Suppression of incommensurate spin-density waves in thin epitaxial Cr(110) layers of a V/Cr multilayer

Abstract

We observed a complete suppression of the incommensurate spin-density wave in thin Cr layers of a V/Cr multilayer in a temperature range from 550 K down to 2 K. The (110)-oriented V/Cr multilayer consisting of 30 nm thick Cr layers and 5 nm thick V layers was investigated by neutron and X-ray diffraction (XRD). From the XRD experiments we were able to determine that the epitaxial strain of the Cr layers in the V/Cr multilayer is about 90% larger than in earlier studied Fe/Cr(110) multilayers. That leads to a completely different magnetic phase diagram as revealed by neutron diffraction experiments. The existence of the commensurate antiferromagnetic structure in the Cr layers can be observed in the whole temperature range without a phase transition to an incommensurate spin-density wave at lower temperatures. In order to elucidate the proximity effects further we also performed experiments in an external magnetic field. Up to a field of 4 T we found no change in the magnetic structure of the Cr films whereas in earlier experiments on Fe/Cr(110) multilayers we could observe a strong perpendicular pinning of the Cr polarization to the Fe magnetization.

Full text

Eur. Phys. J. B 36, 175–181 (2003)
DOI: 10.1140/epjb/e2003-00332-y THE EUROPEAN
PHYSICAL JOURNAL B
Suppression of incommensurate spin-density waves
in thin epitaxial Cr(110) layers of a V/Cr multilayer
H. Fritzsche1,a,S.Bonn
2, J. Hauschild2,K.Prokes
2,andJ.Klenke
2
1National Research Council Canada, Chalk River Laboratories, Chalk River, ON, K0J 1J0, Canada
2Hahn-Meitner-Institut, Glienicker Strasse 100, 14109 Berlin, Germany
Received 17 June 2003 / Received in final form 28 August 2003
Published online 8 December 2003 – c
EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2003
Abstract. We observed a complete suppression of the incommensurate spin-density wave in thin Cr layers
of a V/Cr multilayer in a temperature range from 550 K down to 2 K. The (110)-oriented V/Cr multilayer
consisting of 30 nm thick Cr layers and 5 nm thick V layers was investigated by neutron and X-ray
diffraction (XRD). From the XRD experiments we were able to determine that the epitaxial strain of the
Cr layers in the V/Cr multilayer is about 90% larger than in earlier studied Fe/Cr(110) multilayers. That
leads to a completely different magnetic phase diagram as revealed by neutron diffraction experiments.
The existence of the commensurate antiferromagnetic structure in the Cr layers can be observed in the
whole temperature range without a phase transition to an incommensurate spin-density wave at lower
temperatures. In order to elucidate the proximity effects further we also performed experiments in an
external magnetic field. Up to a field of 4 T we found no change in the magnetic structure of the Cr films
whereas in earlier experiments on Fe/Cr(110) multilayers we could observe a strong perpendicular pinning
of the Cr polarization to the Fe magnetization.
PAC S . 75.30.Fv spin-density waves – 75.70.-i magnetic properties of thin films, surfaces, and interfaces –
61.12.-q Neutron diffraction and scattering
1 Introduction
The discovery of an antiferromagnetic structure in Cr sam-
ples by Shull and Wilkinson [1] in 1953 initiated a huge
amount of scientific investigations on all physical proper-
ties of chromium. Neutron diffraction experiments always
played a key role in revealing the details of the magnetic
structure of chromium. In the beginning the influence of
the sample preparation on the magnetic properties of Cr
bulk samples were the focus of interest. Shull et al. [1]
used a polycrystalline sample and found a commensurate
antiferromagnetic structure (AF0)withaN´eel tempera-
ture TNof about 450 K. This commensurate structure is
characterized by an antiparallel alignment of the Cr polar-
ization vectors of corner atoms and body-centered atoms
within the bcc unit cell. In 1959, Corliss et al. [2] working
on a Cr single crystal found for the first time the incom-
mensurate spin-density wave (ISDW). This ISDW corre-
sponds to a sinusoidal modulation of the antiferromagnetic
arrangement of the Cr moments and in neutron diffrac-
tometry it shows up as satellites around the Cr{100}po-
sitions. The modulation period is temperature dependent
and changes from 6 nm at 2 K to 8 nm at 310 K.
ae-mail: helmut.fritzsche@nrc.gc.ca
After the detailed neutron diffraction study of
Bacon [3] the magnetic phase diagram of Cr single crystals
was clarified. Cr orders at TN= 311 K as an antiferro-
magnet with a transverse ISDW, the so-called AF1struc-
ture, i.e. with the Cr polarization vector perpendicular to
the direction of the modulation period. At a temperature
of 123 K an additional phase transition occurs from the
transversal ISDW to the longitudinal ISDW (AF2struc-
ture) with the polarization vectors parallel (or antiparal-
lel) to the direction of the modulation period.
