IOP PUBLISHINGNANOTECHNOLOGY

Nanotechnology 18 (2007) 235702 (6pp)

doi:10.1088/0957-4484/18/23/235702

Spin configuration in a frustrated
ferromagnetic/antiferromagnetic
thin-film system
T K Yamada1 , E Martı́nez2 , A Vega3 , R Robles4 , D Stoeffler5 ,A L Vázquez de Parga6 , T Mizoguchi1 and H van Kempen7
1

Faculty of Science, Gakushuin University, 171-8588 Mejiro, Tokyo, Japan
Fachbereich Physik, Universität Osnabrück, D-49069 Osnabrück, Germany
3
Departamento de Fı́sica Teórica, Atómica y Óptica, Universidad de Valladolid, 47011
Valladolid, Spain
4
Department of Physics, Uppsala University, SE-75121, Sweden
5
Institut de Physique et Chimie des Matériaux de Strasbourg (UMR C7504 CNRS-ULP),
Strasbourg, France
6
Departamento de Fı́sica de la Materia Condensada, Universidad Autónoma de Madrid,
Cantoblanco 28049, Madrid, Spain
7
Institute for Molecules and Materials, Radboud University, Toernooiveld 1, 6525 ED
Nijmegen, The Netherlands
2E-mail: edmartin@uos.de

Received 6 March 2007, in final form 17 April 2007
Published 8 May 2007
Online at stacks.iop.org/Nano/18/235702
Abstract
We have studied the magnetic configuration in ultrathin antiferromagnetic
Mn films grown around monoatomic steps on an Fe(001) surface byspin-polarized scanning tunnelling microscopy/spectroscopy and abinitio-parameterized self-consistent real-space tight-binding calculations inwhich the spin quantization axis is independent for each site, thus allowing
noncollinear magnetism. Mn grown on Fe(001) presents a layered
antiferromagnetic structure. In the regions where the Mn films overgrows Fe
steps the magnetization of the surface layer is reversed across the steps.
Around these defects a frustration of the antiferromagnetic order occurs. Dueto the weakened magnetic coupling at the central Mn layers, the amount offrustration is smaller than in Cr, and the width of the wall induced by the step
does not change with the thickness, at least for coverages up to sevenmonolayers.
(Some figures in this article are in colour only in the electronic version)

nature of the frustrations, it has not been possible to resolve
the spin configurations until the introduction of the spinpolarized scanning tunnelling microscopy/spectroscopy (SPSTM/STS) [5].
This problem is also important from the technologicalpoint of view. Exchange bias is one of the phenomena
associated with the exchange anisotropy created at the interface
between an antiferromagnetic material and a ferromagnetic
material. Materials exhibiting exchange bias have been usedin several practical applications since their discovery [6–8].
In the world of magnetic devices, the goal is to get smaller.

1. Introduction
The interface of ferromagnetic and antiferromagnetic material
is important from a scientific point of view because thecompeting ferromagnetic and antiferromagnetic interactions
may lead to complex configurations, particularly when
there is frustration in the system. In particular, when
an antiferromagnetic layer is deposited on a ferromagnetic
substrate with an atomic step (‘hidden atomic step’) themagnetic frustration around this extended defect can give riseto interesting magnetic structures [1–4]. Due to the localized
0957-4484/07/235702+06$30.00

