c(2× 2) antiferromagnetic superstructure of Mn overlayers on Pd(001)

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N ELSEVIER

Journal of Magnetism and Magnetic Materials 159 (1996) 201-206

Journalof magnetism and magnetic materials

c( 2 X 2) antiferromagnetic superstructure of Mn overlayers on Pd( O01) Jamil Khalifeh Department of Physics, University of Jordan, Amman, Jordan

Received 11 September 1995; revised 30 October 1995

Abstract A self-consistent real-space calculation within the d-band tight-binding Hubbard Hamiltonian in the unrestricted Hartree-Fock approximation is carried out to examine the magnetic structure of epitaxial ultrathin body-centered tetragonal (bct) Mn layers on the surface (001) of Pd for different Mn thicknesses (l to 5 atomic layers). In plane ferromagnetic p(1 x 1) and c(2 x 2) superstructure phases are considered throughout this calculation. The c(2 x 2) in plane antiferromagnetic solution is found more stable for the monolayer in agreement with ab initio methods. The layer antiferromagnetic solutions are found more stable for thicker films so that Mn forms ferromagnetic (001) sheets and these sheets align antiferromagnetically. PACS: 75.30.Pd; 73.61.At

1. Introduction

Electronic and magnetic properties of low dimensional systems is a subject of growing interest in both fundamental as well as applied science. Epitaxial growth of 3d-magnetic transition metals on magnetic and nonmagnetic transition metal substrates has attracted much attention in recent years. Our main objective is to study the magnetic structure of Mn/Pd(001). Mn is located between Cr and Fe, where Cr is characterized by a dominant antiferromagnetic bulk structure and Fe is ferromagnet. However, the manganese-palladium system is of particular interest in view of the fact that the misfit between their lattice parameters is rather small which allows Mn to be epitaxially grown in a bct structure on a palladium substrate. Also, palladium is a paramagnetic element magnetically located at the verge of

being magnetic and its presence at the interface of manganese, which is characterized by the most complicated elemental magnetic and crystal structure, is sufficient to induce a sizeable magnetic moment. Experimental works have shown that metastable or alternate phases of transition metals can be stabilized by epitaxial growth on appropriate substrates. For example, Prinz et al. [1] have succeeded to grow a bcc Co layer and measured a ferromagnetic moment of 1.53 /xB in this layer. Furthermore, Heinrich et al. [2] were able to grow bcc Mn on a (100) Fe substrate and demonstrated that bcc Mn, like bcc Co, can be stabilized at room temperature and below by epitaxial growth. They also suggested that layers of Mn could be produced at other lattice constants by appropriate choice of substrates. Furthermore, Tian et al. [3,4] have reported on the epitaxial growth of Mn on Pd(001) surface up to thicknesses of 21

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layers. Their experiments show that many-layer epitaxial films of Mn can be grown on Pd(001) with a body-centered tetragonal (bct) structure, as determined by low-energy electron diffraction (LEED) intensity analysis. From a theoretical point of view, density-ftmctional theory has been used by Fuster et al. [5] to compute the ferromagnetic moment as a function of lattice constant for bcc and fcc Mn. The magnetic structure of Mn is found to be highly sensitive to the lattice constant. They extended their work to fcc Mn where a transition from zero moment to high moment is found as the atomic volume increases. Also, Fry et al. [6] employed the Linear Combination of Gaussian Orbitals (LCGO) method to calculate the ferromagnetic moment versus lattice constant curve for bcc Mn and found a low-spin to high-spin transition. Earlier the augmented-spherical-wave (ASW) method has been employed by Kubler [7] to investigate the stability of bcc Mn at a single value of lattice constant. Using total energy calculations, he found an antiferromagnetic state to be prefered energetically to both ferromagnetic and nonmagnetic states. Moruzzi et al. [8] have examined the transition from nonmagnetic to ferromagnetic behaviour for elemental V, Cr, Mn and Fe by analyzing self-consistent parameter-free total-energy band-structure calculations in the local-spin-density approximation utilizing a fixed-spin-moment procedure. They have shown that ferromagnetic bcc Mn undergoes a second-order transition to the paramagnetic state under compression and a first-order transition from a lowspin state to a high-spin state with expansion. Neither group dealt with the antiferromagnetic state. However, Fujii et al. [9] have carried out total-energy band calculations by the L M T O - A S A method for bcc Mn as a function of lattice constant for paramagnetic, ferromagnetic and antiferromagnetic states. They found that bcc Mn undergoes a first-order transition from a low-spin state to a high-spin state in the ferromagnetic and antiferromagnetic states. The above authors concluded that bcc Mn prefers the p aramagnetic state below lattice parameter a = 2.68 A, the low-spin ferromagnetic state between 2.68 and 2.95 A and the high-spin antiferromagnetic state above 2.95 A. Among those three states, the low-spin ferromagnetic state has the lowest value of the total