The deviation in Cr polycrystalline samples from the
above described ideal behavior could be explained by
strain-induced effects [4–6]. The most significant features
in these strained Cr samples were the elevation of TNfrom
311 K to about 450 K and the coexistence over a wide
temperature range of the commensurate AF0structure
and the incommensurate AF1and AF2structure. Conse-
quently, the phase transitions from AF0to AF1and from
AF1to AF2are not sharply defined but are smeared over
a large temperature range [4–6].
The observation of an oscillating exchange coupling
of ferromagnetic films across nonmagnetic spacer layers in
Fe/Cr multilayers [7] lead to a renaissance of the investiga-
tion of the magnetic structure of Cr. In addition to the tra-
ditional neutron diffraction technique the nuclear methods

176 The European Physical Journal B
of perturbed angular correlation (PAC) spectroscopy [8] as
well as 119Sn M¨ossbauer spectroscopy [9,10] was used to
reveal the magnetic structure of thin Cr films.
Most of the experiments were performed either on
(100)-oriented single Cr films or on (100)-oriented Fe/Cr
multilayers. For Cr films with a thickness tCr >5nmthe
phase diagram strongly depends on temperature. Gener-
ally, there is a phase transition from the AF0structure
to the paramagnetic phase at temperatures far above the
bulk N´eel temperature [11–14]. When lowering the tem-
perature a phase transition to an ISDW is observed. For
films with tCr <5 nm either the AF0phase [11] or the
paramagnetic phase was observed [8,15]. Investigations on
(110)-oriented Fe/Cr multilayers [16–18] with tCr =30nm
showed a similar temperature dependence as the (100)-
oriented Cr films.
In order to study the influence of the ferromagnetic
layer on the magnetic structure of the Cr layers it is im-
portant to perform experiments with Cr layers in contact
with paramagnetic layers. In literature experiments are re-
ported on V/Cr multilayers [10], Ag/Cr multilayers [19],
Sn/Cr multilayers [20] or on Cu or Pd covered Cr single
films [21]. We chose V as paramagnetic material for our
investigations and present a detailed neutron diffraction
study on a V/Cr(110) multilayer with tCr =30nm.We
also applied an external magnetic field in order to com-
pare directly to earlier investigations on Fe/Cr(110) mul-
tilayers [17] which revealed a perpendicular pinning of the
Cr polarization to the Fe magnetization. Additional infor-
mation on the strain in the Cr layers could be obtained
by performing X-ray diffraction (XRD) experiments.
2 Experimental details
The multilayer was prepared in ultrahigh vacuum by
means of molecular beam epitaxy on Al2O3(1120) single
crystals, covered with a buffer layer of 100 nm V(110). The
deposition rates were 0.013 nm/s for the V(110) buffer,
0.014 nm/s for the Cr(110) layers, and 0.01 nm/s for
the V(110) spacing layers, respectively. The preparation
temperature was 520 K in order to get a sample of good
crystalline quality and smooth interfaces as was checked
with standard techniques of surface science like low en-
ergy electron diffraction and Auger electron spectroscopy.
The thickness of the Cr layers was tCr =30nmandthe
thickness of the V layer tV= 5 nm. The V/Cr bilayer was
repeated 13 times in order to get a reasonable signal-to-
noise ratio for the neutron diffraction experiments.
The antiferromagnetic structure of the Cr layers has
been investigated by neutron diffraction on the triple-axis
spectrometer E1 and the two-axis diffractometer E4 at
the Hahn-Meitner-Institut, Berlin. We used a pyrolytic
graphite monochromator to select a wavelength of λ=
0.24 nm together with a graphite filter that reduces the
λ/2 contribution of the monochromator by a factor of
about 5000. We applied an external vertical magnetic field
using the VM3 magnet of the Hahn-Meitner-Institut.
