Magnetic configurations of hexagonal iron rheniummultilayers

H. Zenia a, S. Bouarab a,*, C. Demangeat b

a Laboratoire de Physique et Chimie Quantique, Facult�ee des Sciences, Universit�ee Mouloud Mammeri de Tizi-Ouzou,

15000 Tizi-Ouzou, Alg�eerieb Institut de Physique et Chimie des Mat�eeriaux de Strasbourg, 23 Rue du Loess, F-67037 Strasbourg, France

Received 9 April 2002; accepted for publication 25 May 2002

Abstract

We present ab initio calculation of the electronic structure and magnetic properties of Fe/Re multilayers assum-

ing hcp crystallographic phase. The system is modeled according to recent structural analysis which shows that Fe/Re

has bct(0 0 1) ordering for 06 tRe 6 8 �AA after which a structural phase transition occurs to an hcp phase. Antiferro-

magnetic and ferromagnetic orders appear more stable than the nonmagnetic (NM) state, only when the Fe atoms

begin to adopt an expanded volume of about 27% accompanied by an axial distortion (c=a ¼ 1:42). The sizeable

magnetic moments calculated on Fe atoms contrast with the paramagnetic bulk hcp. These results are discussed and

compared with recent experimental data on hcp Fe/Re superlattices and also with magnetic properties of Fe/Ru

multilayers.

� 2002 Elsevier Science B.V. All rights reserved.

Keywords: Density functional calculations; Metal–metal interfaces; Magnetic interfaces; Iron; Rhenium

1. Introduction

Until the work of Perjeru et al. [1] the hexago-

nal closed-packed (hcp) structure for bulk Fe, Fe

multilayers, Fe alloys has been generally associ-

ated with a paramagnetic state. Perjeru et al. [1]

within magneto-optical Kerr effect (MOKE) and

X-ray magnetic circular dichroism (XMCD) onFe/Re multilayers with an Fe thickness fixed at 8 �AAand a variable thickness of Re found a sizeable

magnetic moment on the Fe atoms. For a low

thickness of Re the system behaves with a bct

structure but a transition towards hcp phase

appears at Re thickness of about 8 �AA. For all

thicknesses of Re the magnetic moment per Fe

atom remains about 2 lB which is roughly the

magnetic moment of the ground state of Fe in bcc

structure [2]. Therefore, the magnetic momentsobtained for the Fe/Re superlattices in the bct

configuration is not surprising. The surprise arises

for the hcp phase of Fe/Re superlattices because

hcp-Fe is known to be nonmagnetic (NM) so that,

Re being also NM in the bulk, it is by no means

clear why if two NM elements are in close con-

tact, XMCD displays a considerable polarization.

*Corresponding author. Tel./fax: +213-26-21-48-48.

E-mail address: sbouarab@yahoo.fr (S. Bouarab).

0039-6028/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0039-6028 (02 )02297-5

Surface Science 521 (2002) 49–56

www.elsevier.com/locate/susc

Perjeru et al. [1] have explained this onset of

magnetization via a considerable increase of the

volume of Fe in the hcp phase of Fe/Re multi-

layers. Indeed, it is known from density functional

(DFT) calculations that e-Fe has NM ground state

[3,4] but a small increase in the atomic volume canlead to FM state [4] and e-Fe stabilized under

normal conditions in thin films when grown on

hcp elements with large lattice parameter can

therefore present a magnetic moment.

The purpose of the present communication is

therefore to perform DFT calculations on these

hcp Fe/Re superlattices in order to confirm (or

kill) the explanation given by Perjeru et al. [1]. Toour knowledge, the Fe/Re system is the unique

case where hcp Fe quenched in hcp lattice presents

such high magnetic moment. Let us notice how-

ever that the group of Piecuch [5–7] has also

shown that Fe can adopt an expanded hcp struc-

ture in Fe/Ru superlattices but in that case the Fe

layer at the interface with Ru is mainly magneti-

cally dead. Another study [8] showed that hcp Festabilized in Fe/Ru(1 0 2) multilayers has no mag-

