoted to a comparison between the magnetism in FeJPdJFe, sandwiches and in (Fe,Pd,), superlattices. The results obtained with it = 2, 3 are very similar. We have compared two types of approximations: 1) global neutrality approach which allows charge transfer between the layers, the total number of electrons being kept constant and 2) a local neutrality approach. Both approaches do give almost the same polarization map. We have therefore restricted our calculations for the exchange coupling to the sandwich case (section 5). In this case we save a reasonable amount of computing time. Also, we have restricted our calculation to global neutrality for Fe,/Pd,/Fe, sandwiches. We discuss particularly, through total-energy-calculation, the stability of the ferromagnetic (F) and antiferromagnetic (AF) coupling between Fe, films through Pd, spacers. Section 6 is devoted to the conclusion.
n + 3 atoms (n Pd atoms, the Fe interface, the Fe subsurface and the centre of the Fe(001) slabs). Canonical hopping integrals are used [25]. Their values are adjusted in order to recover the d bandwidth given by Varma and Wilson [26]. We have taken, for J, the exchange integral, the value which gives the bulk magnetic moment of Fe at the centre of the 20-layer slabs. In the case of Pd, we cannot proceed in such manner because bulk palladium is non-magnetic. Therefore, we fix Jr, in order to recover the results of Moruzzi and Marcus [4] displaying onset of ferromagnetism when the Pd lattice is expanded by 6%. Let us note that we have taken for Nd (number of d electrons), the value 7 for Fe [24] whereas Nd = 9.52 for Pd [18]. For Fe, we take the hopping integrals corresponding to bulk Fe. The x, y coordinates of the Pd and Fe atoms in the (001) crystallographic face are identical: thus, the lattice parameter of Pd on Fe(001) is a little bigger than that of Pd bulk. Therefore, the hopping of Pd are modified through the inverse of the fifth power with distance [251: this small decrease of the hoppings is not enough to lead to the onset of ferromagnetism in the bulk. At the Pd/Fe interface, the hopping PFePd are given by:
2. Methodology
P FePd
Up to now, Huang et al. [8] have investigated the onset of ferromagnetism in Pd/Fe,/Pd(OOl) free-standing slabs through spin-polarized-selfconsistent localized-orbital calculations. In their calculation, the Pd monolayer has a magnetic moment of 0.37~, whereas, the iron atoms posses a magnetic moment of 2.74 and 2.37pB at the interface and at the centre of the slab respectively. We have recently shown [24] that, in order to recover the bulk magnetic moment of Fe at the centre of the free-standing slab, it is necessary to take into account 11 layers when 6 levels of the continued fraction are used. In order to avoid the computation in an 11 layer slab plus it layers of Pd, we mimic the semi-infinite Fe systems through a slab of 20 layers where only the surface and the subsurface layers are modified as compared to the bulk. Therefore, the calculations for 12layers of Pd on semi-infinite Fe(001) is performed on
A delicate problem is the determination of the relative positions of the Fe and Pd bands. To resolve that we have used two types of approximations: the first consists to an adjustment of the bulk Fermi levels in order to minimize charge transfer between Fe and Pd. A global neutrality condition is used for the derivation of the selfconsistent equations [16]; a local neutrality condition is used for the second type of approximation. Additional intrasite matrix elements are derived in order to get this local neutrality. The case of IZ layers of Pd on semi-infinite Fe(001) is mimicted by taking into account a slab of 20 Fe layers. In order to avoid surface effect at the centre of the slab (considerd as the bulk), at least 20 Fe layers must be considered. Only the local neutrality approximation has been used here. In the case of Fe,/Pd,/Fe, sandwiches and (Fe,/Pd,), superlattices, both local and global
=
\lPFeFePPdPd *
(1)
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neutrality approximations have been tested. The polarization of Pd is not greatly modified either through global or local neutrality. Therefore, in many cases, we have restricted our calculations in the global neutrality approximation. For sandwiches, we have investigated both ferromagnetic (F) and antiferromagnetic (AF) coupling through Pd spacers. A priori, the F coupling, at least for a small number of Pd layers must be stable because AF coupling between Fe films induces AF coupling in the Pd spacer. Antiferromagnetism in bulk Pd is unlikely as shown by Moruzzi and Marcus [27]. For a higher number of Pd layers, because of the fact that the polarization of Pd is rather limited (4 to 5 layers from Fe), the difference in energy between F and AF couplings slow down so that our method is unable to give pertinent results because this difference of energy becomes marginally small. All calculations have been performed within the recursion method [28] with 13 levels of the continued fraction.
