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Composition-dependent ratio of orbital-to-spin magnetic moment

in structurally disordered FexPt1Àxnanoparticles

M. Ulmeanu,1C. Antoniak,1U. Wiedwald,1M. Farle,1Z. Frait,2and S. Sun3

1Institut fu

¨r Physik, Universita

¨t Duisburg-Essen, Lotharstrasse 1, D-47048 Duisburg, Germany

2Institute of Physics, Academy of Science of the Czech Republic, Na Slovance, 18221 Prague 8, Czech Republic

3IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA

共Received 12 September 2003; revised manuscript received 3 December 2003; published 20 February 2004兲

The ratio of orbital-to-spin magnetic moment

L

eff/

S

eff averaged over the element-speciﬁc contributions of Fe

and Pt has been measured for 3-nm FexPt1⫺xnanoparticles at room temperature using the multifrequency

electron paramagnetic resonance method for different concentrations of Fe. From a detailed g-factor analysis

we determine that the ratio decreases from

L

eff/

S

eff⫽0.049 for x⫽0.43 to

L

eff/

S

eff⫽0.016 for x⫽0.70 which is

much smaller than the bulk iron value (

L

Fe/

S

Fe⫽0.045). The observed concentration dependence is much

stronger than the one calculated for FexPt1⫺xbulk samples and reveals likely changes of the conﬁned elec-

tronic structure of the nanoparticle system. The ratio

L

eff/

S

eff takes the lowest value at the concentration (x

⫽0.70) where the magnetic anisotropy energy vanishes in bulk alloys. For x⬎0.72 a phase transition from a

fcc to the Fe bcc structure occurs resulting in the increased bulk ratio again.

DOI: 10.1103/PhysRevB.69.054417 PACS number共s兲: 76.50.⫹g, 81.07.⫺b

Much of the interest in nanoparticle systems of transition-

metal compounds like FePt, FePd, and CoPt is related to

their large magnetocrystalline anisotropy energy 共MAE兲,

which is of the order of 0.5 meV per magnetic 3datom

(106J/m3),1and makes these materials potential building

blocks for ultrahigh-density magnetic recording media and

permanent magnets.2The understanding and the control of

MAE in these nanoscale building blocks is a crucial task to

design new devices with desired magnetic properties. Unfor-

tunately, it is not evident that bulk properties can be directly

applied to nanoparticle systems. The conﬁnement and the

complicated interplay of s,p, and dstates in a 4-nm com-

posite nanoparticle may result in dramatic changes3in the

magnetic properties of Fe and Pt which have been

measured4–6 and calculated7–9 in bulk systems. This in turn

may alter the magnitude and anisotropy of the orbital mag-

netic moment 共which is related to the MAE兲and also the

magnitude of the induced magnetic moment on the Pt site.

Furthermore, also the surface magnetic anisotropy is of high

importance in nanoparticles with up to few nanometers in

diameter, since the ratio of surface-to-volume atoms ap-

proaches 30–40% in a 4-nm particle. Consequently, a study

of the intrinsic magnetic properties like the ratio of orbital-

to-spin magnetic moment and a microscopic understanding

of the mechanisms contributing to the large magnetocrystal-

line anisotropy of these materials are of fundamental interest.