As a quantitative measure for the intensity of the
Bragg reflection we took the integrated intensity around
the corresponding reflection. Due to the shape of the sam-
ple the intensity is strongly influenced by geometrical ef-
fects which depend on the sample orientation with respect
to the neutron beam and detector. Therefore, we normal-
ized the intensity of the magnetic Cr{100}reflections mea-
sured with λto the intensity of the structural Cr{200}
reflections measured with λ/2=0.12 nm by removing the
λ/2 filter. This has the additional advantage that eventual
beam inhomogeneities are also eliminated.
The X-ray measurements were performed on a two-axis
diffractometer (model D8 ADVANCE, Bruker-axs) using
Cu Kα radiation. The instrument was equipped with a
pyrolytic graphite monochromator in front of the detec-
tor. The epitaxial strain of the Cr layers was calculated
from the Cr Bragg peak positions as determined from θ-
2θscans. If the crystalline quality is very high the Cu
Kα1radiation [22] with λ=0.1540593 nm and the Cu
Kα2radiation [22] with λ=0.1544414 nm can be re-
solved. In cases when the double peak could not be re-
solved we took the relative intensity I(Kα2)/I(Kα1)=
0.52 to calculate the weighted mean of Cu Kα1and Cu
Kα2resulting in λ=0.15419 nm for the Cu Kα radia-
tion [22].
3X-raydiffraction
The structural properties of the multilayer was checked by
X-ray diffraction (XRD). In order to determine the out-
of-plane lattice constant of the Cr layers we performed
θ-2θscans. For high precision measurements it is very
important to calibrate the instrument with a well-known
standard sample. We took the Al2O3(1120) substrate re-
flections to calibrate the 2θ-axis. With the lattice con-
stant [23] a=0.4759 nm we can calculate the out-of-plane
lattice spacing d=a/2 and the corresponding 2θ-value as
given in Table 1. The θ-2θ-scan of the Al2O3(1120) reflec-
tion with the calibrated θ-axis is shown in Figure 1a. For
the substrate reflection the doublet of the Cu Kα radia-
tion is clearly observable. Therefore, the calibration could
be done with high accuracy.
The Cu Kα doublet could not be resolved for the
V(110) and Cr(110) reflection of the multilayer as can be
seen from Figure 1b. Therefore, we took the averaged λof
the Cu Kαradiation to calculate the Cr out-of-plane lat-
tice spacing d=(0.2033 ±0.0001) nm. That corresponds
to an out-of-plane strain o=(−0.0030 ±0.0007) along
[110] compared to the bulk value [24] of 0.20393 nm. An
overview is given in Table 1.
This measured out-of-plane compression can be inter-
preted as a Poisson contraction due to the in-plane stress.
The in-plane strain ican be easily estimated under the
assumption that the in-plane stress is homogeneous. Then
the minimization of the elastic energy leads to the expres-
sion [25]
i=−o
c11 +c12 +2c44
c11 +3c12 −2c44
(1)
with the elastic constants c11,c12,andc44. The Cr bulk
values are [26] c11 =34.8×1010 Pa, c12 =6.7×1010 Pa,

H. Fritzsche et al.: Spin-density waves in thin Cr(110) films of a V/Cr multilayer 177
Fig. 1. X-ray θ-2θdiffraction scans a) for the substrate reflec-
tion Al2O3(1120) and b) the V(110) and Cr(110) reflections.
Please note the different scales in a) and b).
Tabl e 1. Measured (2θmeas) and calculated (2θbulk)2θva l-
ues [24,23] for the Cr film and the sapphire substrate. From
2θmeas the corresponding lattice spacing dwas calculated.
λ(nm) 2θmeas (◦)2θbulk (◦)d(nm)
Cr 0.15419 44.568 44.426 0.2033
Al2O30.15406 37.776
Al2O30.15444 37.874
and c44 =10.0×1010 Pa. Inserting these values into equa-
tion (1) we get i=0.0053 ±0.0013 for the strain along
the in-plane directions [001] and [110].