3. n Pd layers on semi-infinite Fe(OO1) The lattice parameter of Pd in this configuration is equal to 6uFe, where uFe is the lattice parameter of bulk Fe. Therefore, the hopping integrals of Pd show a small decrease as compared to those of bulk Pd. The local neutrality is assumed in this section. Moreover, the difference between output and input magnetic moments must be smaller than 1O-4 for each layer. The results are reported in fig. 1. It can be seen that the magnetic moments on the iron atoms at the Pd/Fe(OOl) interface are increased as compared to bulk iron. This magnetic moment decreases slightly when going from semi-infinite Fe(001) to the case of it layers of Pd on Fe(001). More precisely, the magnetic moment at the Fe interface decreases when the number of Pd layers increases from 1 to 2. For thicker Pd slabs, the value of the magnetic moment at the iron interface does not change very much. This is probably related to the fact that we have restricted the hopping integrals up to second nearest neighbors. Fig. 1 displays a decrease of the magnetic moment on Pd atoms in the layer adjacent to Fe
b)
-0.20
]
I
I
1
Pd(l)
Pd(l+l)
Pd(It2)
Pd(I+i)
Pd(It4)
Fig. 1. Magnetic moment p &J per atom, for n layers of Pd on Fe(OOl), in the local neutrality approximation. Negative polarization is obtained only in the case of Pd, /Fe(OOl). ( A ) Pd, /Fe(OOl); (0) Pd, /Fe(OOl); (01 Pd, /Fe(OOl); (0) Pd, /Fe(OOl); (W) Pd, /Fe(OOl). In (a), Fe(B) is relative to bulk Fe, whereas Fe(I) and Pd(1) denote the interface atoms; Pd(I + p) is relative to Pd atoms (p = n - 1). The polarization of Pd is much lower than that of Fe so, we report in (b) the Pd atoms with a different scaling.
when one increases the number of Pd layers. The magnetic moment decreases from 0.35 to 0.27~~ when one goes from n = 1 to 3. When n is higher than 2, this magnetic moment remains constant. A very strange effect appears for it = 4. In this particular case, a negative polarization appears for atoms of Pd which are not at the interface with Fe. This specific magnetic distribution remains if we perform the calculation with a small variation of the exchange integral J. For 12= 5, only the magnetization at the interface with iron remains important: at the Pd surface the magnetic moment is roughly zero whereas, for the
H. Nait-Laziz
et al. / The Pd polarization
other layers, only low magnetic moments remain. This thickness effect is reminiscent to the one already found in the case of Pd slabs [15] and in the case of Pd overlayers on Ag(001) [181.
4. Comparison between Fe, /Pd,/Fe, wiches and (Fe, / Pd,), superlattices
sand-
In the preceding section we have discussed the magnetization map of an Pd, slab on semi-infinite Fe(001). A local neutrality approximation was used to perform this calculation. This type of calculation needs more CPU than the one performed in the case of global neutrality. In this section we discuss and compare the results obtained for FeJPdJFe, sandwiches and (Fe,/Pd,), superlattices. We discuss and compare also the results obtained in the case of local and global neutrality. Table 1 reports the results obtained for IZ= 2, 3. For (FeJPd,), superlattices and for FeJPdJFe,, sandwiches, the results obtained in the local neutrality approximation are the same as long as magnetic moments on the Pd atoms are considered. The same result holds also if we compare the two systems in the global neutrality approximation. Therefore, we can restrict our calculation to one type of approximation, i.e. the cheapest one. Extrapolation to the other physical situation is straightforward.
369
at the Pd / Fe interface
Comparison between local and global neutrality has also been performed for systems with the same configuration. Table 1 shows that the magnetic moments on Pd atoms are greater in the global neutrality approximation as compared to the local neutrality approximation. However, these results are qualitatively the same so that we restrict the determination of the exchange coupling between Fe films through Pd, spacers to the case of sandwiches. Moreover, experimental results [2] have been performed on Fe/Pd/Fe trilayer. We restrict therefore our determination of the exchange coupling of Fe through Pd spacer to the case of Fe,/Pd,/Fe, (section 5).