FexPt1⫺xhas a continuous range of solid solutions, and

both stoichiometric and nonstoichiometric alloys with vari-

ous degrees of order can be prepared. The phase diagram is

rather complex, showing three ordered phases as a function

of Fe concentration,10 i.e., ferromagnetic Fe3Pt and antifer-

romagnetic FePt3with cubic Cu3Au-type 共or L21) structure,

while ferromagnetic FePt presents a tetragonal CuAuI-type

共or L10) structure with the largest value for MAE of 5–8

⫻106J/m3. One should note that this extremely large value

is almost by two orders of magnitude larger than the one of

the disordered fcc phase that the alloys presents in the

nonannealed state.3

It has been widely accepted that the MAE is related to the

magnitude and anisotropy ⌬

Lof the orbital magnetic

moment.11 In an itinerant binary system consisting, for ex-

ample, of a 3danda5delement the total moment cannot be

attributed to one or the other element alone. Hybridization

and polarization effects have to be taken into account. X-ray

magnetic circular dichroism has been considered to be the

appropriate method of choice to determine the element spe-

ciﬁc orbital and spin magnetic moment in composite materi-

als with high precision. However, recent results indicate that

the application of the so-called ‘‘sum rules’’ may lead to

erroneous results due to hybridized end states in a binary

system without ﬁrst-principle theoretical support.12 A

method which directly measures the ratio of the effective

orbital

L

eff and spin

S

eff magnetic moments inherent in the

hybridized band structure of both elements is the para- and

ferromagnetic resonance.13,14 In this classical technique one

measures the precession of the coupled magnetic moments of

Fe and Pt in the crystal potential and a detailed analysis15

yields the gfactor which is related to the effective ratio

L

eff/

S

eff .

The aim of the present work is to investigate the inﬂuence

of the composition on the spin and orbital magnetic moments

of the fcc disordered phase of FexPt1⫺xnanoparticles. An

experimental determination of the orbital-to-spin ratio for

different compositions will be given. The contribution of the

orbital magnetism, which is responsible for the MAE, is

found to decrease as a function of increasing Fe content

much stronger than in bulk disordered alloys, indicating the

importance of surface and ﬁnite-size effects in these compos-

ite nanoparticles.

Monodisperse FexPt1⫺xnanoparticles with a particle size

distribution

⭐5% were synthesized by the high-

temperature solution phase decomposition of Fe(CO)5and

reduction of Pt(acac)2in the presence of oleic acid, oley-

lamine, and 1,2-hexadecanediol 共forming a protective ligand

shell兲as described elsewhere.16 The composition of the

PHYSICAL REVIEW B 69, 054417 共2004兲

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FexPt1⫺xnanoparticles was controlled by tuning the molar

ratio of the metal precursors. The resulting solution was

dried forming an air-stable powder, which could be redis-

persed in hexane at any concentration.

To determine the size distribution of the particles, a drop-

let of the hexane solution was evaporated onto a transmission

electron microscope 共TEM兲amorphous carbon covered Cu

grid. The arrays were examined with a Philips CM12 Twin

共120 kV兲TEM to determine the particle diameter, the inter-

particle spacing and the degree of ordering. The nanopar-

ticles exhibit spherical morphology, for two compositions

Fe58Pt42 and Fe70Pt30 the mean particle diameter is 2.6 nm

with a standard deviation of 0.1 nm. In Fig. 1 we show one

example of many TEM micrographs for Fe43Pt57 that pre-

sents nanoparticles with sizes in the range of 3.6⫾0.1 nm.

Also, energy dispersive x-ray analysis 共EDX兲in the TEM

and Rutherford Backscattering 共RBS兲measurements were

performed to determine the chemical composition of the

FexPt1⫺xnanoparticles. A detailed statistical analysis of the

EDX spectra recorded for many particles showed that the

nominal Fe43Pt57 ,Fe

58Pt42 and Fe70Pt30 particle composition

varied by up to 3% around the nominal composition 共Table

I兲. From our high-resolution 共HR兲-TEM investigations, there

is no indication of an ordered phase in the as prepared state.

A typical HRTEM image of one Fe70Pt30 nanoparticle is

shown in the inset of Fig. 1 as an example.

To check for the presence of Fe oxides in the Fe70Pt30

nanoparticles, we performed near-edge x-ray-absorption ﬁne

structure 共NEXAFS兲spectroscopy at the Fe L3and L2ab-

sorption edges in total electron yield mode at beam line

D1011 at MAX laboratory synchrotron facility, Lund, Swe-

den. Our results are in excellent agreement with those of

Anders et al.17 who reported that the presence of a very thin

Fe oxide layer of less than 0.4 nm has to be assumed to

explain the observed spectra. Also, in agreement with this

work, we ﬁnd that annealing of the particles removes some

of the oxides and produces a more metallic spectrum.

