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Forcing Ferromagnetic Coupling Between Rare-Earth-Metal and 3d Ferromagnetic Films

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Abstract

Using density functional calculations, we have studied the magnetic properties of nanocomposites composed of rare-earth-metal elements in contact with 3d transition metals (Fe and Cr). We demonstrate the possibility to obtain huge magnetic moments in such nanocomposites, of order 10mu(B)/rare-earth-metal atom, with a potential to reach the maximum magnetic moment of Fe-Co alloys at the top of the so-called Slater-Pauling curve. A first experimental proof of concept is given by thin-film synthesis of Fe/Gd and Fe/Cr/Gd nanocomposites, in combination with x-ray magnetic circular dichroism.
Forcing Ferromagnetic Coupling Between Rare-Earth-Metal and 3dFerromagnetic Films
Biplab Sanyal,
1,
*Carolin Antoniak,
2
Till Burkert,
1
Bernhard Krumme,
2
Anne Warland,
2
Frank Stromberg,
2
Christian Praetorius,
3
Kai Fauth,
3
Heiko Wende,
2
and Olle Eriksson
1
1
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
2
Faculty of Physics and Center for Nanointegration Duisburg-Essen (CeNIDE), University of Duisburg-Essen,
Lotharstr. 1, 47048 Duisburg, Germany
3
Faculty of Physics and Astronomy, University of Wu
¨rzburg, Am Hubland, 97074 Wu
¨rzburg, Germany
(Received 6 December 2009; published 15 April 2010)
Using density functional calculations, we have studied the magnetic properties of nanocomposites
composed of rare-earth-metal elements in contact with 3dtransition metals (Fe and Cr). We demonstrate
the possibility to obtain huge magnetic moments in such nanocomposites, of order 10B=
rare-earth-metal atom, with a potential to reach the maximum magnetic moment of Fe-Co alloys at the
top of the so-called Slater-Pauling curve. A first experimental proof of concept is given by thin-film
synthesis of Fe=Gd and Fe=Cr=Gd nanocomposites, in combination with x-ray magnetic circular
dichroism.
DOI: 10.1103/PhysRevLett.104.156402 PACS numbers: 71.20.Eh, 75.30.Cr, 75.50.Bb
Magnetic materials with a large saturation magnetic
moment are used in various applications, such as write
heads in computer hard disks, electromagnetic motors,
generators, and transformers. Improved and more efficient
materials are continuously sought after, but, for the last
75 years, the largest room temperature saturation moment
(2:45B=atom), as described by the maximum of the
Slater-Pauling curve, has been provided by an FexCo1x
(x0:7) alloy comprised of 3dtransition metal elements
[1]. Mn, with an atomic magnetic moment that in the dilute
limit approaches 4B=atom in certain compounds, can be
used in multilayers with Fe and Fe-Co alloys [2]. However,
the magnetic coupling between Mn and Fe or Co provides
antiparallel atomic moments, which reduce the net mag-
netic moment, and pure Mn does not order ferro-
magnetically.
Some experimental studies have proposed Fe4Nas a
candidate material [3] for which the saturation moment
per atom is suggested to be larger than that of Fe-Co alloys
at the Slater-Pauling maximum (SPM), but several other
reports contradict this finding [4]. Also, theoretical studies
[5] showed that the addition of Mn to Fe4Nincreases the
unit cell volume and hence the magnetization, but the
magnetic moment per atom was found not to exceed that
of the Fe-Co alloys. Bergman et al. [6] found from their
calculations that a high saturation magnetization can be
obtained by a close packing of small Fe clusters in a Co
matrix. This study was tied intimately to an experimental
effort [7], but no definite conclusion was made about
reaching a saturation moment at room temperature that is
larger than that of the SPM.
In order to realize a combination of both large moment
and high Curie temperature, we propose here multilayers
of rare-earth-metal and 3dtransition metals (nanolami-
nates). We verify our proposition by quantum mechanical
calculations, which have been proven to be extremely
successful in reproducing the magnetic properties of ma-
terials. In addition to the theoretical work, we have also
performed thin-film synthesis as well as element-specific
measurements of the magnetism as a function of tempera-
ture, using the x-ray magnetic circular dichroism (XMCD)
technique.