5. Exchange coupling in Fe,/ Pd,/Fe,
trilayers
We have determined the magnetization Fe,/Pd,/Fe, trilayer in two cases:
map of
1) the Fe, films are coupled ferromagnetically through the Pd spacer; 2) the Fe, films are coupled antiferromagnetitally through the Pd spacer. For each case we have also determined the total energies i.e. E(F) for the F coupling and E(AF) for the AF coupling. This calculation has been performed in the global neutrality approximation i.e., at each iteration step, the Fermi level is computed in order to keep the number of
Table 1 Magnetic moments p &I for 2 and 3 layers of Pd in Fe, /Pd, /Fe, sandwiches and (Fe, /Pd,), superlattices in the Local (L) and in the Global (G) neutrality approximations. Index I stands for atoms at the Pd/Fe interface; indices I + 1 and I-l are for atoms near the interface (Pd I +1 and Fe,_,); index C is relative to the centre of the Fe, slab; Indices S and S - 1 are for Fe surface and subsurface
’
Super lattices
Fer
Fer-i
Fe,
Fcr-i
Fe,
P4
Pd 1+1
(Fe, (Fe, (Fe, (Fe,
2.645 2.615 2.662 2.596
2.085 2.116 2.093 2.121
2.031 1.993 2.055 2.023
2.085 2.116 2.093 2.121
2.645 2.615 2.662 2.596
0.359 0.354 0.378 0.340
0.156 0.117
Fes 2.585 2.666 2.604 2.674
Fes-1 2.089 2.085 2.092 2.089
Fe, 1.992 1.944 2.004 1.962
Fer-i 2.083 2.124 2.088 2.126
Fer 2.677 2.630 2.683 2.613
Pdr 0.371 0.354 0.383 0.340
/Pd,),, /I’d,), /I’d,), /Pd,),
G L
G L
Sandwiches Fe, /Pd, /Fes Fe, /Pd, /Fe, Fe, /Pd, /Fe, Fe, /Pd, /Fe,
G L G L
Pd I+1
0.153 0.117
H. Nait-Laziz
et al. / The Pd polarization
at the Pd / Fe interface
000 -31 Fe
,
,
,
,
,
,
,
,
,
,
I
Fe
Fe
Fe
Fe
Pd
Pd
Fe
Fe
Fe
Fe
Fe
Fig. 2. Magnetic moment p (~~1 per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
electrons constant. Results of the magnetization map are reported in figs. 2-6 corresponding to n = 2-6 layers of Pd. From these figures it can be shown that the AF coupling between Fe layers reduces strongly the Pd polarization present in the case of F coupling. Also, the magnetic moment of the Fe atoms at the Fe/Pd interface is smaller in the AF coupling as compared to the F one. Charge transfer between layers are not very important (smaller than 0.1 electrons in all cases considered). The difference A E = E(F) - E(AF) of the total energies between F and AF couplings are reported in fig. 7. Up to five layers of Pd, the F
-3,
Fe
I
Fe
I,,
Fe
Fe
Fe
,
,
,
,
,
,
,
,
Pd
Pd
Pd
Pd
Fe
Fe
Fe
Fe
Fig. 4. Magnetic moment p &) per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
000 0 -31 Fe
)
,
,
,
,
I
,
I
,
,
,
I
,
,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Pd
Pd
Fe
Fe
Fe
Fe
e
Fig. 5. Magnetic moment p (~~1 per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
2 ‘-
2 z ~_~~~~~~~~~~~~~___________ .2 $
-I-
%
9 Fe
,
,
,
,
,
,
,
,
,
,
,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Fe
Fe
Fe
Fe
_2_
000
-3
Fe
Fig. 3. Magnetic moment p (cc,& per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
Fe
,
,
,
,
,
,
,
,
,
,
0 ,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Pd
Pd
Pd
Fe
I,
Fe
(
Fe
Fe
Fig. 6. Magnetic moment p (& per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
H. Nait-Laziz
I
I
I
1
Pd2
Pd3
Pd4
Pd5
Thickness
et al. / The Pdpolarization
1
-1
Pd6
at the Pd /Fe interface
371
case of Rh overlayers on Ag(OOl), all self-consistent calculations do obtain a magnetic moment for the Rh atoms [13,32,33]. However, Mulhollan et al. [34] have shown through SMOKE that long-range spin-ordering is absent above 40 K. This absence of magnetism may be due to the fact that while the formation of a Rh monolayer on Ag surface may be possible, the Rh layer is then immediately covered by a layer of Ag [35]. This diffusion eliminates automatically all possible onset of magnetism as shown through tight-binding calculations using k-space recursion [361.
of the Pd spacer
Fig. 7. Difference of energy AE between ferromagnetic E(F) and antiferromagnetic E(AF) coupling between the Fe films versus the number of layers n in the Pd spacer. AE = E(F)E(AF) is negative whenthe ferromagneticcouplingis stable.
coupling is found stable. For 6 layers of Pd, the AF coupling becomes more stable. This result compares -qualitatively with the experiment of Celinski et al. [2] but the number of layers necessary to move from F to AF is half of those reported in ref. [2]. The discrepancy may be due to different reasons: 1) In the present calculation we have choosen the lattice parameter for Pd equal to au,,, a value which is a little greater than the bulk one. In some calculations, which consider one monolayer of Fe on Pd(OOl), the distance between Fe atoms is a little bit smaller than that of pure Fe [93. Also, the distance between Fe and Pd planes is given by: (uFe + a,,)/2 where uFe and uPd are respectively the lattice parameters of bulk Fe and Pd. In order to be complete, the effect of such a small variation has to be studied. 2) Besides this possible effect of the relaxation on the exchange coupling, the interface roughness between Pd/Fe may have a considerable effect on the exchange coupling. This has been discussed in great detail in the case of Fe/Cr [29]. These results do show the presence of an oscillation with a small period which has been already obtained through tight-binding calculation [30] and a long period oscillation which may be related to surface roughness [31]. Also in the
All these results and many others pledge for a more careful analysis of the diffusion process at the Pd/Fe interface and also to a study of the total energy of the system versus lattice relaxation.