energy. In a recent work, we have studied the magnetic order in ultrathin Fe layers on Pd(001) [10]. For one Fe overlayer, the Fe magnetic moment is strongly enhanced (2.95 /~B) and an induced magnetic moment on the Pd interface (0.4 /-~B) ferromagnetically coupled with that of Fe is observed. A different behaviour of Cr overlayers on a Pd(001) substrate is found as Cr is antiferromagnetic in the bulk whereas Fe is a well-known ferromagnet [11]. In this work we try to follow the sequence of bcc 3d-transition metals which have particular magnetic structure such as Mn. This paper is organized as follows: a short description of the theoretical method is given in Section 2, results and discussion are presented in Section 3, and finally Section 4 is devoted to the conclusions.

2. Theoretical method In this work we investigate the magnetic structure of Mn overlayers deposited at the (001) surface of palladium for thicknesses varying from 1 to 5 monolayers. Our attention is focused on the stability of the p(1 × 1) ferromagnetic phase for thick layers and its competition with the antiferromagnetic c(2 X 2) superstructure on the one hand and to study the influence of the number of overlayers on the magnetism of the M n / P d interface on the other. The spinpolarized electronic structure is determined by solving self-consistently a d-band model Hamiltonian in the mean field approximation. The local densities of states per spin orbital are calculated within the framework of the recursion real-space technique. More details about the formalism used in this calculation have been described elsewhere [11,12]. It is well-known that the choice of Pd(001), by experimentalists, for epitaxial deposition of Mn thin films is usually made on the basis of an expected very small misfit between the lattice parameter of the surface square net of Pd(001) and the lattice parameter of Mn. Pd has a fcc structure with lattice constant a(Pd) (7.35 a.u.) while Mn, at low temperatures, has a bcc structure with lattice constant a(Mn) (5.40 a.u.). In fact, there is small mismatch (3.67%) of their primitive 2D square nets, as a(Mn) is greater than a ( P d ) / ~ - . A constant bulk volume of Mn is maintained for all Mn/Pd(001) systems and a bct

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structure is considered so that c / a = 1.12. The layer spacing at the interface of M n layers to the substrate is taken as the average value o f the layer distance b e t w e e n M n layers and the corresponding distance in the Pd substrate. Canonical hopping integrals of M n and Pd in the paramagnetic phase are adjusted to reproduce their bandwidths according to [13]. The e x c h a n g e integral of Pd is taken from the fact that bulk Pd b e c o m e s magnetic with six percent lattice expansion [14]. This corresponds to a value o f JPd = 0.559 eV which we h a v e used in other recent works [10,1 1]. On the other hand, JMn = 0.75 eV and this choice is considered f o l l o w i n g Christensen et al. [15].

e x c h a n g e integral, J ( M n ) . In the case o f one M n layer we observe a huge increase of the magnetic m o m e n t o f M n (4 / % ) and an induced magnetic m o m e n t of Pd (0.43 / % ) f e r r o - m a g n e t i c a l l y - c o u p l e d with M n for the p ( l X 1) IF phase. For the c(2 X 2) A F superstructure, the M n magnetic m o m e n t is also large but smaller than the p(1 X 1) f e r r o m a g n e t i c phase value (3.70 /zB). The M n magnetic m o m e n t s obtained in this calculation are c o m p a r a b l e to those o f the ab initio [16] results for the c(2 X 2) and p(1 X 1) structures. The saturation of m a g n e t i c moments to a m a x i m u m value o f (4 /z B) as shown in Fig. l a is due to the 'd' band approximation. Fig. lb shows the total energy per atom for the p(1 × 1) IF and c(2 X 2) I A F phase in d e p e n d e n c e on the M n e x c h a n g e integral, J ( M n ) . Our calculations indicate that the I A F superstructure is m o r e stable and appears at l o w e r values o f the M n e x c h a n g e integral, J ( M n ) , in a g r e e m e n t with the a b o v e - m e n t i o n e d ab initio results, in which they found that early transition metals V, Cr, and M n prefer the antiferromagnetic configuration, whereas Fe, Co, and Ni favor the f e r r o m a g n e t i c structure. Fig. l a shows that as a function o f JMn, a first order phase transition from the n o n m a g n e t i c to the magnetic p ( l X 1) is found and a second order phase