We will demonstrate here an avenue to provide ferro-
magnetic materials with large magnetic moments at room
temperature by combining the large saturation moments
of the rare-earth-metal atoms with the high critical tem-
peratures of Fe or Co. In the past, multilayers composed
of Fe and Gd have been studied [8], and it is encourag-
ing to observe that thin layers of Gd in contact with Fe have
a large atomic moment of the Gd atom, even at room
temperature (6:8B=atom). However, it is well known
that magnetic 3delements couple their spin moments
antiferromagnetically to the spin moments of the rare-
earth-metal atoms [9], and in the Fe=Gd multilayer [10],
it was indeed found that the Fe and Gd moments couple in
antiparallel alignment, resulting in a reduced magnetic
moment.
We propose instead that one should consider monolayers
(MLs) of rare-earth-metal (R¼Gd, Tb, or Dy) elements
on a film of Fe (or an Fe-Co alloy), separated by 1 ML of
Cr. The combination R=Cr=Fe has been chosen since it is
known that rare-earth-metal moments couple antiferro-
magnetically with Cr [11,12], and Cr in turn couples anti-
ferromagnetically with Fe [13]. Hence, an effective
ferromagnetic coupling is expected between the rare-
earth-metal and the Fe magnetic moments, as is shown
schematically in Fig. 1. It is essential that this coupling is
sufficiently strong to provide a large ordering temperature.
We will show below that this is indeed true for the systems
proposed here.
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0031-9007=10=104(15)=156402(4) 156402-1 Ó2010 The American Physical Society
Experimental evidence for ferromagnetic coupling be-
tween the Relement and Fe is given by the analysis of the
element-specific spin alignment by means of x-ray absorp-
tion spectroscopy and its associated XMCD presented in
this work. As a prototype system, epitaxially grown nano-
composite layers of Gd13=Crn=Fe15 with different Cr in-
terlayer thickness, n, was investigated. By means of
RHEED measurements, it was controlled that the growth
is epitaxial and that the Gd caxis is oriented in the film
plane. Measurements at the Fe L3;2absorption edges in the
energy range 680 eV E790 eV and Gd M5;4absorp-
tion edges in the energy range 1150 eV E1280 eV
were performed in total electron yield (TEY) mode at the
PM-3 bending magnet beam line at BESSYII synchrotron
radiation source in magnetic remanence after saturation in
fields of 3T under grazing x-ray incidence (¼70
with respect to the sample normal). After each scan, either
the helicity of x-ray photons or the direction of remanent
sample magnetization was reversed. However, as discussed
below, the increase of the magnetic ordering temperature
of Gd necessary for large magnetic moments at room
temperature depends on the coupling strength with Fe
which is very sensitive to structural changes or diffusion
processes.
The calculations were done by two different methods
based on density functional theory. The VASP [14] plane
wave code was used with the all-electron projector aug-
mented wave method and the generalized gradient approxi-
mation to obtain the equilibrium interlayer separations
along the stacking direction by minimizing the Hellman-
Feynman forces. The kinetic energy cutoff was chosen to
be 400 eV. The calculated equilibrium separation between
the Rand the Cr layer is 1.98 A
˚, whereas it is 1.21 A
˚
between the Cr and the first Fe layer. At the fourth Fe layer,
the value for bulk Fe (1:43
A) is attained. Because of
structural relaxations, the Ratoms move outwards and the
R-Cr interlayer distance becomes larger compared to that
of bulk Fe or Cr, whereas the Fe-Cr distance is reduced to a
small degree.
The calculated equilibrium structure was then used to
calculate the magnetic moments and interatomic exchange
interactions by a fully relativistic implementation of the
full-potential linear muffin tin orbitals (FP-LMTO) method
[15]. A double basis was used to ensure a good conver-
gence of the wave function. The 4fstates of the rare-earth-
metal atoms were treated as core states with the spin mo-
ments constrained to the values derived from Hund’s rules,
i.e., ms¼7B(Gd), 6B(Tb), and 5B(Dy).