6. Conclusion and outlook In this paper we have reported results concerning n adlayers of Pd on Fe(OOl), (FeJPd,), superlattices and Fe,/Pd,/Fe, sandwiches. Our method gives results in qualitative agreement with the SCLO calculation of Huang et al. [81 for the case of Pd monolayer on Fe(001). This gives some confidence for the other results reported in this paper. We notice especially the antiparallel coupling of the Pd layers in the case of Pd,/Fe(OOl). Determination of the exchange coupling in the trilayer FeJPdJFe,, for II = 2 to 6 shows that the ferromagnetic coupling is stable until IZ= 5, whereas, the antiferromagnetic coupling do show a greater stability for it = 6. This is in qualitative agreement with SMOKE results of Celinsky and Heinrich [2]. The quantitative disagreement may be related to the relaxation at the interface, surface roughness or/and interdiffusion. The theoretical models assume usually sharp interfaces. A first improvement towards “real systems” is to consider ordered compounds at the interface. This has been done for Fe/Cr [31] and Ni/Cu [37] in a tight-binding scheme. The magnetic moment distribution is strongly modified as compared to the abrupt interface. In such a case, the number of inequivalent atoms increases drastically. An-
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H. Nait-Laziz et al. / The Pd polarization at the Pd / Fe interface
other limitation is the nature of the real interface: probably the interdiffusion occurs on more than one plane and only partial chemical order occurs. These types of effect are under present investigation.
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The Pd polarization H. Nait-Laziz,
S. Bouarab,
at the Pd/Fe
interface
C. Demangeat
IPCMS, lJMR46, Universite Louis Pasteur, 4 rue Blake Pascal, 67070 Strasbourg, France
A. Mokrani Laboratoire de Physique du Solide Thkorique, 2, rue de la Houssini&e, 44072 Nantes, France
and H. Dreysse Laboratoire de Physique des Solides, BP 239, 54506 Vandoeuvre-les-Nancy, France
Received 8 April 1992; in revised form 19 June 1992
The electronic and magnetic properties of the ground state (T = 0 K) at the Pd/Fe(OOl) interface were investigated through the mean-field parameterized tight-binding method. Structurally, the Pd overlayers occupy the fee sites of the substrate, with a few percent expansion of the Pd-Pd distances as compared to the bulk fee Pd. We report results concerning deposition of n Pd layers on semi-infinite Fe. Ferromagnetic polarization of the Pd, layers are obtained up to n = 3. For n = 4, we have obtained ferromagnetic polarization of the nearest neighbour Pd overlayer but negative polarization for the three other planes. For n = 5, all the Pd atoms are polarized ferromagnetically unless the surface which has a quasi-zero magnetic moment. In the case of sandwiches Fe,,, /Pd, /Fe,,, or superlattices (Fe,Pd,), we investigate both ferromagnetic and antiferromagnetic couplings between Fe films through the Pd spacer. For completeness we perform also total energy calculations in order to study the exchange coupling displayed by Celinski and Heinrich [J. Magn. Magn. Mater. 99 (1991) L25]. Similar trends are found: ferromagnetic coupling is shown to be stable until ‘n= 5 for Fe, /Pd, /Fe, sandwiches; antiferromagnetic coupling is however stable for n = 6. We discuss the importance of the interface roughness on this oscillation.
1. Introduction
Recent experiments have revealed that Fe/Pd multilayers show ferromagnetic coupling between Fe layers through Pd spacer up to 12 layers of the non-magnetic compound [1,2]. For a higher number of Pd layers, a marginally small antiferromagnetic coupling is present. As it is well known, Pd Correspondence to: Dr. C. Demangeat, IPCMS, UMR46, Universite Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg, + 33-88-41-61-09; telefax: + 33-88-41-60-88; France. Tel.: email: [email protected]. 0304-8853/93/$06.00
is an incipient ferromagnet: a small percentage of Fe causes ferromagnetism and theoretically a paramagnetic-ferromagnetic (P-F) phase transition occurs in bulk Pd with 6% lattice expansion [3-51. Furthermore, giant moments for Fe impurities in Pd have been observed [6]. Electronic structure calculations based on density functional theory and the Korringa-Kohn-Restocker Green’s function method yield a consistent picture of the behavior of local moments of 3d impurities in Pd [7]. The calculated local impurity moments are in good agreement with experiment. However, less than 30% of the total induced
0 1993 - Elsevier Science Publishers B.V. All rights reserved