The magnetic properties of the nanoparticles were studied

using a superconducting quantum interference device

共SQUID兲magnetometer. The Fe70Pt30 nanoparticles exhibit

superparamagnetic behavior at room temperature and have a

blocking temperature in the range 50–75 K.

The samples for the magnetic resonance measurements

were prepared by redispersing 1 mg of the nanoparticle pow-

der in a hexane solvent. Many layers of nanoparticles for

each composition were formed on a quartz substrate by dry-

ing the solution in air yielding a noise-free resonance signal

as depicted in Fig. 2.

Ferromagnetic resonance 共FMR兲measurements were per-

formed at 9, 24, and 79 GHz at room temperature. The mag-

netic ﬁeld was applied in the plane or perpendicular to the

plane of the sample. No angular dependence was observed

for the magnetic response of the nanoparticles, indicating

that the multilayered samples are isotropic. In a period of

time of over eight months the same samples and freshly pre-

pared ones have been measured three times in order to check

the reproducibility and the accuracy of the g-factor determi-

nation. No changes within the given error bars were observed

indicating no long term degradation effects for the FexPt1⫺x

nanoparticles protected by a ligand shell. Additional high-

sensitivity measurements on a single particle layer of

Fe70Pt30 obtained by drying a dispersion with a much smaller

particle concentration on silicon yielded the same angular

independent gfactor indicating that at 300 K additional lay-

ers do not modify the local magnetic ﬁeld in which the par-

ticle’s magnetic moment precesses. This indicates that the

magnetostatic interaction for the ligand separated nanopar-

FIG. 1. TEM micrographs of the Fe43Pt57 nanoparticles dried on

a conventional TEM grid. The inset shows a typical high-resolution

image of a Fe70Pt30 nanoparticle revealing the perfect crystallinity

of the chemically disordered particle.

TABLE I. Composition, diameter, and gfactor of the nanopar-

ticles. The gfactor (g⫽2.09) of bulk bcc Fe is given also for ease

of comparison.

Fe content

关at %兴

Mean diameter

关nm兴gfactor

43⫾3 3.6⫾0.1 2.098⫾0.015

58⫾3 2.6⫾0.1 2.070⫾0.015

70⫾3 2.6⫾0.1 2.032⫾0.010

100 2.090

FIG. 2. The magnetic resonance spectra for Fe70Pt30 nanopar-

ticles at: 共a兲

⫽9.829 GHz, 共b兲

⫽24.121 GHz, and 共c兲

⫽79.344 GHz.

M. ULMEANU et al. PHYSICAL REVIEW B 69, 054417 共2004兲

054417-2

ticles is very weak at room temperature. The FMR spectra at

three microwave frequencies for the Fe70Pt30 sample mea-

sured at room temperature are shown in Fig. 2. All spectra

were ﬁtted with Lorentzian line shapes and the resonance

ﬁeld Bres was determined. The asymmetry of the FMR spec-

trum measured at 79 GHz is due to a small misalignment of

the sample in the experimental setup.