It is important to note that the calculated lattice con-
stant along with the calculated strain are values which
result from an averaging over the whole film. Theoreti-
cal calculations [27] and experiments [28] show that the
strain relaxation is proportional to the inverse film thick-
ness above the pseudomorphic regime. As a consequence,
a large distribution of lattice constants exists. This broad
distribution of lattice spacings causes a broad peak in a
θ−2θscan at the Cr(110) position as can be seen in
Figure 1b. The evaluation of rocking scans around the
Cr(220) reflection gives a grain size of 7.5 nm.
4 Neutron diffraction
The antiferromagnetic structure of Cr was investigated
by classical neutron diffraction. The scattering cross sec-
tion of an unpolarized neutron beam with a magnetization
wave M(r) can be written as:
dσ
dΩ =|Mq|2sin2θq(2)
where θqis the angle between Mand qand Mqis the
Fourier component of M(r). For neutrons generally the
contribution of the magnetic and nuclear part to the scat-
tering cross section are of the same order of magnitude.
For the case of a bcc crystal it is well-known that the struc-
ture factor vanishes for those (HKL) reflections for which
the sum (H+K+L) is odd. Hence, the measured inten-
sity at the position of these reflections, e.g. the Cr{100}
reflections, is of pure magnetic origin. It is worthwhile to
mention that this selection rule is also strictly valid for
our Cr film which has a body-centered tetragonal struc-
ture because of the strain.
4.1 Temperature dependence of the antiferromagnetic
structure
At 295 K we investigated all three independent Cr{100}
reflections and scanned along the H,K,andLdirections
of reciprocal space. The results are shown in Figure 2 for
the Cr(001) reflection, in Figure 3 for the Cr(010) reflec-
tion, and in Figure 4 for the Cr(100) reflection. These
scans are a direct proof of the existence of the commen-
surate AF0structure in the Cr layers. An ISDW would
show up in the scans as satellite peaks at about ±0.04
for transverse scans and at 0.96 and 1.04 for longitudinal
scans. That is definitely not visible.
First of all, it is remarkable that we do not observe
thesameintensityforallthreeindependentCr{001}re-
flections because in bulk Cr the probability for all these
reflections is a priori the same. According to equation (2)
only magnetization components perpendicular to qare
contributing to the integrated intensity. Therefore, it is
straightforward to calculate the orientation of the polar-
ization S. Based on the normalized integrated intensities
of the magnetic {001}reflections, shown in Table 2, we
obtain for the polarization vector |Sx|2,|Sy|2,|Sz|2=
(0.9,1.0,0.2) with an error of ±0.1. This means that the
averaged polarization vector is roughly parallel to [221],
19◦off the surface normal [110].
We even observed the AF0structure down to 2 K with-
out an indication of a phase transition to an ISDW. As
can be estimated from Figure 5, a phase transition from
the commensurate phase to the paramagnetic state occurs
at TN≈600 K. The solid line was plotted as a guide to
the eye.
4.2 Magnetic field dependence
of the antiferromagnetic structure
There are two main results of the investigations on the
magnetic field dependence of the antiferromagnetic struc-
ture of bulk Cr samples. Firstly, by applying a magnetic
field of about 3 T during the sample cooling through

178 The European Physical Journal B
Fig. 2. Neutron diffraction scans in the a) H-direction, b) K-
direction, and c) L-direction through the Cr(001) reflection
of the V/Cr(110) multilayer, measured at 295 K on E1. The
solid line represents a Gaussian fit to the experimental data.
All scans shown in Figures 2–4 were measured with the same
number of monitor counts.
its N´eel temperature (the so-called field-cooling) a single
qstate can be produced with qbeing parallel to the mag-
netic field direction [29]. Secondly, when applying a mag-
netic field in the transverse SDW state the polarization
vector of the domains rotate into a direction perpendicu-
lar to the field [30]. Generally, the perpendicular orienta-
tion of the polarization of the antiferromagnet is preferred
because the perpendicular susceptibility is larger than the
one parallel to the field.
Recently, the dependence of the antiferromagnetic
structure on magnetic fields in (110)-oriented Fe/Cr mul-
tilayers has been reported [17]. The (110) surface creates a
uniaxial anisotropy with [001] as the easy axis and [110] as
the hard axis of the Fe magnetization. At 300 K the stable
phase is the CSDW with the Cr polarization aligned per-
pendicular to [001]. When rotating the Fe magnetization
from the easy axis into the in-plane hard-axis direction
Fig. 3. Neutron diffraction scans in the a) H-direction, b) K-
direction, and c) L-direction through the Cr(010) reflection
of the V/Cr(110) multilayer, measured at 295 K on E1. The
solid line represents a Gaussian fit to the experimental data.