In Fig. 2, we show the calculated layer-projected mag-
netic moments obtained from the FP-LMTO calculations.
As the rare-earth-metal elements preserve their atomic spin
and orbital moments of the strongly localized 4fshell [16],
the orbital moments are easily evaluated and added to the
calculated 4fspin moments [the orbital moments are ml¼
0B(Gd), 3B(Tb), and 5B(Dy)]. We observe that the
Fe and rare-earth-metal magnetic moments are aligned
parallel to each other and the smaller Cr magnetic moment
is aligned antiparallel to the Fe and Ratoms, confirming
our coupling scheme outlined in Fig. 1. It should be noted
that the rare-earth-metal moment in this system is slightly
larger than the corresponding atomic 4fmoment, due to
the fact that the 4fspin moment induces a magnetic mo-
ment in the conduction band. We also note that the Fe
moment closest to the Cr atom is reduced compared to bulk
Fe, whereas the other Fe atoms have a slightly enhanced
magnetic moment.
We extended our study to include additional Rlayers in
order to investigate the possible further enhancement of the
magnetic properties. For 3 MLs of Dy, the average mag-
netic moment is calculated to be 3:68B=atom; this aver-
age is obtained from 3 Dy, 1 Cr, and 3 Fe MLs from the Fe-
Cr interface. The difference in the total energy of a ferro-
magnetic (FM) and an antiferromagnetic (AFM) ordering
FIG. 2 (color online). Calculated layer-projected magnetic
moments of the R=Cr=Fe (R¼Gd, Tb, and Dy) multilayers.
The atomic orbital moments of the rare-earth-metal atoms were
derived from Hund’s rules and added to the calculated spin
moments.
FIG. 1 (color online). Left: Schematic diagram of the magnetic
interactions between the rare-earth-metal (R) and the 3dtran-
sition metals Fe and Cr. Right: Structure of the considered
system.
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between the rare-earth-metal and Fe layers is a mea-
sure of the interatomic exchange interaction and hence
provides an estimate of the Curie temperature. In Fig. 3,
we present these values for the R=Cr=Fe multilayers
studied here. Again, it becomes clear that the rare-
earth-metal and Fe magnetic moments prefer to align
ferromagnetically, in accordance with the discussion
around Fig. 1. We also calculated the energy of a configu-
ration when half of the Ratoms had their spins turned
antiparallel to Fe, and the energy cost of this configu-
ration was similar to the data shown in Fig. 3(e.g., for a
Dy layer, this energy is 110 meV=rare-earth-metal atom
higher than the FM coupling). In addition, for the system
with 3 Dy layers, the calculated exchange interaction
between Dy and Fe was found to be 90 meV. The large
values of these energy differences, of the order of
100 meV=rare-earth-metal atom, signify that the FM in-
teraction between Ratoms and Fe is strong and that the
mean-field value of the Curie temperature is comparable to
that of bulk Fe, i.e., of the order of 1000 K. Our results are
in agreement with the study in Ref. [17] where the critical
temperature of two atomic species that in elemental form
have quite different ordering temperatures, one lower and
one higher ordering temperature, was demonstrated to
show ordering in a compound at the higher ordering
temperature.
As a proof of concept of the proposed coupling scheme,
the spin alignment was probed by means of XMCD for
13 MLs Gd coupled to 15 MLs Fe either directly as a
reference sample for the well-known AFM coupling, or via
3, 4, or 5 MLs of Cr interlayer. Gd was used here as a
representative Relement, with an exchange coupling to the
3dfilm which is similar to that of Dy and Tb. Our experi-
mental results are shown in Fig. 4. As expected, without Cr
interlayer and for even numbers of MLs of Cr (data not
shown), Gd couples antiferromagnetically to Fe moments.