netic moment. This difference of behavior between

Fe/Ru and Fe/Re superlattices may be related to

the predominant immiscibility between Fe and Re

(at least over most of the composition range)

whereas hcp FeRu alloys can be prepared. An-

other big difference is that the in-plane interatomic

distances in hcp Re are expanded by about 3%with respect to hcp Ru and this could give more

support to a possible onset of magnetic polariza-

tion of hcp Fe on Re(0 0 1). The (1 1 1) surface of

fcc metals being also of hcp symmetry the growth

of Fe on these close packed structure could have

some interest in the present discussion. Indeed,

within pulsed laser deposition (PLD) Shen et al. [9]

succeeded in growing isotropic Fe films onCu(1 1 1) with ferromagnetic (FM) behavior at

least up to 3 ML. DFT calculations by the group

of Kr€uuger [10,11] displayed reasonable agreement

with the experimental results.

In this work, we carried out ab initio study in

the framework of the tight-binding linear muffin-

tin orbital method (TB-LMTO) in the atomic

sphere approximation (ASA) on Fen/Re7 (n ¼1,3,5) multilayers in hcp structure with various

structural and magnetic configurations. As a first

step, we assume that the Fe film adopts an ideal

hcp structure (c=a ¼ 1:633) with the calculated

lattice constant (a ¼ 2:75 �AA) of Re substrate. Forcomparison we have also considered the experi-

mental [1] lattice constants (a ¼ 2:75 �AA, c ¼ 4:45�AA) for which the hcp structure is slightly distortedaxially (c=a ¼ 1:618). In the second part of this

paper and following the possible intermixing at the

interface reported by Perjeru et al. [1], we investi-

gate the effect of interdiffusion at the Fe/Re in-

terface. Finally as last step towards a more realistic

modeling study, we report also on the effect of

perpendicular interlayer relaxation on the mag-

netic properties of such multilayers. We focus es-pecially on the onset of magnetic order in the hcp

Fe film as function of the atomic volume rather

than on the energy minimum which can be con-

sidered as semi-quantitative since ASA relaxation

gives only a general trend.

2. Methodology

Our work has been performed using the TB-

LMTO–ASA method [12,13]. This method con-

sists of resolving self consistently the Kohn–Sham

equations in a minimum basis approach. The ex-

change and correlation effects were taken into

account within the generalized gradient approxi-

mation (GGA) functional due to Langreth andMehl-Hu [14]. The choice for the functional has

been made because it yields accurate bulk prop-

erties for hexagonal iron. To simulate Fe/Re

multilayers, we have used the well-known super-

cell technique consisting of a periodical repeti-

tion of a set of thin symmetry preserving films

[15]. We have fixed the Re thickness to 7 ML�s andvaried the number of Fe ML�s to study the possi-ble dependence of magnetic and structural prop-

erties on the film thickness. In order to investigate

possible intermixing at the Fe–Re interface we

have doubled the cell perpendicular to the c-axisleading to planes containing two inequivalent

atoms each. The electronic and magnetic struc-

tures are calculated using an increasing number

of k-points in the irreducible Brillouin zoneuntil convergence which is achieved for 168 k-points.

50 H. Zenia et al. / Surface Science 521 (2002) 49–56

3. Results

3.1. Pure hexagonal iron and rhenium

Rhenium is a 5d transition metal with half filledband and hcp phase. Watson et al. [16], have

shown that hcp Re structure is more favored under

compression than the bcc phase, confirming ex-

perimental results [17] that, down to a volume

fraction V =V0 of 0.734, Re remained in the hexa-

gonal phase. Furthermore, Re is found to be

thermally stable to a temperature of more than

3000 K. These features make Re very suitablesubstrate for stabilizing thin hexagonal metallic

films. Besides, the Re single crystal surface is

known to provide a very smooth hexagonal lattice

with low mean corrugation amplitude. Thus,

the effects of surface roughness inherent to other

substrates are expected to be less important. Fig. 1

displays the total energy variation with lattice

parameter (a) assuming an ideal c=a ratio. Thecalculated lattice constant aRe ¼ 2:75 �AA is in

agreement with experimental [18] data (2.76 �AA) forNM ground state.