Paramagnetic resonance describes the resonant absorption

of microwaves which matches the Zeeman energy levels

splitting in a paramagnetic material. Crystal-ﬁeld effects

modify the electronic states, and in a cubic crystal the orbital

moment is nearly completely quenched.18 In a classical pic-

ture the magnetization precesses around the direction of an

effective static magnetic ﬁeld and the torque acting on the

magnetization is a direct measure of the local magnetic ﬁeld

composed of the external and all intrinsic magnetic ﬁelds. In

the case of superparamagnetic particles the particle’s effec-

tive magnetic moment precesses uncorrelated to neighboring

particles as long as the measurement is performed high

above the blocking temperature of the particle. In this case,

the intrinsic magnetic ﬁelds due to the dipolar interaction

between particles is very weak and averages out due to the

thermal ﬂuctuations of the particles over the time window of

the measurement 共nanoseconds兲. This offers the unique op-

portunity to observe in single crystalline ferromagnetic nano-

particles the magnetic resonance undisturbed by the presence

of large intrinsic magnetic ﬁelds, thus facilitating the deter-

mination of the gfactor. In Refs. 19–22 the following rela-

tion between the gfactors measured by magnetic resonance

in ferromagnetic 共FMR兲compounds and the magnetization

contributions due to spin and orbital angular momentum was

derived, which for small orbital contributions is given by19

L

S

⫽g⫺2

2.共1兲

Note that in binary, strongly exchange coupled systems

like FePt with an induced polarization at the Pt site the ef-

fective orbital and spin contributions are measured.

Usually the determination of the gfactor based on FMR

measurements is very complicated due to large intrinsic mag-

netic anisotropy ﬁelds which are temperature dependent. In

ensembles of superparamagnetic nanoparticles above their

blocking temperature, however, the intrinsic magnetic ﬁelds

become negligibly small due to thermal ﬂuctuations. A

straight forward gfactor analysis in terms of the paramag-

netic resonance condition for FexPt1⫺xalloys becomes now

possible.

The gfactor for the case of paramagnetic solids can be

directly deduced from the slope of the linear dependence of

the resonance ﬁeld versus the Larmor frequency according to

the following equation:

h

⫽g

BBres ,共2兲

where

Bis the Bohr magneton, his the Planck constant,

and Bres is the resonance ﬁeld obtained from the derivative of

the absorptive part

⬙of the complex rf susceptibility

共

兲

which is conventionally measured at constant microwave fre-

quency

as a function of the external magnetic ﬁeld.

Frequency-dependent measurements yield an accurate g

value according to the standard paramagnetic resonance con-

dition 共2兲.15,22 The number of magnetic moments which is

detectable in an FMR experiment is of the order of

1010–1014 depending on the linewidth of the signal.13

We ﬁnd that the resonance ﬁelds for each composition

depend linearly on the microwave frequency as expected ac-

cording to Eq. 共2兲. No difference between in-plane and out-

plane resonance ﬁelds was observed as stated above. In Fig.

3, we show the result for the Fe43Pt57 and Fe70Pt30 composi-

tion for clarity only, since the data points for the intermediate

concentration fall in between the plotted data. One can see

that there are only small changes in the slope and only the

large range in frequencies allows to distinguish the small

differences between the samples. This linear dependence

clearly shows that no ferromagnetic contributions 共that is to

say additional internal magnetic ﬁelds兲have to be considered

in this multilayered thin ﬁlm sample. Such–even small—

internal ﬁelds due to for example demagnetization ﬁelds of

dipolar origin would lead to a difference between in-plane

and out-of-plane measurements as observed, for example, in

layers of Co/CoO core shell nanoparticles.23

The gfactors 共Table I兲are directly calculated from the

slopes of the data in Fig. 3 for the different compositions

according to the paramagnetic resonance condition. The error

bars for the determination of the gfactor and the respective

concentrations are given in Fig. 4 and Table I. One ﬁnds that

only for the highest Pt concentrations, i.e., Fe43Pt57, the g

factor is larger than the one of bulk bcc Fe (g⫽2.09),14

while for the other two compositions, Fe58Pt42 (g⫽2.070)

and Fe70Pt30 (g⫽2.032), the gfactor is lower. Before dis-

cussing the composition dependence, we would like to point

out that there is a size difference between the Fe43Pt57 共di-

ameter 3.6 nm兲and the other two compositions 共diameter 2.6

nm兲. From our results we cannot exclude that the ratio

L/

Sfor the 3.6-nm nanoparticle could be slightly smaller

than the one for 2.6-nm particles due to the smaller surface

contribution.24 However, for these diameters 共2.6 nm vs 3.6

nm corresponding to more than 1000 atoms per cluster兲the

possible size dependent reduction of the ratio averaged over

the particle is very small, and one may conclude that the

composition dependence is the more important factor.