This behavior was also found for 3 MLs Cr, which is in
contrast to what is expected from the scheme outlined in
Fig. 1. It is possible that interface alloying between Cr and
Fe over a few atomic layers distorts the coupling expected
from Fig. 1, for thin Cr films. However, a FM coupling
between Gd and Fe could be achieved for a 5 MLs Cr
interlayer, which is clearly indicated by the ratio of the
x-ray absorption signals with reversed direction of magne-
tization or reversed helicity of incident photons, þ=
as a function of photon energy (Fig. 4)[18]: The signal at
the Gd M5absorption edge points down (<1), and at the
M4edge it points up (>1) like Fe at its L3and L2edge,
respectively.
The potential of using the suggested nanocomposites
depends on their performance at room temperature, and
hence the XMCD signal at the Gd M5;4absorption edges
was measured at different temperatures between 11 and
300 K. As suggested in the literature [10,19], the experi-
mental data was simulated by a simple model with an
enhanced Curie temperature (T
C1000 K) of Gd in the
interface region, as depicted in Fig. 4, due to the exchange
coupling. The general trend of the temperature dependence
of the Gd magnetization can be explained by the following
model: For the directly coupled case (Fe=Gd), the thick-
FIG. 3. Calculated total energy difference between an antifer-
romagnetic (AFM) and a ferromagnetic (FM) ordering within the
rare-earth-element layer for R=Cr=Fe (R¼Gd, Tb, and Dy) and
Gd=Cr=Fe0:7Co0:3.
FIG. 4 (color online). Upper panel: XMCD measurements at
the Fe L3;2and Gd M5;4absorption edges at T¼11 K in
magnetic remanence exemplarily shown for the directly coupled
Fe=Gd reference sample and the ferromagnetically coupled
Gd13=Cr5=Fe15 sample. Lower panel: Temperature dependence
of XMCD at the Gd sites in an external magnetic field of 1T.
Experimental data are represented by symbols, solid lines rep-
resenting a simulation assuming two regions with different Curie
temperatures due to the coupling at the interface to Fe or Fe=Cr,
respectively, as depicted in the inset. Contributions of the region
with enhanced Curie temperature T
Care plotted by dashed lines.
PRL 104, 156402 (2010) PHYSICAL REVIEW LETTERS week ending
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ness of the interface regime of the Gd layer, where the
Curie temperature T
Cis enhanced, is the largest.
Consequently, the inner part of the Gd film, where the
Curie temperature is lower (it is actually reduced compared
to bulk values due to finite-size effects), is thinnest for this
system. Figure 4also shows that the thicker the Cr inter-
layer becomes, the smaller is the effective coupling be-
tween Fe and Gd. Therefore, the thickness of the Gd
interface region with enhanced ordering temperature is
reduced. To analyze this simple model, we fitted the data
in Fig. 4according to the procedure described in Ref. [10].
In the case of the directly coupled Fe=Gd sample, the
interface region with enhanced TCcorresponds to 4 MLs
Gd. The remaining 9 MLs Gd exhibit a TCof about 80 K.
By introducing a Cr interlayer, the Gd interface region with
enhanced TCbecomes smaller, i.e., 1 ML Gd interface for
5 MLs Cr. Our analysis suggests that the interface Gd
region has a magnetic moment at room temperature, which
is 70% (5B=atom) of the saturation moment at 0 K.
Therefore, the thickness of the inner Gd part is 12 MLs
connected to a TCof 110 K. This value can be compared to
the TCof a 13 MLs thick Gd reference sample without Fe
that was found to be around 120 K. The low TCof the
uncoupled Gd layers is the reason for the strong tempera-
ture dependence of the XMCD signal at low temperatures.
The interface magnetism yields an additional contribution
to the XMCD which is almost linear in the temperature
range examined here. This leads to an XMCD signal at
300 K of about 20% of the saturation value for the Fe=Gd
reference sample in good agreement to values reported in
the literature [10,19]. The smaller, but clearly nonvanish-
ing contribution in the case of the sample with 5 MLs Cr
interlayer of about 6% proves the FM coupling between Fe
and Gd.