While Fe adopts an hcp structure in Fe/Re

multilayers [1], we carried out a study of magnetic

properties of the bulk Fe in this structure. Fig. 2

shows the Fe total energy variation in FM, Anti-

ferromagnetic (AFM) and NM configurations for

an ideal c=a ratio. The equilibrium lattice para-

meter aFe ¼ 2:43 �AA is in agreement with experi-

mental [19] data and other theoretical results

[20,21]. The NM phase is the ground state and is

located on the brink of a phase transition to AFM

ordering at a ¼ 2:51 �AA. A second order NM–AFMtransition occurs at a ¼ 2:46 �AA. At aRe ¼ 2:75 �AA(lattice parameter of the ground state of hcp Fe),

the FM phase is the ground state with a moment

of 2.83 lB. The increase of the Fe lattice parameter

imposed by the larger Re one in Fe/Re multilayers

plays a major role in the stabilization of the FMFig. 1. Calculated total energy of bulk ideal (c=a ¼ 1:633) hcp

Re versus in-plane lattice parameter (a).

Fig. 2. Calculated total energy and magnetic moments of ideal

(c=a ¼ 1:633) hcp Fe against the in-plane lattice constant (a).

H. Zenia et al. / Surface Science 521 (2002) 49–56 51

phase in Fe layers as reported by the experimental

work by Perjeru et al. [1].

3.2. Fen/Re7 multilayers in ideal hexagonal structure

We first discuss the results of magnetic prop-erties of Fen/Re7(0 0 0 1) superlattices with n ¼ 1, 3

and 5. As stated in the introduction we assume hcp

structure in the whole system with two sets of

lattice parameters corresponding to the experi-

mental situation [1] (a ¼ 2:75 �AA, c ¼ 4:45 �AA) andto the calculated equilibrium in-plane lattice con-

stant strained to the ideal hcp phase of the Re

substrate (a ¼ 2:75 �AA, c=a ¼ 1:633). By takingseven layers of Re (13 �AA) we are above the criticalthickness of tRe ’ 9 �AA from which the Fe/Re

multilayers adopt an hcp structure [1]. We checked

that 7 ML�s give rise to bulk atomic state in the

middle of the Re slab. For the study of the spin

polarization we consider three possible magnetic

configurations, FM, AFM and NM. In the case of

1 ML of Fe we investigate the in-plane row-by-rowAFM phase whereas for higher thicknesses we

consider an interplane coupling assuming collinear

spin orientation.

The magnetic ground states of Fe1/Re7 are

summarized on Table 1 for the experimental and

theoretical lattice spacings. One can notice a quasi-

degeneracy of the FM and AFM configurations

with a difference of 4 meV/atom between them sothat it is difficult to distinguish between the two

magnetic orders. The Fe atoms bear a magnetic

moment of 2.13 lB in the case of ideal hcp phase

with the calculated Re in-plane lattice parameter.

In the Re interface layer the induced spin polari-

zation is 0.05 lB with antiparallel orientation with

respect to adjacent Fe moments. The reducedmagnetic moments of Fe atoms compared to hcp

bulk (at aRe) results from a strong hybridization

with Re.

The results obtained in the case of Fen/Re7multilayers (n ¼ 3, 5) for the two sets of parame-

ters are very similar, so we discuss here only those

obtained with the calculated in-plane lattice pa-

rameter (a ¼ 2:75 �AA) for ideal hcp structure (Table2). For Fe3/Re7 multilayers, the FM order is the

ground state, lying 16.64 meV/atom lower than

the AFM solution and well below the NM state.

The interface Fe atoms display a large magnetic

moment of 2.59 lB whereas the inner Fe layer

bears a moment of 2.87 lB. The iron spin polari-

zation induces a small magnetic moment of 0.11

lB on the interface Re atoms oriented antiparallelto those of Fe. The use of GGA for the exchange

and correlation functional, with its tendency to

overestimate magnetic moments, may be one of

the reasons of the discrepancy between the calcu-

lated and the measured [1] magnetic moments on

Fe sites which are only 2.2 lB.