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T K Yamada et al

W tips were cleaned by Ar sputtering and annealing andthen covered with 10 nm Fe. SP-STS measurements were
performed in two different ways: in the first one, I (V ) curves
were obtained at every pixel of a constant-current topographic
image and then numerically differentiated. In the second
one, d I/dV maps were obtained with a lock-in amplifier
modulating the sample bias voltage by 40 mV at 2 kHz.
The growth conditions are very important because Mn andFe tend to intermix and the magnetic properties of the Mn
are very sensitive to the atomic structure [16]. In this work,
Mn was grown on an Fe(001) whisker at 100 ◦ C at a rateof 0.6 nm min−1 , and the surface topography and electronic
structure was characterized by means of scanning tunnelling
microscopy/spectroscopy (STM/STS) at RT in UHV using aclean W tip. Atomically and chemically resolved STM images
show that the Mn film grows with the same in-plane lattice
constant as Fe(001) and that the Fe atoms intermix with thefirst, the second, and the third Mn layer. The concentrationof intermixed Fe decreased with film thickness. Furthermore,
STM shows that the growth mode changes from layer-bylayer to layer-plus-islands for coverages higher than 4 ML
(monolayers) of Mn. If the temperature of the substrate isincreased by a few degrees, this transition from layer-by-layer
to layer-plus-islands growth takes place for thicker Mn layers,
and the intermixed Fe is present in more Mn layers. Basedon apparent step height measurements, made by choosing thebias voltage carefully to avoid the influence of the electronic
structure on the results, we conclude that the first two Mn
overlayers show significant higher step heights than the Fe
single step and that the Mn film relaxes by about 0.02 nm at
the third layer. From the fourth layer the interlayer spacings aregeometrically the same (about 0.165 nm) and the structure is abody-centred tetragonal (bct) structure [17]. This bct Mn(001)
has a layered antiferromagnetic arrangement [10, 11].
When a Mn film is grown across an Fe step (hidden), theMn film tends to produce a flat surface. We always find steps
0.02 nm high, which corresponds to the difference between theinterlayer distances for Fe and Mn. Across one of these steps,
the Mn thickness changes by one layer (see figure 1(c)). Dueto the LAF structure, the magnetization of the surface layer isreversed across these steps. d I/dV maps obtained with clean
W tips around these defects show the same electronic structure
on both sides. However, when using Fe-covered W tips, acontrast of magnetic origin is obtained across the hidden step,as can be seen in figure 1(b). The average profile measured in
the white box shown in panel (b) can be seen in panel (d), andit gives a domain wall width of around 1.16 nm (2–4 lattice
parameters).
To study the possible influence of the set-point values
on the observed domain width, we systematically changed
the set-point voltage and set-point current. Firstly, the setpoint currents were varied with fixed set-point voltage, andthus with varying tip–sample distance (figure 2(a)). In
addition, the set-point voltage and current were varied suchthat the tunnelling resistance stayed constant, and thus withapproximately constant tip–sample separation (figure 2(b)).
From the results given in figures 2(a) and (b), we can conclude
that our values for the domain wall width do not depend on theparticular set point used.
In figure 2(c) we show the result of 40 measurements
taken with six different magnetic tips for hidden steps covered

The smaller the space that one bit of information occupies, themore data you can get into a device. Between two magnetic
domains with opposite magnetization directions there always
exists a domain wall. Therefore a deep understanding of theparameters that control the domain wall width are crucial inorder to achieve higher density for data storage.
Mn is exactly in the middle of the 3d transition metal
series, just between Fe, which is a natural ferromagnet in thebulk, and Cr, which is an antiferromagnet. Therefore, Mnstands as one of the more complex 3d transition metals fromthe point of view of the magnetic coupling, and it is a clear
candidate to exhibit a great variety of magnetic structures.
Mn systems have been experimentally investigated by spinpolarized electron energy-loss spectroscopy [9], scanningelectron microscopy with polarization analysis [10] and SPSTM/STS [11, 12]. A layered antiferromagnetic (LAF)
arrangement was found in Mn film. Recently, some of
the authors [13] have studied the same system using theab initio tight-binding linear muffin-tin orbital (TB-LMTO)
method [14], assuming the experimental interlayer distances
and a p(1 × 1) magnetic arrangement at the surface, as
experimentally observed [11]. Different magnetic solutions
with energy differences of a few meV were obtained, with the
LAF configuration the less energetic state, in good agreementwith the experiments. The LAF as well as the closest
metastable solutions had some common features: (i) parallel
coupling at the interface between Mn and Fe, (ii) antiparallel
coupling between the Mn-surface and subsurface layers and(iii) antiparallel coupling between the two Mn layers closest to
the interface. This set of solutions only differs in the couplingsat the central Mn layers, that are parallel or antiparalleldepending on the Mn thickness, which makes these systems
clear candidates to exhibit noncollinear magnetic arrangements
under structural defects like monoatomic steps. Using theory,
Hafner and Spišák [15] have found complex magnetic couplingin Mn films on Fe(001) allowing atomic relaxations, obtaining
an in-plane antiferromagnetic structure.
In this paper, the magnetic structure of thin Mn films
grown on Fe(001) is studied. In particular, we focus ourattention on the magnetic structure of the Mn films aroundsteps on the Fe(001) substrate. In section 2, by means
of SP-STM/STS, we measure in real space and with highspatial resolution the magnetic structure of the films aroundthese defects. The experimental results are interpreted, insection 3, with the help of ab initio-parameterized selfconsistent real-space tight-binding (TB) calculations in which
the spin quantization axis is independent for each site, thus
allowing noncollinear magnetism. Throughout the paper,comparisons are made with the Cr/Fe(001) system to get a
deeper understanding of which material parameters are crucial
for determining the resulting magnetic structure. Finally, in
section 4 we summarize our conclusions.