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moment is confined to the 42 Pd atoms in the first three shells around Fe. Due to the limited size of the cluster considered, these authors [7] were able to obtain the giant moment only by “fitting the unknown parameter”. Up to now, calculations concerning the Pd/Fe interface have been restricted to the case of a Pd/Fe,/Pd slab [8] or as Fe monolayer on Pd 293. In the spin-polarized self-consistent localized orbitals calculations of Huang et al. [8] the Pd monolayer has a magnetic moment of 0.37~~. The magnetic moment of an adjacent iron atom is 2.74pg, significantly larger than the central plane value of 2.37~~. The d bands of the two metals are found strongly hybridized. B&gel et al. [9] through Full-Potential-Linearized-Plane-Wave (FLAPW) method investigated the entire 3d transition-metal series as monolayer on Pd(001) and concluded that Fe/Pd(OOl) is ferromagnetic with Fe inducing moments of 0.32 and 0.17~~ in the first and second Pd layers respectively. However, from this calculation which uses a nine-layer (001) films containing seven layers of Pd and one 3d monolayer on each surface, only polarization up to second Pd layer are reported. It has also been argued recently that a few monolayers of Pd on Ag(OO1) may present magnetism [lo]. This experiment based on ElectronCapture-Spectroscopy (ECS) has suggested the existence of ferromagnetism in thin epitaxial films of Pd grown on Ag(001). However, experiments utilizing the Surface-Magneto-Optic-Kerr-Effect (SMOKE) fail to detect magnetism of Pd on Ag(OOl)/ll/ or Pd on Au(OO1) [12]. Recent calculations by Eriksson et al. [13] and Zhu et al. [14] do not display any onset of magnetism for an overlayer of Pd on Ag(OO1) or Au(OO1). We have recently argued [15,161, using tight-binding calculations, that the onset of ferromagnetism versus the exchange integral J, in the case of Pd films or overlayer on Ag(OOl), is obtained for a J smaller than the one necessary to get ferroniagnetism in the bulk. In the case of free-standing monolayer, we do not find any magnetism contrary to the calculation by. Zhu et al. [14]. This absence of magnetism is related to the small Density-ofStates (DOS) at the Fermi level of the monolayer. Our result is however in full agreement with
at the Pd /Fe interface
recent Linearized-Muffin-Tin-Orbital (LMTO) calculations showing no magnetism in the Pd monolayer range [17], for bulk lattice-parameter. Magnetism may however be obtained by changing the lattice parameter [8]. But, by increasing the number of Pd layers in the slab, magnetism appears more readily than in the bulk case. A thickness effect of the onset of magnetism may be present [15,18]. Free-standing Pd slabs, with bulk lattice-parameter are however only a “theoretician” model so that we have also performed calculation of n Pd layers epitaxially grown on Ag(OO1) [161. The results obtained are qualitatively similar with those of free-standing slabs i.e. our results display a strong thickness dependence of the onset of magnetism versus J. Therefore, these results can give an explanation concerning those obtained on Pd overlayer on Ag(OO1) through SMOKE [ll] and on thicker slab by ECS [lo]. Such thickness dependence has been already observed by Moodera and Meservey [193 in the case of V epitaxially grown on Ag(OO1). Polarization of Pd at the Fe/Pd interface is confirmed through SMOKE experiments [20], Angle-Resolved-Photoemission-Spectroscopy (ARPES) [21], Mijssbauer-spectroscopy [22], spin-resolved and spin-integrated photoemission 1231. In the case of Pd/Fe(OOl) interfaces, the films grow pseudomorphically [1,2,20,21] but, whereas Fe on Pd(001) is body-centered-tetragonal, Pd on Fe(001) expands its lattice parameter in order to accomodate for pseudomorphic growth [1,2]. Epitaxial growth of Pd(ll1) films on Fe(ll0) [231 or Fe(llO)/Pd(lll) superlattices [22], because of the considerable lattice mismatch, does require a special analysis. In this paper, using a mean-field parametrized tight-binding method, we present electronic and magnetic properties for an IZlayers Pd film grown on semi-infinite Fe(OOl), for Fe,/Pd,/Fe,, sandwiches and (Fe,/Pd,), superlattices. In all cases, the structural approach is an adjustment of the Pd lattice to that of Fe. In this “ideal” case, the lattice parameter of Pd is equal to that of Fe times fi. This expansion is however too small to induce magnetism in the bulk case [3-51. Magnetism is therefore obtained through the combined effect of strong hybridization between the
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d orbitals of Fe and Pd, and the lattice expansion. In section 2, the methodology and computational details are given. The results concerning the polarization of n layers of Pd on semi-infinite Fe(001) are presented in section 3. Section 4 is devoted to a comparison between the magnetism in FeJPdJFe, sandwiches and in (Fe,Pd,), superlattices. The results obtained with it = 2, 3 are very similar. We have compared two types of approximations: 1) global neutrality approach which allows charge transfer between the layers, the total number of electrons being kept constant and 2) a local neutrality approach. Both approaches do give almost the same polarization map. We have therefore restricted our calculations for the exchange coupling to the sandwich case (section 5). In this case we save a reasonable amount of computing time. Also, we have restricted our calculation to global neutrality for Fe,/Pd,/Fe, sandwiches. We discuss particularly, through total-energy-calculation, the stability of the ferromagnetic (F) and antiferromagnetic (AF) coupling between Fe, films through Pd, spacers. Section 6 is devoted to the conclusion.