We suggest here that Ratoms in R=Cr=Fe nanocompo-
site films may possess a large magnetic moment with
ordering temperatures much above room temperature. In
order to reach as big enhancement as possible, further
improvements in the film growth must be achieved, in
particular, any alloying between the Fe and Cr layers
must be avoided so that ferromagnetic coupling between
Fe and Gd can be reached for as thin Cr layers as possible,
ideally 1 ML.
A further improvement of the desired magnetic proper-
ties is expected if Fe is replaced by an Fe0:7Co0:3alloy.
From our calculations for Gd=Cr=Fe0:7Co0:3, we find in-
deed an increase of the Fe-Co moments (Fig. 2), but it is
not as pronounced as in bulk Fe-Co alloys. Further-
more, the antiparallel Cr moment is found to decrease,
and the net effect is that the total magnetic moment of
the Gd=Cr=Fe0:7Co0:3system is considerably larger com-
pared to the Gd=Cr=Fe system. In addition, the interatomic
exchange interaction becomes 20% larger than that of
Gd=Cr=Fe, as can be seen in Fig. 3. Hence, both the low
temperature saturation moment and the ordering tempera-
ture of the Rlayer is increased compared to the Gd=Cr=Fe
system.
Based on our experimental and theoretical work, we
conclude that an optimal experimental realization of a
high moment material would be a nanocomposite material,
with a combination of magnetic materials which involves
1–3 layers of Dy separated by 1 Cr layer from 5–7 layers of
an Fe0:7Co0:3alloy. The experimental realization sets high
demands on the thin-film growth by avoiding the alloying
between Fe and Cr.
We gratefully acknowledge the BESSY II staff, espe-
cially T. Kachel and H. Pfau for their support. This work
was funded by the Swedish Research Council (VR),
STINT Institutional Grant for Young Researchers, Go
¨ran
Gustafsson foundation, German Reasearch Foundation
(DFG) within the framework of SFB491, and the German
Federal Ministry of Education and Research (BMBF, 05
ES3XBA/5). We also thank Swedish National Infra-
structure for Computing for the allocation of supercom-
puter time. O. E. acknowledges support from ERC.
*Biplab.Sanyal@fysik.uu.se
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We have studied the influence Cr and Pd spacers on structure and magnetic ordering in Fe/Gd superlattices. The insertion of Cr and Pd spacers in Fe/Gd has been found to cause structural changes in Gd layers. In particular, an additional fcc Gd phase appears in Fe/Cr/Gd along with the main hcp Gd phase, while there is amorphous Gd structure in Fe/Pd/Gd. By combining SQUID magnetometry and polarized neutron reflectometry we have shown that interlayer Fe-Gd exchange coupling through Pd spacers is much stronger than through Cr one.
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Single molecule magnets comprising rare earth metals are of high interest due to the unquenched orbital moments of the rare earth ions that result in a large energy barrier for magnetization reversal. We investigate the magnetic properties of polynuclear 3d−4f15-MC-5 metallacrowns using x-ray magnetic circular dichroism of powder samples at a temperature of 7 K in a magnetic field of 7 T. The sum rule analysis reveals element-specific spin and orbital moments. The magnetic moments of the 3d transition metal Ni(II) ions are coupled antiferromagnetically to each other and contribute only little to the total molecular moment. The spin and orbital moments of the rare earth ions are unexpectedly smaller than the ionic values resulting from Hund's rules. We explain the reduction of the orbital magnetic moment by a finite magnetic anisotropy. Considering an energy functional including magnetic anisotropy and Zeeman energy the powder average reveals a magnetic anisotropy of 28 meV (340 K) in the case of Dy(III) and 7 meV (85 K) in the case of Tb(III). The spin moments agree with the ionic value, too, when the expectation values of the dipole operator are considered.