2. Experimental results
All measurements were performed in an ultra-high vacuum(UHV) chamber (∼5 × 10−11 mbar) at room temperature (RT).
An STM was attached to the chamber, which is equipped withmolecular beam epitaxy, Auger spectroscopy, field-emission
spectroscopy, sample heating and sputtering facilities [11].
2Nanotechnology 18 (2007) 235702

T K Yamada et alcomputer requirements are demanded. We have employed an
ab initio-parameterized self-consistent real-space tight-binding
method in which the spin quantization axis is independent foreach site, thus allowing noncollinear magnetism. This method
has been recently developed and used satisfactorily for the
study of supported Cr films on Fe substrates with monoatomic
steps [18]. The Hamiltonian in our method can be split intoa band term Hband and an exchange term Hexch , which in theorthogonal |i α basis of atomic site i and orbital α and withthe usual notation are

H = Hband + Hexch0
Hband =[(iα
+ Uiα, jβ n̂ j b  + Z i iα )δi j δαβ
i, j
α,β
αβ
+ ti j (1 − δi j )]|i α jβ|

Hexch =



1
0

0
1

(1)





cos θ
(− 12 Jiα μiα )|i αi α| iφi ie sin θii,αe−iφi sin θi− cos θi

Hband contains both the non-diagonal matrix elements
αβ(hopping integrals, ti j , between orbitals α and β of different
sites i and j , which are assumed to be spin independent)
and the spin-independent part of the diagonal matrix elements0+ Uiα, jβ n̂ j b  + Z i iα ), being the sum of the local level(iα0iα , the electrostatic level shift Uiα, jβ n̂ j b  accounting forthe charge variations parameterized by the Coulomb integral
Uiα, jβ and the crystal-field potential Z i iα , where Z i isthe local atomic coordination of site i . Hexch describes themagnetic part, through the exchange parameter Jiα multipliedby the magnitude of the local magnetic moment, μiα , whose
direction is given by the angles (θi , φi ) in the spin-rotation
matrix. The spin–orbit contribution is not considered here.
The Hamiltonian has been parameterized to DFT TB-LMTO
calculations of thin Mn films supported on ideal Fe(001) [13]in order to take into account the effects of surface, interface
and bulk. The transferability of the parameterization has
been checked in systems of 6 and 7 Mn ML on Fe(001),
comparing the results with those obtained with the TB-LMTO
method [13], finding similar values for the energy differences
and magnetic moments.

Figure 1. (a) STM image after deposition of 5 Mn ML(70 × 70 nm2 ). The dotted line marks the position of the hidden step.
(b) d I /dV map taken at +0.2 V. The numbers indicate the Mn local
thickness. (c) Model of the Mn structure around the hidden step.
(d) Average experimental profile across the hidden step measured
inside the white box shown in (b).

by different Mn thicknesses. There is no clear dependence
between the width of the domain wall and the thickness of
the Mn film in the range explored. The error bars in thesemeasurements simply reflect the fact that the tips are different
and the resolution of the magnetic images is affected.