Since the gfactor is related to the ratio of the orbital-to-

FIG. 3. Resonance ﬁeld as a function of the microwave fre-

quency for Fe43Pt57 and Fe70Pt30 particles at room temperature. The

error bar for resonance ﬁelds is smaller than the symbol size.

COMPOSITION-DEPENDENT RATIO OF ORBITAL-TO-... PHYSICAL REVIEW B 69, 054417 共2004兲

054417-3

spin magnetic moment we can discuss the results directly in

terms of the variation of this ratio as a function of Fe con-

centration. At this point one has to remember that the aver-

aged moments of the binary alloy enter the experimentally

determined ratio. As mentioned before, the measured ratio

does not reﬂect the ratio of the individual Fe or 共induced兲Pt

moment alone but rather the averaged collective response of

both elements at their respective concentrations, i.e., xfor Fe

and (1⫺x) for Pt. Hence the ratio Rshould be deﬁned by

R⫽x

L

Fe⫹共1⫺x兲

L

Pt

x

S

Fe⫹共1⫺x兲

S

Pt ⬅

L

eff

S

eff ⫽g⫺2

2,共3兲

which takes into account that the effective magnetic moment

depends on the type and number of nearest neighbors. One

should note that by calculating the effective ratio according

to Eq. 共3兲we implicitly assume that the induced orbital mo-

ment of Pt couples more strongly to the one of Fe than to its

own spin moment. This can be paraphrased as a type of

Russel-Saunders 共LS兲coupling versus a JJ-type of coupling

for which one would calculate ﬁrst the ratios

L/

Sfor Fe

and Pt individually and add the two ratios to determine the

effective experimentally measured value. As shown below

we ﬁnd reasonable evidence that the ‘‘LS’’ type of coupling

关Eq. 共3兲兴 is the appropriate coupling scheme for the moment

contributions in the FePt binary alloy.

In Fig. 4 we show the experimental result for R共right

scale兲obtained from Eq. 共3兲together with the ratio calcu-

lated according to Eq. 共3兲from the experimental and theo-

retical orbital and spin magnetic moments of Fe and Pt given

in Refs. 7 and 8. The coupling of the Pt and Fe moments is

assumed ferromagnetic, which in general has been theoreti-

cally predicted and experimentally conﬁrmed in the concen-

tration range x⬎30%. Only ordered FePt3crystals show an

antiferromagnetic 共AFM兲coupling between adjacent Fe

planes, which may involve a frustrated AFM coupling be-

tween the induced Pt moment and the one of Fe. Recently, a

near energetic degeneracy between ferro- or antiferromag-

netic in alternating Fe layers has been calculated for the FePt

composition in bulk samples.25 The tendency for ferromag-

netic order has been found to become more favorable when

the chemical disorder is increased which corresponds to our

samples. So, the assumption of ferromagnetic coupling in

our particles seems well justiﬁed. Considering the possibly

modiﬁed electronic structure in our nanoparticles another

type of coupling than in bulk samples cannot be completely

excluded. Also, one may notice, that in other 3d/5dinter-

faces, the alignment of orbital and spin magnetic moments

has been found to violate Hund’s third rule allowing for a

parallel alignment of the induced spin moment while the

induced orbital moment is oppositely oriented.26–28 After cal-

culating all combinations of parallel and antiparallel combi-

nations of Fe and Pt orbital and spin magnetic moments7,8 we

ﬁnd the best correlation of the concentration dependence of

the literature bulk data 共open symbols in Fig. 4兲to our ex-

perimental data when we assumed parallel alignment of the

moments 共e.g., FePt3:8

S

Fe⫽3.14

B,

L

Fe⫽0.1

B,

S

Pt

⫽0.30

B,

L

Pt⫽0.05

B; FePt:7

S

Fe⫽2.89

B,

L

Fe

⫽0.11

B,

S

Pt⫽0.35

B,

L

Pt⫽0.05

B;Fe

3Pt:8

S

Fe

⫽2.51

B,

L

Fe⫽0.09

B,

S

Pt⫽0.29

B,

L

Pt⫽0.05

B).