All scans shown in Figures 2–4 were measured with the same
number of monitor counts.
by applying a magnetic field of 0.45 T the intensity of
the Cr(001) reflection decreases by a factor of two. That
was interpreted as a simultaneous rotation of the Fe and
Cr moments pinned together in its initial perpendicular
orientation.
In order to study the proximity effects we performed
experiments in external fields on V/Cr multilayers as well.
That enables us to compare directly the case of nonmag-
netic layers to the case of ferromagnetic layers in contact
with the Cr layers. As in our previous experiments on the
Fe/Cr multilayers we applied the external magnetic field
along the in-plane [110] direction and measured the in-
tensity of the Cr(001) reflection at room temperature as
a function of the magnetic field. In Figure 6 the rocking
scans around the Cr(001) reflection for a) µ0H=0Tand
b) µ0H= 4 T are displayed. The rocking curve in a) was
measured with 1.2 million monitor counts, whereas the

H. Fritzsche et al.: Spin-density waves in thin Cr(110) films of a V/Cr multilayer 179
Fig. 4. Neutron diffraction scans in the a) H-direction, b) K-
direction, and c) L-direction through the Cr(100) reflection
of the V/Cr(110) multilayer, measured at 295 K on E1. The
solid line represents a Gaussian fit to the experimental data.
All scans shown in Figures 2–4 were measured with the same
number of monitor counts.
Tabl e 2. Integrated intensity of the magnetic Cr{001}reflec-
tions normalized to the respective nuclear Cr{002}reflections.
Direction Cr(001) Cr(010) Cr(100)
H1.67 ±0.04 1.00 ±0.06 1.08 ±0.05
K1.72 ±0.04 1.16 ±0.07 1.09 ±0.05
L1.69 ±0.04 0.93 ±0.06 1.07 ±0.05
curve displayed in b) was measured for 2 million moni-
tor counts. In order to compare both curves directly, all
measured points in a) were multiplied by a factor of 5/3.
From the Gaussian fits displayed in Figure 6 as solid
lines we could determine the integrated intensities. For the
case of zero field we get I0= 523 ±14 and for the applied
field of 4 T we get I4= 871 ±16. After the correction for
the monitor counts, i.e. multiplying I0by the factor 5/3,
300 350 400 450 500 550 600
0.0
0.2
0.4
0.6
0.8
1.0
I
Cr(001)
/
I
Cr(002)
(
ar
b
. un
i
ts
)
temperature (K)
Fig. 5. Temperature dependence of the integrated intensity of
the Cr(001) reflection normalized to the integrated intensity of
the Cr(002) reflection. The solid line represents a guide to the
eye.
Fig. 6. Rocking scan around the Cr(001) reflection at an ex-
ternal magnetic field of a) 0 T and b) 4 T. The rocking curve
in zero field was measured for 1.2 million monitor counts and
the curve in a field of 4 T was measured for 2 million monitor
counts. In order to compare the graphs directly all measured
points in a) were multiplied by a factor of 5/3. The solid lines
are Gaussian fits.
the integrated intensity in zero field equals 872 and is the
same within the error limits as in a field of 4 T. So, even
a magnetic field of 4 T cannot influence the antiferromag-
netic structure of these thin Cr layers.

180 The European Physical Journal B
5 Discussion
The neutron diffraction experiments on (110)-oriented
V/Cr multilayers reported in this article enables us to
compare directly to earlier experiments on Fe/Cr mul-
tilayers and to study the proximity effects on the anti-
ferromagnetic structure of thinCrlayersincontactwith
nonmagnetic and ferromagnetic layers, respectively. The
commensurate phase which is stable at room tempera-
ture is not due to the presence of a ferromagnetic layer
because it exists in the Fe/Cr as well as in the V/Cr mul-
tilayer. The enhanced N´eel temperature of about 600 K
was also observed in both types of multilayers. However,
there is a big difference in the temperature dependence
of the antiferromagnetic structure for temperatures be-
low room temperature. For the Fe/Cr(110) multilayer a
transition to the ISDW is observed whereas for the V/Cr
sample only the commensurate phase is observed down to
T=2K.M¨ossbauer measurements performed on V/Cr
multilayers [10] confirm that there is no phase transition
below room temperature because the spectra for a Cr film
thickness of 8 nm show no difference at room temperature
and at 15 K.