Thesis
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We have calculated spin and orbital moments for Fe clusters of sizes up to 700 atoms embedded as impurities in a bcc Co matrix. The calculations have been carried out using relativistic first-principles real-space density functional theory, and we have made a comparison with earlier experimental studies. For Fe atoms close to the FeCo interface, the spin moments are found to increase while atoms far from the interface exhibit bulklike moments. The Co moments remain essentially unchanged and close to the moment of bulk bcc Co. With increasing cluster size, the average moments of the cluster atoms decrease due to the decreased surface to volume ratio. The orbital moments of both Fe and Co are calculated to be small and they stay almost constant regardless of cluster size. Our results for spin moments agree with experimental data but the calculated orbital moments are slightly underestimated. A simplified model indicates that a compound of close-packed Fe clusters surrounded by Co show higher average total moments compared to bulk and multilayer systems with a similar concentration. This increase seems to disappear when cluster-cluster interactions are taken into account. The general trend is that for a given alloy concentration of FexCo1−x, clustering tends to lower the average magnetic moment compared to that of ordered structures and random alloys.
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The temperature evolution of the magnetization depth profile in Gd layers of a strongly coupled Gd50 Å /Fe15 Å 15 multilayer is studied using x-ray resonant magnetic scattering (XRMS) and x-ray magnetic circular dichroism (XMCD) techniques. XRMS yields a spatially resolved, element-specific, magne-tization depth profile, while XMCD spatially averages over this profile. The combined data inequivocally show the presence of an inhomogeneous magnetic profile within the Gd layers at all measured temperatures between 20 and 300 K. These inhomogeneous profiles, which feature enhanced magnetic ordering near the Gd/ Fe interface, were refined using both a kinematic Born approximation and a recently developed distorted-wave Born approximation, both of which include the contribution of structural and magnetic interfacial roughness. Calculations of the static magnetic configuration within a mean-field approach that neglects interfacial rough-ness are in agreement with the measured inhomogeneous profile and its temperature evolution. The results suggest that the enhanced Gd magnetization near the interface arises from its proximity to magnetically ordered Fe.
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Electronic structure calculations of magnetic properties for Mn-based alloys are performed. The full-potential linear augmented-Slater-type-orbital implementation of the local-density approximation is employed. Theoretical predictions for magnetic moments of MnxFe4-xY (Y=N/C/B/Be) are in good agreement with the reported experiments. Using the energy minimum criterion, the magnetic ordering of a particular phase has been determined. Simulations suggest that lattice expansions enhance magnetic moments of Mn atoms both in face-centered-cubic and body-centered-cubic crystal lattice structures with maximum magnetization Ms found to be 25 and 28 KG corresponding to a 15% and 12% increase in the lattice constant, respectively. Simulations predict that an approximately 12% increase in the magnetization Ms can be achieved with Mn3FeN compared to that with Fe4N.
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We study the non-collinear magnetism of FexCo1−x/Mnn multilayers which are particularly interesting for their experimental behaviour as well as for theoretical reasons because they allow to study the magnetic properties of thin Mn layers with varying boundary conditions by changing the concentration x. For perfect interfaces, even if a non-collinear Mn spacer is obtained for small Fe concentrations when collinear solutions are expected, the interlayer coupling energy follows a parabolic law as a function of the angle between successive ferromagnetic magnetizations. We also examine the role of interfacial monoatomic steps on the magnetic order in such multilayers.
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Polarized neutron reflection was used to determine the magnetic structure of two different antiferromagnetically coupled multilayer systems, Fe/Gd and Fe/Cr. In Fe/Gd, the Fe and Gd moments are coupled antiparallel at the interface. At low temperatures a surface-induced magnetic phase transition was found. In Fe/Cr, annealing at temperatures of up to 425°C resulted in the degrading of antiferromagnetic coupling between Fe layers and in the formation of ferromagnetically coupled regions.