n + 3 atoms (n Pd atoms, the Fe interface, the Fe subsurface and the centre of the Fe(001) slabs). Canonical hopping integrals are used [25]. Their values are adjusted in order to recover the d bandwidth given by Varma and Wilson [26]. We have taken, for J, the exchange integral, the value which gives the bulk magnetic moment of Fe at the centre of the 20-layer slabs. In the case of Pd, we cannot proceed in such manner because bulk palladium is non-magnetic. Therefore, we fix Jr, in order to recover the results of Moruzzi and Marcus [4] displaying onset of ferromagnetism when the Pd lattice is expanded by 6%. Let us note that we have taken for Nd (number of d electrons), the value 7 for Fe [24] whereas Nd = 9.52 for Pd [18]. For Fe, we take the hopping integrals corresponding to bulk Fe. The x, y coordinates of the Pd and Fe atoms in the (001) crystallographic face are identical: thus, the lattice parameter of Pd on Fe(001) is a little bigger than that of Pd bulk. Therefore, the hopping of Pd are modified through the inverse of the fifth power with distance [251: this small decrease of the hoppings is not enough to lead to the onset of ferromagnetism in the bulk. At the Pd/Fe interface, the hopping PFePd are given by:
2. Methodology
P FePd
Up to now, Huang et al. [8] have investigated the onset of ferromagnetism in Pd/Fe,/Pd(OOl) free-standing slabs through spin-polarized-selfconsistent localized-orbital calculations. In their calculation, the Pd monolayer has a magnetic moment of 0.37~, whereas, the iron atoms posses a magnetic moment of 2.74 and 2.37pB at the interface and at the centre of the slab respectively. We have recently shown [24] that, in order to recover the bulk magnetic moment of Fe at the centre of the free-standing slab, it is necessary to take into account 11 layers when 6 levels of the continued fraction are used. In order to avoid the computation in an 11 layer slab plus it layers of Pd, we mimic the semi-infinite Fe systems through a slab of 20 layers where only the surface and the subsurface layers are modified as compared to the bulk. Therefore, the calculations for 12layers of Pd on semi-infinite Fe(001) is performed on
A delicate problem is the determination of the relative positions of the Fe and Pd bands. To resolve that we have used two types of approximations: the first consists to an adjustment of the bulk Fermi levels in order to minimize charge transfer between Fe and Pd. A global neutrality condition is used for the derivation of the selfconsistent equations [16]; a local neutrality condition is used for the second type of approximation. Additional intrasite matrix elements are derived in order to get this local neutrality. The case of IZ layers of Pd on semi-infinite Fe(001) is mimicted by taking into account a slab of 20 Fe layers. In order to avoid surface effect at the centre of the slab (considerd as the bulk), at least 20 Fe layers must be considered. Only the local neutrality approximation has been used here. In the case of Fe,/Pd,/Fe, sandwiches and (Fe,/Pd,), superlattices, both local and global
=
\lPFeFePPdPd *
(1)
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neutrality approximations have been tested. The polarization of Pd is not greatly modified either through global or local neutrality. Therefore, in many cases, we have restricted our calculations in the global neutrality approximation. For sandwiches, we have investigated both ferromagnetic (F) and antiferromagnetic (AF) coupling through Pd spacers. A priori, the F coupling, at least for a small number of Pd layers must be stable because AF coupling between Fe films induces AF coupling in the Pd spacer. Antiferromagnetism in bulk Pd is unlikely as shown by Moruzzi and Marcus [27]. For a higher number of Pd layers, because of the fact that the polarization of Pd is rather limited (4 to 5 layers from Fe), the difference in energy between F and AF couplings slow down so that our method is unable to give pertinent results because this difference of energy becomes marginally small. All calculations have been performed within the recursion method [28] with 13 levels of the continued fraction.
3. n Pd layers on semi-infinite Fe(OO1) The lattice parameter of Pd in this configuration is equal to 6uFe, where uFe is the lattice parameter of bulk Fe. Therefore, the hopping integrals of Pd show a small decrease as compared to those of bulk Pd. The local neutrality is assumed in this section. Moreover, the difference between output and input magnetic moments must be smaller than 1O-4 for each layer. The results are reported in fig. 1. It can be seen that the magnetic moments on the iron atoms at the Pd/Fe(OOl) interface are increased as compared to bulk iron. This magnetic moment decreases slightly when going from semi-infinite Fe(001) to the case of it layers of Pd on Fe(001). More precisely, the magnetic moment at the Fe interface decreases when the number of Pd layers increases from 1 to 2. For thicker Pd slabs, the value of the magnetic moment at the iron interface does not change very much. This is probably related to the fact that we have restricted the hopping integrals up to second nearest neighbors. Fig. 1 displays a decrease of the magnetic moment on Pd atoms in the layer adjacent to Fe
b)
-0.20
]
I
I
1
Pd(l)
Pd(l+l)
Pd(It2)
Pd(I+i)
Pd(It4)
Fig. 1. Magnetic moment p &J per atom, for n layers of Pd on Fe(OOl), in the local neutrality approximation. Negative polarization is obtained only in the case of Pd, /Fe(OOl). ( A ) Pd, /Fe(OOl); (0) Pd, /Fe(OOl); (01 Pd, /Fe(OOl); (0) Pd, /Fe(OOl); (W) Pd, /Fe(OOl). In (a), Fe(B) is relative to bulk Fe, whereas Fe(I) and Pd(1) denote the interface atoms; Pd(I + p) is relative to Pd atoms (p = n - 1). The polarization of Pd is much lower than that of Fe so, we report in (b) the Pd atoms with a different scaling.