When comparing the properties of Fe/Cr and V/Cr
multilayers not only the interfaces are electronically dif-
ferent but also the structure of the Cr layers is different
because of the different epitaxial strain due to the differ-
ent lattice constants. For the Fe/Cr system there is only
a very small misfit
ηFe/Cr =aFe −aCr
aCr
=−0.0062 (3)
with the Fe lattice constant [24] aFe =0.2866 nm and the
Cr lattice constant [24] aCr =0.2884 nm. The real epi-
taxial strain in the Cr layers depends also on the used
substrate because the substrate induces strain as well.
Obviously, the strain in Fe/Cr multilayers is about the
same as in strained bulk Cr crystals because they have
similar temperature dependent phase diagrams. For the
case of strained Cr bulk samples it was already con-
cluded that the strain is the origin of the commensurate
AF0structure [4–6] and the coexistence of the ISDW and
the CSDW. For Ag/Cr multilayers which exhibit an even
smaller misfit of ηAg/Cr =−0.0028 only the longitudinal
ISDW was observed [19].
However, for the V/Cr multilayer there is a large mis-
fit of ηV/Cr =0.047 resulting in an averaged out-of-plane
strain of o=−0.0030 as measured by XRD and an av-
eraged in-plane strain of i=0.0053 as deduced from
elasticity theory. The amount of stress is higher com-
pared to the Fe/Cr multilayers which were prepared on
a V(110) single crystal [17,18]. From X-ray measurements
we determined o=(−0.0016 ±0.0005) and calculated
i=0.0028 ±0.0008 for these Cr layers. Obviously, the
larger amount of strain present in the V/Cr multilayer
leads to a complete suppression of a transition to an ISDW
at lower temperatures. It is unclear whether the small
grain size of 7.5 nm also affects the magnetic properties. In
general the magnetic properties depend on the film thick-
ness, e.g. for Fe/Cr multilayers the ISDW is not observable
below 5 nm [8,11, 15] and measurements on V/Cr multi-
layers as a function of Cr film thickness [10] show that
the Cr magnetism breaks down for film thicknesses below
1 nm. Because of the fact that the grain size is larger than
the periodicity of the ISDW we believe that the influence
of the grain size is rather limited.
The experiments performed in external magnetic fields
showed that the antiferromagnetic structure in the Cr lay-
ers remained unchanged up to a field of 4 T. That be-
haviour is different compared to Cr bulk samples where a
magnetic field of about 2 T leads to a reorientation of the
Cr polarization perpendicular to the field [30] for those
domains with an initial parallel polarization.
6Conclusion
The performed X-ray and neutron diffraction experiments
on V/Cr multilayers and comparison to earlier exper-
iments on Fe/Cr multilayers [17,18] clearly show that
strain plays a crucial role for the phase diagram of thin Cr
layers. As determined by XRD the strain in the V/Cr(110)
multilayer is 90% higher compared to the Fe/Cr(110)
multilayer. That higher amount of strain in the V/Cr
multilayer suppresses the incommensurate phases in the
whole temperature range under investigation, i.e. from
2 K to 550 K in contrast to the Fe/Cr multilayers where
a phase transition takes place from the AF0structure to
the ISDW. In the Ag/Cr system where the misfit is even
smaller than in the Fe/Cr multilayers the commensurate
phase was not observed [19].
The experiments in external magnetic fields show that
the antiferromagnetic structure does not change up to a
magnetic field of 4 T. That behavior is different for Cr bulk
samples. Furthermore, the comparison with experiments
on Fe/Cr(110) multilayers where the Cr polarization could
be rotated easily by rotating the Fe magnetization [17]
confirms the extraordinary strong exchange coupling at
the Fe/Cr interface.