It is obvious that the element-speciﬁc moments do not

vary much as a function of composition, however, the

weighting by the atomic percentage xpresent in the sample

yields the composition dependence of the averaged ratio,

which is consistent with our experimental data. The differ-

ence between the literature and the experimental ratio may

have two reasons. First, all calculations were done for inﬁ-

nite samples and the ﬁnite geometry of the nanoparticles

including the large surface contribution was not taken into

account. Recently, it was shown by resonant magnetic dif-

fraction experiments at the Pt L3absorption edge5of Fe38Pt62

and Fe56Pt44 nanoparticles of approximately 5 nm diameter

that the Pt magnetic moment is signiﬁcantly smaller than for

the respective bulk alloys. Second, the implicit assumption

of collinear magnetic moments in our analysis of the experi-

mental gfactor may only be a good approximation. To

clarify these issues additional measurements to determine the

orbital and spin magnetic moment at the Fe and at the Pt

edge of monodisperse nanoparticles are highly desirable.

In summary, by multifrequency magnetic resonance ex-

periments we have shown that the averaged ratio of orbital-

to-spin magnetic moment of FexPt1⫺xnanoparticles de-

creases as a function of increasing Fe content. At the Fe rich

composition x⫽0.70 which corresponds to the range where

the magnetic anisotropy energy in disordered bulk alloys

vanishes we ﬁnd a very small nearly negligible ratio indicat-

ing the expected relation between MAE and orbital moment

anisotropy. It is demonstrated that paramagnetic resonance of

superparamagnetic particles well above the blocking tem-

perature is a valuable tool to determine microscopic mag-

netic properties of nanoparticles with high precision and high

sensitivity.

We thank M. Spasova, B. Rellinghaus, and M. Cerchez

for helpful discussions, and S. Stappert and H. Za

¨hres for

help in the TEM measurements. This project was supported

by the European Community, Contract No. HPRN-CT-1999-

00150, the Access to Research Infrastructure Action of the

Improving Human Potential Programme, and the Deutsche

Forschungsgemeinschaft.

FIG. 4. Experimental gfactor and ratio of orbital-to-spin mag-

netic moment as a function of Fe concentration xof the nanopar-

ticles 共solid triangles兲. The value for bulk Fe (x⫽100) is also given

as a reference. For comparison the ratio calculated from literature

data 共see text兲is also shown 共open squares兲.

M. ULMEANU et al. PHYSICAL REVIEW B 69, 054417 共2004兲

054417-4

1G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans, Phys.

Rev. B 44, 12 054 共1991兲.

2S. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser, Science

287, 1989 共2000兲.

3B. Stahl, J. Ellrich, R. Theissmann, M. Ghafari, S. Bhattacharya,

H. Hahn, N. S. Gajbhiye, D. Kramer, R. N. Viswanath, J.

Weissmuller, and H. Gleiter, Phys. Rev. B 67, 014422 共2003兲.

4S. Imada, T. Muro, T. Shishidou, S. Suga, H. Maruyama, K.

Kobayashi, H. Yamazaki, and T. Kanomata, Phys. Rev. B 59,

8752 共1999兲.

5O. Robach, C. Quiros, S. M. Valvidares, C. J. Walker, and S.

Ferrer, J. Magn. Magn. Mater. 264, 202 共2003兲.

6H.-G. Boyen, G. Ka

¨stle, F. Weigl, P. Ziemann, K. Fauth, M.

Heßler, G. Schu

¨tz, B. Stahl, J. Ellrich, H. Hahn, F. Banhart, M.