3. Results and discussion Our calculations are p e r f o r m e d for different thicknesses of Mn. Different solutions have been obtained and the results are s u m m a r i z e d in Table 1. Fig. 1 presents the m a g n e t i c m o m e n t s and energies of M n m o n o l a y e r deposited on Pd(001) surface. Fig. l a displays magnetic m o m e n t s for the p(1 × 1) in-plane f e r r o m a g n e t i c (IF) and c(2 × 2) in-plane antiferromagnetic ( I A F ) phase in d e p e n d e n c e on the M n

Table 1 Magnetic moments (in Bohr magnetons) of n Mn overlayers on Pd(001) for n = l to 5, where Jpj = 0.559 eV and JMn = 0.750 eV. IAF is the c(2 × 2) superstructure, IF is the p(1 x 1) F structure, and LAF refers to layer antiferromagnetic n

Magnetic structure

1

IAF

2

IF IAF

3

4

5

LAF, IF LF, IF IAF LAF, IF IAF LAF, IF IF IAF LAF, IF

Pd

Mn

( I - 1)

(I)

0.035 - 0.035 0.012 0.022 - 0.022 - 0.044 -0.113 - 0.032 0.032 0.014 -0.019 0.019 - 0.009 - 0.045 - 0.025 0.025 - 0.003

0.000 0.000 0.427 - 0.051 0.051 - 0.350 0.124 - 0.027 0.027 0.318 -0.40 0.040 - 0.314 0.310 - 0.034 0.034 0.324

(I) -

-

-

-

-

3.696 3.696 3.99 l 2.953 2.953 3.000 3.056 3.156 3.156 2.913 3.083 3.083 2.977 3.117 3.120 3.120 3.031

(I+ 1)

(1+2)

(I+3)

(I+4)

3.227 - 3.227 3.089 3.550 2.035 - 2.035 - 2.339 2.132 - 2.132 2.252 - 2.631 2.147 - 2.147 - 2.283

3.256 - 3.256 3.042 1.904 - 1.904 - 2.203 - 2.395 2.250 - 2.250 2.100

3.222 - 3.222 3.081 3.211 1.923 - 1.923 -2.122

3.210 -3.210 3.110

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012 013 014 01 016 017 018 Exchange Integral J M n ( eV ) Fig. 1. Mn monolayer deposited on Pd(001) surface: (a) magnetic moments for the p(l × 1) in-plane ferromagnetic and c ( 2 × 2 ) in-plane antiferromagnetic phase in dependence on the Mn exchange integral, J(Mn); (b) total energy per atom for the p(l × 1) in-plane ferromagnetic and c ( 2 × 2 ) in-plane antiferromagnetic phase in dependence on the Mn exchange integral, J(Mn).

Pd(001) in dependence on the number of Mn layers for the layer antiferromagnetic (LAF) configuration. It is clearly seen that as the Mn films become thicker the magnetic moments at the surface and the interface decrease and stablize to a limiting value which is relatively large (3 /~B). Polarization of the Pd substrate in dependence on the number of Mn layers (LAF) is shown in Fig. 3. The magnetic moment at the Pd interface is roughly 10% of the magnetic moment at the Mn interface and this value decreases by addition of more Mn overlayers. Pd interface and the layer just below are characterized by a c(2 × 2) IAF superstructure simi-

o,4~ transition to the magnetic c(2 X 2) superstructure is observed. Our calculations indicate that up to JM. = 0.4148 eV the magnetic moment of Mn does not exceed 0.001 /x B. A sudden jump in the magnetic moment to a value of 1.342 /x B occurs at JM. = 0.4150 eV. A close look at Fig. lb shows that the stability of the two configurations remains the same for reasonable values of JMn' A totally different behaviour from that of Cr/Pd(001) system in which a first order phase transition happens in the two magnetic structures [11]. Fig. 2 displays the magnetic moments at the surface and at the interface of Mn bct layers on