when one increases the number of Pd layers. The magnetic moment decreases from 0.35 to 0.27~~ when one goes from n = 1 to 3. When n is higher than 2, this magnetic moment remains constant. A very strange effect appears for it = 4. In this particular case, a negative polarization appears for atoms of Pd which are not at the interface with Fe. This specific magnetic distribution remains if we perform the calculation with a small variation of the exchange integral J. For 12= 5, only the magnetization at the interface with iron remains important: at the Pd surface the magnetic moment is roughly zero whereas, for the
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other layers, only low magnetic moments remain. This thickness effect is reminiscent to the one already found in the case of Pd slabs [15] and in the case of Pd overlayers on Ag(001) [181.
4. Comparison between Fe, /Pd,/Fe, wiches and (Fe, / Pd,), superlattices
sand-
In the preceding section we have discussed the magnetization map of an Pd, slab on semi-infinite Fe(001). A local neutrality approximation was used to perform this calculation. This type of calculation needs more CPU than the one performed in the case of global neutrality. In this section we discuss and compare the results obtained for FeJPdJFe, sandwiches and (Fe,/Pd,), superlattices. We discuss and compare also the results obtained in the case of local and global neutrality. Table 1 reports the results obtained for IZ= 2, 3. For (FeJPd,), superlattices and for FeJPdJFe,, sandwiches, the results obtained in the local neutrality approximation are the same as long as magnetic moments on the Pd atoms are considered. The same result holds also if we compare the two systems in the global neutrality approximation. Therefore, we can restrict our calculation to one type of approximation, i.e. the cheapest one. Extrapolation to the other physical situation is straightforward.
369
at the Pd / Fe interface
Comparison between local and global neutrality has also been performed for systems with the same configuration. Table 1 shows that the magnetic moments on Pd atoms are greater in the global neutrality approximation as compared to the local neutrality approximation. However, these results are qualitatively the same so that we restrict the determination of the exchange coupling between Fe films through Pd, spacers to the case of sandwiches. Moreover, experimental results [2] have been performed on Fe/Pd/Fe trilayer. We restrict therefore our determination of the exchange coupling of Fe through Pd spacer to the case of Fe,/Pd,/Fe, (section 5).
5. Exchange coupling in Fe,/ Pd,/Fe,
trilayers
We have determined the magnetization Fe,/Pd,/Fe, trilayer in two cases:
map of
1) the Fe, films are coupled ferromagnetically through the Pd spacer; 2) the Fe, films are coupled antiferromagnetitally through the Pd spacer. For each case we have also determined the total energies i.e. E(F) for the F coupling and E(AF) for the AF coupling. This calculation has been performed in the global neutrality approximation i.e., at each iteration step, the Fermi level is computed in order to keep the number of
Table 1 Magnetic moments p &I for 2 and 3 layers of Pd in Fe, /Pd, /Fe, sandwiches and (Fe, /Pd,), superlattices in the Local (L) and in the Global (G) neutrality approximations. Index I stands for atoms at the Pd/Fe interface; indices I + 1 and I-l are for atoms near the interface (Pd I +1 and Fe,_,); index C is relative to the centre of the Fe, slab; Indices S and S - 1 are for Fe surface and subsurface
’
Super lattices
Fer
Fer-i
Fe,
Fcr-i
Fe,
P4
Pd 1+1
(Fe, (Fe, (Fe, (Fe,
2.645 2.615 2.662 2.596
2.085 2.116 2.093 2.121
2.031 1.993 2.055 2.023
2.085 2.116 2.093 2.121
2.645 2.615 2.662 2.596
0.359 0.354 0.378 0.340
0.156 0.117
Fes 2.585 2.666 2.604 2.674
Fes-1 2.089 2.085 2.092 2.089
Fe, 1.992 1.944 2.004 1.962
Fer-i 2.083 2.124 2.088 2.126
Fer 2.677 2.630 2.683 2.613
Pdr 0.371 0.354 0.383 0.340
/Pd,),, /I’d,), /I’d,), /Pd,),
G L
G L
Sandwiches Fe, /Pd, /Fes Fe, /Pd, /Fe, Fe, /Pd, /Fe, Fe, /Pd, /Fe,
G L G L
Pd I+1
0.153 0.117
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000 -31 Fe
,
,
,
,
,
,
,
,
,
,
I
Fe
Fe
Fe
Fe
Pd
Pd
Fe
Fe
Fe
Fe
Fe
Fig. 2. Magnetic moment p (~~1 per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
electrons constant. Results of the magnetization map are reported in figs. 2-6 corresponding to n = 2-6 layers of Pd. From these figures it can be shown that the AF coupling between Fe layers reduces strongly the Pd polarization present in the case of F coupling. Also, the magnetic moment of the Fe atoms at the Fe/Pd interface is smaller in the AF coupling as compared to the F one. Charge transfer between layers are not very important (smaller than 0.1 electrons in all cases considered). The difference A E = E(F) - E(AF) of the total energies between F and AF couplings are reported in fig. 7. Up to five layers of Pd, the F
-3,
Fe
I
Fe
I,,
Fe
Fe
Fe
,
,
,
,
,
,
,
,
Pd
Pd
Pd
Pd
Fe
Fe
Fe
Fe
Fig. 4. Magnetic moment p &) per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
000 0 -31 Fe
)
,
,
,
,
I
,
I
,
,
,
I
,
,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Pd
Pd
Fe
Fe
Fe
Fe
e
Fig. 5. Magnetic moment p (~~1 per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
2 ‘-
2 z ~_~~~~~~~~~~~~~___________ .2 $
-I-
%
9 Fe
,
,
,
,
,
,
,
,
,
,
,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Fe
Fe
Fe
Fe
_2_
000
-3
Fe
Fig. 3. Magnetic moment p (cc,& per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
Fe
,
,
,
,
,
,
,
,
,
,
0 ,
Fe
Fe
Fe
Fe
Pd
Pd
Pd
Pd
Pd
Pd
Fe
I,
Fe
(
Fe
Fe
Fig. 6. Magnetic moment p (& per atom, for a trilayer Fe, /Pd, /Fe, for ferromagnetic (0) and antiferromagnetic (0) coupling.