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Gd/Fe and Fe/Gd bilayers have been prepared in ultrahigh vacuum on Cr/Si(1 0 0) at 300 K. Magnetic properties of the bilayers have been studied using polarized neutron reflectometry and SQUID magnetometry. As features common to both kinds of bilayers we have found an antiferromagnetic coupling between the Fe layer and the parts of the Gd layer being close to the interface while the magnetizations of other parts of the Gd layers are consistent with the presence of canted spin or domain structures. On the other side, it comes out that Gd/Fe bilayers exhibit clear differences in spin structures, remanent magnetizations, and coercive fields in the temperature range 5 K ⩽ T ⩽ 300 K compared to those of the Fe/Gd bilayers. This indicates that differences of interfacial and structural properties of the two bilayer systems have significant influences on their magnetic properties.
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The Curie temperature and the local spontaneous magnetization of ferromagnetic nanocomposites are investigated. The macroscopic character of the critical fluctuations responsible for the onset of ferromagnetic order means that there is only one Curie temperature, independent of the number of magnetic phases present. The Curie temperature increases with the grain size and is, in general, larger than predicted from the volume averages of the exchange constants. However, the Curie-temperature enhancement is accompanied by a relative reduction of the spontaneous magnetization. Due to the quadratic dependence of the permanent-magnet energy product on the spontaneous magnetization, this amounts to a deterioration of the magnets performance. The length scale on which an effective intergranular exchange coupling is realized (coupling length) depends on the Curie-temperature difference between the phases and on the spacial distribution of the local interatomic exchange. As a rule, it is of the order of a few interatomic distances; for much bigger grain sizes the structures mimic an interaction-free ensemble of different ferromagnetic materials. This must be compared to the magnetic-anisotropy coupling length, which is of the order of 10 nm. The difference is explained by the nonrelativistic character of the Curie-temperature problem. © 2000 American Institute of Physics.
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Magnetization-versus-applied-field curves M(H) are calculated for an [Fe(3.48 nm)/Gd(5.43 nm)]15 multilayer film using the Gd magnetization depth profiles derived from the resonant x-ray magnetic scattering data collected with an applied field of 2.4 kOe. Stable magnetic structures for other field strengths are calculated by minimizing the sum of the Fe-Fe, Gd-Gd and Gd-Fe exchange energies and the Zeeman energy in a temperature range of 140-240 K. The calculated curves fit very well the slowly rising M(H) curves observed at temperatures between 140 and 200 K, where the Gd layers are ferromagnetic, over a wide field range up to 50 kOe on adjusting a molecular-field constant for the Fe-Gd interfaces, the only one free parameter used. The concave magnetization depth profiles in the Gd layers are essential to reproduce the observed M(H) curves. The discrepancies between the observed and calculated curves in low-field regions represent the limitation of the single-magnetic-domain model used in the calculation.
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Calculations are made of the mean magnetic moment per atom of the transition metal and the rare-earth metal in the intermetallic compounds, Gd1-x,Nix, Gd1-x Fex, Gd1-x Cox, and Y1-x Cox. A simple model of the disordered alloy consisting of spins localized on the rare-earth atoms and interacting with a narrow d-band is considered. The magnetic moment of the alloy at zero temperature is calculated within the molecular field and Hartree-Fock approximations. Disorder is treated in the coherent potential approximation. Results are in good agreement with the experimental data obtained for the crystalline and amorphous intermetallic compounds.Es werden Rechnungen des mittleren magnetischen Moments pro Atom des Übergangsmetalls und des Metalls der Seltenen Erde in den intermetallischen Verbindungen Gd1-x Nix Gd1-x Fex, Gd1-x Cox,und Y1-x Cox durchgeführt. Dazu wird eineinfaches Modell der gestörten Legierung be-trachtet, das aus an den Seltenen-Erdatomen lokalisierten Spins besteht, die mit einem schmalen d-Band wechselwirken. Das magnetische Moment der Legierung am Nullpunkt wird innerhalb der Molekularfeldnherung und der Hartree-Fock-Nherung berechnet. Fehlordnung wird in der Nherung des kohrenten Potentials behandelt. Die Ergebnisse befinden sich in guter Übereinstim-mung mit den experimentellen Werten für kristalline und amorphe intermetallische Verbindungen.