For Fe5/Re7 superlattice (Table 3), the FM

order is also clearly the ground state with energydifference of 33.78 meV/atom with respect to the

AFM state. One can notice that at the same lattice

spacings (a ¼ 2:75 �AA, c=a ¼ 1:633) pure hcp iron

displays a moment (2.83 lB) very similar to that of

the central layer (2.80 lB). For comparison be-

tween the Fe/Re and Fe/Ru multilayers we report

also on Table 3 the moments obtained by Spi�ss�aak

Table 2

Total energy differences DE and magnetic moments on Fe and

Re atoms (I is the index of interface layers) of Fe3/Re7 multi-

layers in FM, interplane AFM and NM arrangements for ideal

hcp structure (a ¼ 2:75 �AA, c=a ¼ 1:633)

Fe3/Re7 Magnetic

configura-

tion

DE (meV/

atom)

lFeðIÞ(lB)

lFeðI�1Þ(lB)

lReðIÞ(lB)

FM 0.00 2.59 2.87 )0.11AFM 16.63 2.33 )2.81 )0.13NM 102.78 – – –

Table 1

Total energy differences DE and magnetic moments on interface

(I) Fe and Re atoms of Fe1/Re7 multilayers in FM, in-plane

AFM and NM arrangements for the experimental and theo-

retical parameters

Lattice spacings Magnetic

configura-

tion

DE (meV/

atom)

lFe

(lB)

lReðIÞ(lB)

Experimental [1] AFM 0.00 2.05 0.05

a ¼ 2:76 �AA FM 4.07 1.86 )0.14c=a ¼ 1:618 NM 11.13 – –

Theoretical AFM 0.00 2.13 0.05

a ¼ 2:75 �AA FM 4.12 2.09 )0.14c=a ¼ 1:633 NM 13.65 – –

52 H. Zenia et al. / Surface Science 521 (2002) 49–56

et al. [20] with the Vienna ab initio simulationpackage for Fe5/Ru5 in ideal hcp structure (aRu ¼2:70 �AA). FM order appears as the ground state for

both multilayers with nearly the same magnetic

moments. Let us remember that in Fe5/Ru5 mul-

tilayers the FM configuration was also favored

over any possible AFM state in both hcp and hp

phases [20]. The Fe spin polarization at this ex-

panded volume (44%) in Fe5/Re7 in ideal hcpstructure does not seem to be strongly affected by

the Re substrate. The complexity of Fe/Re or Fe/

Ru multilayers is particularly reflected in the

structural properties and a question of funda-

mental interest remains unresolved: from which

expanded volume and its corresponding perpen-

dicular interlayer spacings, Fe hcp becomes mag-

netically ordered on Re(0 0 0 1).

3.3. Interlayer relaxation effects

As a result of the large lattice mismatch be-

tween elemental Fe and Re, the Fe atoms adopt

very large excess volume per atom when deposited

on Re if a regular hcp structure is assumed. From

experimental point of view, Fe was found to adoptsizeable expanded hcp volume on Re(0 0 0 1) [1] or

Ru [5–8]. Ab initio calculations by Spi�ss�aak et al.

[20] displayed, for Fe/Ru multilayers, very similar

behavior as that reported here for the Fe/Re

multilayers. However, the relaxation effect of the

Fe interlayer distances along the [0 0 1] direction in

Fe/Ru superlattices stabilizes the FM hp structure

rather than the hcp one. A full structural relax-ation of interlayer distances in Fe5/Ru5 superlat-

tice leads also to stabilize the hp geometry with

average axial ratio cFe=aRu ¼ 1:47 corresponding

to an expanded volume of 6.7% with respect to

hypothetical bulk hp (24.5% with respect to hcp

Fe).

Fig. 3 shows the dependence of the total energyin Fe5/Re7 multilayer on axial distortion cFe=aRe(aRe ¼ 2:75 �AA) in the Fe film along with the be-

havior of the magnetic moments on each Fe atom.