Bu

¨ttner, M. G. Garnier, and P. Oelhafen, Adv. Funct. Mater. 13,

359 共2003兲.

7A. B. Shick and O. N. Mryasov, Phys. Rev. B 67, 172407 共2003兲.

8V. N. Antonov, B. N. Harmon, and A. N. Yaresko, Phys. Rev. B

64, 024402 共2001兲.

9R. Hayn and V. Drchal, Phys. Rev. B 58, 4341 共1998兲.

10H. Okamoto, in Binary Phase Diagrams 共ASM International,

Cleveland, OH, 1996兲.

11 F.Wilhelm, P. Poulopoulos, P. Srivastava, H. Wende, M. Farle, K.

Baberschke, M. Angelakeris, N. K. Flevaris, W. Grange, J.-P.

Kappler, G. Ghiringhelli, and N. B. Brookes, Phys. Rev. B 61,

8647 共2000兲.

12A. Scherz, H. Wende, K. Baberschke, J. Mina

´r, D. Benea, and H.

Ebert, Phys. Rev. B 66, 184401 共2002兲.

13M. Farle, Rep. Prog. Phys. 6, 755 共1998兲.

14C. Kittel, Phys. Rev. 76, 743 共1949兲; J. Pelzl, R. Meckenstock, D.

Spoddig, F. Schreiber, J. Pﬂaum, and Z. Frait, J. Phys.: Condens.

Matter 15, S451 共2003兲, and references therein.

15A. N. Anisimov, M. Farle, P. Poulopoulos, W. Platow, K. Baber-

schke, P. Isberg, R. Wappling,A. M. N. Niklasson, and O. Eriks-

son, Phys. Rev. Lett. 82, 2390 共1999兲.

16S. Sun, E. E. Fullerton, D. Weller, and C. B. Murray, IEEE Trans.

Magn. 37, 239 共2001兲.

17S. Anders, M. F. Toney, T. Thomson, J.-U.Thiele, B. D. Terris, S.

Sun, and C. B. Murray, J. Appl. Phys. 93, 7343 共2003兲.

18G. Y. Guo and H. Ebert, Phys. Rev. B 53, 2492 共1996兲.

19Ch. Kittel, Phys. Rev. 76, 743 共1949兲.

20J. H. Van Vleck, Phys. Rev. 78, 266 共1950兲.

21R. A. Reck and D. L. Fry, Phys. Rev. 184, 492 共1969兲.

22A. J. Meyer and G. Asch, J. Appl. Phys. 32, 330S 共1961兲.

23U. Wiedwald, M. Spasova, E. L. Salabas, M. Ulmeanu, M. Farle,

Z. Frait, A. Fraile Rodriquez, D. Arvanitis, N. S. Sobal, M.

Hilgendorff, and M. Giersig, Phys. Rev. B 68, 064424 共2003兲.

24C. Binns, S. H. Baker, K. W. Edmonds, P. Finetti, M. J. Maher, S.

C. Louch, S. S. Dhesi, and N. B. Brookes, Physica B 318, 350

共2002兲.

25G. Brown, B. Kraczek, A. Janotti,T. C. Schulthess, G. M. Stocks,

and D. Johnson, Phys. Rev. B 68, 052405 共2003兲.

26F. Wilhelm, P. Poulopoulos, H. Wende,A. Scherz, K. Baberschke,

M. Angelakeris, N. K. Flevaris, andA. Rogalev, Phys. Rev. Lett.

87, 207202 共2001兲.

27F. Wilhelm, P. Poulopoulos, H. Wende,A. Scherz, K. Baberschke,

M. Angelakeris, N. K. Flevaris, andA. Rogalev, Phys. Rev. Lett.

90, 129702 共2003兲.

28H. Wende, A. Scherz, F. Wilhelm, and K. Baberschke, J. Phys.:

Condens. Matter 15, S547 共2003兲.

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