H. Nait-Laziz
I
I
I
1
Pd2
Pd3
Pd4
Pd5
Thickness
et al. / The Pdpolarization
1
-1
Pd6
at the Pd /Fe interface
371
case of Rh overlayers on Ag(OOl), all self-consistent calculations do obtain a magnetic moment for the Rh atoms [13,32,33]. However, Mulhollan et al. [34] have shown through SMOKE that long-range spin-ordering is absent above 40 K. This absence of magnetism may be due to the fact that while the formation of a Rh monolayer on Ag surface may be possible, the Rh layer is then immediately covered by a layer of Ag [35]. This diffusion eliminates automatically all possible onset of magnetism as shown through tight-binding calculations using k-space recursion [361.
of the Pd spacer
Fig. 7. Difference of energy AE between ferromagnetic E(F) and antiferromagnetic E(AF) coupling between the Fe films versus the number of layers n in the Pd spacer. AE = E(F)E(AF) is negative whenthe ferromagneticcouplingis stable.
coupling is found stable. For 6 layers of Pd, the AF coupling becomes more stable. This result compares -qualitatively with the experiment of Celinski et al. [2] but the number of layers necessary to move from F to AF is half of those reported in ref. [2]. The discrepancy may be due to different reasons: 1) In the present calculation we have choosen the lattice parameter for Pd equal to au,,, a value which is a little greater than the bulk one. In some calculations, which consider one monolayer of Fe on Pd(OOl), the distance between Fe atoms is a little bit smaller than that of pure Fe [93. Also, the distance between Fe and Pd planes is given by: (uFe + a,,)/2 where uFe and uPd are respectively the lattice parameters of bulk Fe and Pd. In order to be complete, the effect of such a small variation has to be studied. 2) Besides this possible effect of the relaxation on the exchange coupling, the interface roughness between Pd/Fe may have a considerable effect on the exchange coupling. This has been discussed in great detail in the case of Fe/Cr [29]. These results do show the presence of an oscillation with a small period which has been already obtained through tight-binding calculation [30] and a long period oscillation which may be related to surface roughness [31]. Also in the
All these results and many others pledge for a more careful analysis of the diffusion process at the Pd/Fe interface and also to a study of the total energy of the system versus lattice relaxation.
6. Conclusion and outlook In this paper we have reported results concerning n adlayers of Pd on Fe(OOl), (FeJPd,), superlattices and Fe,/Pd,/Fe, sandwiches. Our method gives results in qualitative agreement with the SCLO calculation of Huang et al. [81 for the case of Pd monolayer on Fe(001). This gives some confidence for the other results reported in this paper. We notice especially the antiparallel coupling of the Pd layers in the case of Pd,/Fe(OOl). Determination of the exchange coupling in the trilayer FeJPdJFe,, for II = 2 to 6 shows that the ferromagnetic coupling is stable until IZ= 5, whereas, the antiferromagnetic coupling do show a greater stability for it = 6. This is in qualitative agreement with SMOKE results of Celinsky and Heinrich [2]. The quantitative disagreement may be related to the relaxation at the interface, surface roughness or/and interdiffusion. The theoretical models assume usually sharp interfaces. A first improvement towards “real systems” is to consider ordered compounds at the interface. This has been done for Fe/Cr [31] and Ni/Cu [37] in a tight-binding scheme. The magnetic moment distribution is strongly modified as compared to the abrupt interface. In such a case, the number of inequivalent atoms increases drastically. An-
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other limitation is the nature of the real interface: probably the interdiffusion occurs on more than one plane and only partial chemical order occurs. These types of effect are under present investigation.
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