We focus our discussion especially on the onset of

Table 3

Total energy differences DE and magnetic moments on Fe and Re atoms (I is the index of interface layers) of Fe5/Re7 multilayers in

FM, interplane AFM and NM arrangements. For a qualitative comparison, we report in parenthesis also the calculated magnetic

moments obtained by Spi�ss�aak et al. [20] for Fe5/Ru5 multilayers in ideal hcp structure (aRu ¼ 2:70 �AA)

Fe5/Re7 Magnetic configuration DE (meV/atom) lFeðIÞ (lB) lFeðI�1Þ (lB) lFeðI�2Þ (lB) lReðIÞ (lB)

FM 0.00 2.61(2.59) 2.85(2.75) 2.80(2.75) )0.12(lRu ¼ �0:18)AFM 33.78 2.35 )2.76 2.65 )0.13NM 169.86 – – – –

Fig. 3. Calculated total energies and magnetic moments of Fe5/

Re7 multilayers versus the axial ratio (c=a), where a ¼ 2:75 �AA. I

denotes the interface index.

H. Zenia et al. / Surface Science 521 (2002) 49–56 53

magnetism in hcp Fe and its corresponding mini-

mum volume from which such polarization ap-

pears rather than on the equilibrium volume.

From the fact that bulk hcp Fe is NM, the spin

polarization in Fe/Re multilayers must derive

predominantly from an expanded volume sincebulk Re is also paramagnetic. In the case of

pseudomorphic growth in Fe/Re multilayers, hcp

Fe at volume corresponding to its bulk ground

state is clearly NM.

As seen in Fig. 3, the AFM order appears for

c=a ¼ 1:38, and the FM state for slightly higher

atomic volume (c=a ¼ 1:42). Both AFM and FM

orders appear more stable than the NM state, onlywhen Fe atoms begin to adopt an expanded vol-

ume of about 27% which is accompanied by an

axial distortion (c=a ¼ 1:42). However these two

magnetic orders remain quasi-degenerate up to

c=a ¼ 1:50. For larger volumes the FM phase be-

comes more stable. When both magnetic orders

are present, the central layer bears nearly the same

magnetic moment whereas at the interface the FMorder gives rise to slightly higher moments. The

energy minimum is obtained for an expanded

volume of about 31% corresponding to an axial

ratio of cFe=aRe ¼ 1:48 which is significantly lower

than the experimental value of 1.618 given by

Perjeru et al. [1]. Nevertheless, this result is more

consistent with the calculation of Spi�ss�aak et al. [20]

devoted to Fe5/Re5 multilayers, for which the au-thors found the value cFe=aRu ¼ 1:49, although ourcalculations yield much larger atomic volume for

iron because of the lattice constant of Re which is

larger than that of Ru.

3.4. Interdiffusion effects

A further step into more realistic study is toconsider if the short-range interdiffusion pheno-

mena, at the Fe/Re interface, limited to �1 ML [1]

could influence the magnetic properties of the Fe/

Re multilayers. In order to explore that, we carried

out a calculation in the case of Fen/Re7, n ¼ 1, 3 by

doubling the cell along the growth axis and as-

suming an ideal hcp phase with the calculated Re

lattice constant. We suppose also that the layersaround the interface are of Fe0:5Re0:5 composition.

Interlayer AFM coupling is found to be the

ground state in the case of Fe1/Re7, but the energy

difference with the FM solution is only 1.23 meV/

atom. Moreover this AFM solution lies 6.5 meV/

atom lower than the corresponding ground state of

the perfect Fe/Re interfaces so that interface al-

loying cannot be ruled out during the growingprocess. On one hand, this supports the experi-

mental measurements [1] where alloying is found

to occur although limited to one ML around the

interface. On the other hand this is at odd to the

expected behavior of Fe and Re known to be im-

miscible for most of the composition range. The

magnetic moments on the Fe atoms are of �1.8 lB

whereas on the same mixed layer, Re atoms ac-quire moments of about 0.1 lB oriented antipar-

allel to the neighboring Fe ones.