3. Theoretical results
For the theoretical investigation of our samples, it is importantto point out that when defects are present, as in thissystem, with the consequent lack of symmetry and hundredsof inequivalent sites, real-space methods with reasonable
2.0

2.0

Figure 2. (a) shows the domain wall width versus the tunnelling current (tip–sample separation). (Black) dots, (green) triangles and (red)squares were obtained at a voltage set point of Vs = +1.5 V, Vs = +0.8 V, and Vs = −1.0 V, respectively. (b) shows the domain wall widthversus bias voltage. The experiments were done on hidden steps between 4–5 and 6–7 ML. (c) Domain wall width versus Mn thickness.

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Nanotechnology 18 (2007) 235702

T K Yamada et al

Figure 3. Result of the calculation performed for 4–5, 5–6 and 6–7 monolayers of Mn (left panel) and Cr (right panel) supported on anFe(001) substrate with a monoatomic step (only a portion of the calculated systems is represented). The arrows indicates the orientation of theindividual magnetic moment and its size is proportional to absolute value of the local magnetic moment (average values of the magnetic
surf
inter
surf
inter
moments far from the step: μbulk
Fe = 2.32 μB , μMn = 3.84 μB , μCr = 3.07 μB , μMn = 2.85 μB , μCr = 1.13 μB ). The colour of the circles
is given by the absolute value of the cosine of the angle of the magnetic moment. For Mn and Cr red means a LAF arrangement and yellow
indicates the magnetic moment at 90◦ . For the Fe(001) substrate the blue colour indicates a ferromagnetic arrangement and light blue a
deviation from that.

We have simulated the systems represented in figure 1.
Despite the preservation of the symmetry in the axis parallelto the step, which can be justified by the length of theobserved steps in the system, we have about 40 000 atoms
and up to 600 inequivalent sites to describe the semi-infinite
system. We have considered coverages of 4–5, 5–6 and 6–
7 Mn ML. In all cases, a small step of about 0.02 nm at thesurface is present (as experimentally observed). In figure 3(left panel) we illustrate the noncollinear magnetic moment
distributions obtained in the calculations (only a portion of
the semi-infinite system is shown). To understand the originof the noncollinear magnetic arrangement, we have also
performed TB collinear restricted calculations (not shown),
obtaining different magnetic arrangements, the least energetic
one displaying the LAF order at both sides far from the step,
while just over the step, due to the impossibility of reaching
LAF order together with the parallel coupling at the interface inthe whole system, magnetically frustrated atoms were present.
Previous studies of Cr/Fe interfaces with steps [18] have shownthat this type of frustration in a collinear framework leads
the system to drastically reduce the magnetic moments in thefrustrated region. However, this moment reduction in the caseof Mn is much less noticeable, which is consistent with the factthat the magnetic couplings between Mn layers are weaker andless defined than in Cr, for which the LAF solution is the only
one present [18]. The noncollinear magnetic solutions shownin figure 3 are energetically more stable than the collinear onesin all cases, and they reproduce the experimentally observed
magnetic contrast at the surface between both sides of thestep. This is due to the propagation of the magnetic frustration
originated at the interface step. Far from the step, the systemtends to preserve the magnetic couplings found in the ideal
Mn films on Fe(001) [13], that is the LAF with parallel Fe–
Mn coupling at the interface and antiparallel coupling between
Mn surface and subsurface layers. Moreover, the tendencyof Mn to couple both parallel and antiparallel in the central