References
1. C.G. Shull, M.K. Wilkinson, Rev. Mod. Phys. 25, 100
(1953)
2. L.M. Corliss, J.M. Hastings, R.J. Weiss, Phys. Rev. Lett.
3, 211 (1959)
3. G.E. Bacon, Acta Cryst. 14, 823 (1961)
4. G.E. Bacon, N. Cowlam, J. Phys. C: Solid State Phys. 2,
238 (1969)
5. I.S. Williams, E.S.R. Gopal, R. Street, J. Phys. F: Metal
Phys. 9, 431 (1979)
6. I.S. Williams, R. Street, Phil. Mag. B 43, 893 (1981)
7. P. Gr¨unberg,R.Schreiber,Y.Pang,M.B.Brodsky,H.
Sowers, Phys. Rev. Lett. 57, 2442 (1986)
8. J. Meersschaut, J. Dekoster, R. Schad, P. Belien, M. Rots,
Phys. Rev. Lett. 75, 1638 (1995)
9. K. Mibu, M. Almokhtar, S. Tanaka, A. Nakanishi, T.
Kobayashi, T. Shinjo, Phys. Rev. Lett. 84, 2243 (2000)

H. Fritzsche et al.: Spin-density waves in thin Cr(110) films of a V/Cr multilayer 181
10. M. Almokhtar, K. Mibu, A. Nakanishi, T. Kobayashi, T.
Shinjo, J. Phys.: Condens. Matter 12, 9247 (2000)
11. A. Schreyer, C.F. Majkrzak, T. Zeidler, T. Schmitte, P.
B¨odeker, K. Theis-Br¨ohl, A. Abromeit, J.A. Dura, T.
Watanabe, Phys. Rev. Lett. 79, 4914 (1997)
12. P. Sonntag, P. B¨odeker, A. Schreyer, H. Zabel, K.
Hamacher, H. Kaiser, J. Magn. Magn. Mater. 183,5
(1998)
13. J. Meersschaut, J. Dekoster, S. Demuynck, S. Cottenier,
B. Swinnen, M. Rots, Phys. Rev. B 57, R5575 (1998)
14. E. Kunnen, S. Mangin, V.V. Moshchalkov, Y.
Bruynseraede,A.Vantomme,A.Hoser,K.Temst,
Thin Solid Films 414, 262 (2002)
15. E.E. Fullerton, S. Adenwalla, G.P. Felcher, K.T. Riggs,
C.H.Sowers,S.D.Bader,J.L.Robertson,PhysicaB221,
370 (1996)
16.H.Fritzsche,J.Hauschild,T.Nawrath,A.Hoser,S.
Welzel, H.A. Graf, H. Maletta, Physica B 276-278, 590
(2000)
17. H.Fritzsche,J.Hauschild,A.Hoser,S.Bonn,J.Klenke,
Europhys. Lett. 49, 507 (2000)
18. H. Fritzsche, S. Bonn, J. Hauschild, J. Klenke, K. Prokes,
G.J. McIntyre, Phys. Rev. B 65, 144408 (2002)
19. S. Demuynck, J. Meersschaut, J. Dekoster, B. Swinnen, R.
Moons, A. Vantomme, S. Cottenier, M. Rots, Phys. Rev.
Lett. 81, 2562 (1998)
20. M. Takeda, K. Mibu, T. Shinjo, J. Suzuki, Y. Endoh, Appl.
Phys. A 74, S1554 (2002)
21. P. B¨odeker, A. Schreyer, H. Zabel, Phys. Rev. B 59, 9408
(1999)
22. J. H¨artwig, G. H¨olzer, J. Wolf, E. F¨orster, J. Appl. Cryst.
26, 539 (1993)
23. Landolt-B¨ornstein, new series, group III,Vol.7b1
(Springer Verlag, Berlin, 1975)
24. Landolt-B¨ornstein, new series, group III, Vol. 14a
(Springer Verlag, Berlin, 1988)
25. H. Fritzsche, Ph.D. thesis (TU Clausthal, Clausthal, 1995)
26. Landolt-B¨ornstein, new series, group III, Vol. 29a
(Springer Verlag, Berlin, 1992)
27. P. Bruno, J.P. Renard, Appl. Phys. A 49, 499 (1989)
28. H. Fritzsche, J. Kohlhepp, U. Gradmann, Phys. Rev. B
51, 15933 (1995)
29. A. Arrott, S.A. Werner, H. Kendrick, Phys. Rev. Lett. 14,
1022 (1965)
30. S.A. Werner, A. Arrott, M. Atoji, J. Appl. Phys. 39, 671
(1968)