\ m ~ m / n

=~ 0,3 ~ v

- - u - - Pd(I)

0,21 E

- - o - - Pd(I-1)

0,1 1 0,01

o ~ ° ~ o ~ o ~ o n

1

u

i

i

2 3 4 Number of Mn layers

i

5

Fig. 3. Polarization of the Pd substrate in dependence on the number of Mn layers (LAF).

J. Khalifeh / Journal of Magnetism and Magnetic Materials 159 (1996) 201-206

105-

<

-5 <, -10 -15-20

--Q

I

I

I

I

I

1

2

3

4

5

Number of Mn layers Fig. 4. Total energy difference per atom between the LAF and IAF phase, in dependence on the number of Mn layers.

lar to that of Mn overlayers (Table l). Such polarization has been reported on by Blugel et al. [17] within Full-potential Linear Augmented Plane Wave (FLAPW) method in their investigation of the spin polarized electronic structure of a monolayer of the 3d transition metal series on Pd(001). With the exception of V, all these metals induce a magnetic moment on the 2 layers of Pd, the surface and the layer just below. The enhancement of the magnetic moment in M n / P d system could be due to the polarization of the Pd atoms because Pd is a strong paramagnet and a small addition of magnetic elements induces a magnetic moment at Pd sites [18]. This sort of behavior appeared in the case of F e / P d alloys, as a neutron diffraction study has indicated that Pd atoms carry magnetic moments of about 0.36 /~B [19]. Fig. 4. shows the difference in energy per atom between the LAF and the IAF structures in terms of the number of Mn layers. With the exception of the one overlayer which we discussed above, the LAF magnetic ordering is found more stable. It is worth mentioning that we have imposed other metastable solutions (LF,IF) for n > 2 but they always converged into (LAF,IF) configuration.

205

phase, the Mn magnetic moment is strongly enhanced (3.99 P~B) and an induced magnetic moment on the Pd interface (0.43 /~B) ferro-magneticallycoupled with that of Mn is observed. For the c(2 X 2) antiferromagnetic superstructure, the Mn magnetic moment is also large but smaller than the p(1 × 1) ferromagnetic phase value (3.70 /~B). (ii) For thicker Mn layers, two different solutions are obtained for each system: c(2 × 2) superstructure phase and p(1 X 1) ferromagnetic phase. By considering energy, the LAF solution is found more stable for all thicknesses. A possible explanation for the transition from the IAF to the LAF configuration for thicker Mn layers might be due to the fact that the interatomic exchange energy 12 between second neighbours in the bct lattice leads to the IAF structure for the single monolayer, while the LAF structure is dominated by the (larger) exchange coupling 11 between nearest neighbours. The appearance of various magnetic configurations in the M n / P d system reflects the complicated magnetic structure of Mn bulk form and its dependence on the geometry and lattice parameter. Finally, our results indicate the sensitivity of the magnetic state of Mn to its presence at the interface with Pd. The magnetic moments of Mn for the monolayer case are in reasonable agreement with those of the ab initio methods. On the other hand, no results for thicker films of Mn deposited on the surface (001) of Pd are available in the literature to compare with.

Acknowledgements I would like to thank P. Rennert, W. Hergert and A. Chass6 of Martin Luther University, C. Demangeat and O. Elmouhssine of the group GEMME-IPCMS Strasbourg, for enlightening discussions. A financial support from the Alexander von Humboldt Foundation (Bonn) is highly acknowledged.

4. Conclusion We obtained the following results: (i) for one Mn overlayer, two solutions are found: in plane ferromagnetic p(1 X 1) phase and c(2 X 2) superstructure phase. For the p(1 × 1) ferromagnetic

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J. Khalifeh / Journal of Magnetism and Magnetic Materials 159 (1996) 201-206

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