layers of the ideal Mn films on Fe(001) is also reflected in thenoncollinear arrangements shown in figure 3.
Let us now come to the analysis of the domain-wallevolution as a function of the Mn coverage, in particular
the width of the domain wall. Experimentally, we havefound a domain-wall width of about 2–4 lattice parameters
independently of the Mn coverage. Our theoretical results(figure 3) are also consistent with the experimental finding,as can be deduced from figures 4 and 5, where the cosine of
the angle of the local surface magnetic moment with respect
to the bulk is plotted through the step (red squares). The
central Mn layers decouple the surface from the interface toa large extent, and make these systems behave in a radicallydifferent way from what would be expected if one assumes for
Mn the magnetic coupling of a typical antiferromagnet like Cr
and the associated magnetic frustrations when interfaced withstepped Fe. In fact, we have already indicated before that Mn
and Cr have different magnetic behaviour when deposited on
an atomically flat Fe(001) surface. The magnetic decouplingof the surface layers from the deeper layers coupled to thesubstrate has been also proposed recently by Hafner andSpišák [15]. This provides further support to our results. For
large enough coverages it is expected that Mn will undergoa structural transition [19] with no magnetic domains at thesurface. Our results contrast, however, with those obtainedby Schlickum et al [12]. These authors found an increase of
the domain-wall width on increasing Mn coverage. Growth
conditions are very important for the final structure. In
these experiments we grew the Mn films about ten times
faster than Schlickum et al [12]. The faster deposition
rate for the same sample temperature may lead to a smaller
level of intermixing between Mn and Fe and therefore to adifferent magnetic structure. Furthermore, Schlickum et al [12]explained their results using a simple Heisenberg model for
localized magnetism [12], assuming that Mn behaves like Cr
and considering the same exchange parameter for Mn–Fe and
Mn–Mn.
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Nanotechnology 18 (2007) 235702

T K Yamada et al

Figure 4. Cosine of the angle of the magnetic surface moments with respect to the bulk obtained in the theoretical calculations shown infigure 3 for 4–5, 5–6 and 6–7 ML. Vertical dashed lines specify the size of the domain wall in each case.

Mn overlayers, and it is about two lattice parameters. Thisis due to the weakly defined magnetic coupling at the central
Mn layers that decouple the surface from the interface toa large extent. We compare our findings for the Mn films
with the behaviour of Cr films. In contrast to Mn, ideal Cr
films have strong antiferromagnetic couplings and longer rangeorder than in Mn, up to the point that only one magnetic
arrangement in the system has been found in the collinear
framework, corresponding to an LAF configuration. Thisstrong coupling produces a high amount of frustration on steps
and as a consequence in the case of Cr the domain-wall width
increases with the coverage.

Acknowledgments
Figure 5. (black dots) Average experimental profile across thehidden step measured inside the white box shown in figure 1(b).
(orange squares) Cosine of the angle of the magnetic surface
moments with respect to the bulk obtained in the theoretical
calculation shown in figure 3 for 6–7 ML.

Financial support by the Ministerio de Ciencia y Tecnologı́aand Ministerio de Educación y Ciencia through project
numbers FIS2004-01206 and MAT2005-03415, Junta deCastilla y León (VA068A06) and INTAS (03-51-4778)
is gratefully acknowledged.
HvK thanks the Instituto
Universitario ‘Nicolás Cabrera’ for a visitor’s grant.

In order to further illustrate the different magnetic
behaviour of Mn and Cr, we have performed the same typeof calculation in similar systems, but with Cr instead of Mn
deposited on the stepped Fe substrate and the corresponding
interatomic distances (figure 3, right panel). The difference
between the noncollinear arrangements in Mn/Fe and Cr/Fe isclear. The strong antiferromagnetic character of Cr leads tostrong magnetic frustrations that are propagated towards thesurface occupying a region in which the best compromise to
the antiparallel Cr–Cr and Cr–Fe couplings is achieved. As
a result, the domain-wall width increases with increasing Cr
coverage and the frustration is partially released in the Fe(001)substrate.

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4. Conclusions
In conclusion, we have investigated the magnetic structure on
thin Mn films grown on an Fe(001) surface with a monoatomic
step. In our SP-STM images we found a change in themagnetic contrast when crossing one of those steps due tothe change of the Mn thickness. We have found that thewidth of the domain wall around the substrate steps does notdepend on the thickness, at least for coverages up to seven5

Nanotechnology 18 (2007) 235702

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