Now we discuss the case of larger Fe thickness

namely Fe3/Re7 much closer to the experimental

situation. In this case the FM phase is still, as for

perfect interfaces, more stable than the NM and

AFM solutions. However, such FM order with

interfacial mixing appears less likely than the FMphase without interdiffusion, the energy difference

being 18.45 meV/atom. The interface Fe magnetic

moments are now 2.00 lB i.e. smaller than those of

the perfect interface.

We can conclude by saying that the interdiffu-

sion of 50% Fe–Re composition at the interface

has no effect on the magnetic phases considered in

the case of Fen/Re(0 0 0 1) multilayers with n > 3.The case of 1 ML Fe is not representative of an

hcp structure and the first stages of the growth

process are usually complicated and lead to atomic

structures which are not easily simulated. We can

notice also that the interdiffusion considered does

not give rise to dead magnetic layers in agreement

with the calculated results reported by Spi�ss�aak et al.[20] in Fe/Ru multilayers.

A qualitative comparison can be made with

the growth of Cu multilayers on Re(0 0 0 1) as Fe

may be expected to have similar chemical behav-

ior with Cu. Indeed both metals are claimed to

be immiscible with Re up to very high propor-

tions, the formation of an alloyed structure at the

Cu/Re interface was found to be very unlikely

from temperature-programmed desorption spec-troscopy (TDS) data gathered in the work of

Wagner et al. [22].

54 H. Zenia et al. / Surface Science 521 (2002) 49–56

4. Conclusions

We have presented ab initio study of magnetic

and structural properties of Fe/Re(0 0 0 1) multi-

layers in order to explain the magnetism foundexperimentally. The electronic and magnetic cal-

culations of Fen/Re7 multilayers with n ¼ 1, 3 and

5 in the ideal hcp structure reveal the tendency of

Fe atoms to acquire finite magnetic moments. In-

plane AFM alignment is the ground state in the

case of 1ML Fe, the FM phase becoming more

stable when the Fe film thickness increases, in ac-

cordance with experiment [1]. The Fe magneticmoments in the central layer of the Fe film are

nearly equal to those of bulk Fe atoms (with the

same lattice parameter), whereas the moments on

the Fe interface layer are somewhat reduced by the

hybridization effect with Re. The onset of magne-

tism on the Fe sites gives rise to spin polarization

on the adjacent Re atoms, although with much

smaller magnitudes and always oriented antipar-allel to their neighboring Fe moments. The effects

of interlayer relaxation are studied versus the in-

terlayer distances between the Fe layers while the

lattice spacings in the Re film are fixed to their

ideal values in the hcp phase. In this case, the onset

of AFM order occurs for somewhat smaller ex-

panded volumes accompanied by a significant

axial ratio distortion of c=a ’ 1:38. The FM ordersappears for slightly larger volume than for AFM

with c=a ¼ 1:42. The energy minimum is obtained

for c=a ¼ 1:48 which is still a large excess volume

per atom, compared to Fe bulk equilibrium value

and could explain the onset of magnetic ordering

and the high magnitudes of Fe magnetic moments.

Despite the well-known immiscibility of Re and

Fe, interdiffusion is found to occur at small Felayer thickness and disappears when the number of

Fe layers increases. The present calculation was

restricted to rather small supercell whereas larger

supercells may reveal more complex magnetic

configurations as already discussed for the other

compact Fe phase [23]. Other possible geometric

structures could be also be addressed as well and

could reveal defaults in the hexagonal stackingconsidered so far as seen in Fe/Ru multilayers

where the Fe film is predicted to assume bcc-like

structure at larger Fe film thicknesses in contrast

to the hcp stacking [6,20]. Due to the large lattice

mismatch between Fe and Re, large constraints are

present at the Fe/Re interfaces so that more

complex atomic structures may appear there with

reduced average distance between the Fe atoms.

Consequently, this could lead to smaller momentsas found experimentally.

Acknowledgements

This work was supported by the Algerian pro-

ject ANDRU/PNR3 (AU4 499 02) and by a col-

laborative programs DEF-CNRS and CMEP (99MDU 449) between the University Louis Pasteur

of Strasbourg, France and the University Mou-

loud Mammeri of Tizi-Ouzou, Algeria.

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