JOURNAL OF APPLIED PHYSICSVOLUME 95, NUMBER 12

15 JUNE 2004

Ferromagnetic resonance study of diluted Fe nanogranular films
Satoshi Tomitaa)
PRESTO, Japan Science and Technology Agency (JST), Wako, Saitama 351-0198, Japan

Masayuki Hagiwara and Takanari Kashiwagi
Magnetic Materials Laboratory, RIKEN (The Institute of Physical and Chemical Research), Wako,
Saitama 351-0198, and Graduate School of Integrated Science, Yokohama City University, Tsurumi,
Yokohama 230-0045, Japan

Chusei Tsuruta and Yoshio Matsui
National Institute for Materials Science (NIMS), Namiki, Tsukuba 305-0044, Japan

Minoru Fujii and Shinji Hayashi
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Nada,
Kobe 657-8501, Japan

共Received 5 January 2004; accepted 23 March 2004兲
Ferromagnetic resonance 共FMR兲 in diluted Fe nanogranular films with low volume fractions of Fe( v ) has been studied. Films prepared by a co-sputtering technique are composed of amorphous Fe
nanoparticles embedded in SiO2 glass matrices. The resonance of the FMR uniform mode is foundto be strongly affected by the v , the temperature, and the angle between the film plane and theapplied magnetic field. The present study suggests that the values of these parameters should be
carefully selected in order to realize left-handed materials using diluted ferromagnetic-metal
nanogranular films. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1739526兴

I. INTRODUCTION

Fe volume fraction ( v ). The experimental procedures arebriefly summarized in the following section 共Sec. II兲. Section
III is devoted to the characterization of film composition andstructure, and to FMR studies as a function of the v , thetemperature, and the angle between an applied magnetic field
and the film plane. Finally, in Sec. IV we conclude the paper.

Films consisting of ferromagnetic-metal nanoparticles
embedded in nonmagnetic matrices are known as
ferromagnetic-metal nanogranular films. The structure of the
nanogranular films can be specified by the volume fraction of
the magnetic granules ( v ). In the range of v ⫽50– 60% thenanometer-size granules are in close contact with each other共structural percolation threshold v p ), forming infinite networks of ‘‘wormy’’ textures.1 Just below the v p ,ferromagnetic-metal nanoparticles in the films are closely
packed and separated by very thin nonmagnetic layers. Suchfilms have been intensively studied as promising materials
for use in magnetic data storage media with ultra-high recording density.2–5
In contrast to the ‘‘dense’’ ferromagnetic-metal nanogranular films, ‘‘diluted’’ films with very low v , in which
the ferromagnetic-metal granules are completely isolated
by matrices, have received little attention. Diluted
ferromagnetic-metal nanogranular films are, however, of interest for realizing left-handed materials 共LHMs兲6 having simultaneously negative electrical permittivity 共⑀兲 and negative magnetic permeability 共␮兲 in the microwave region.7
This is based on the fact that ␮ of ferromagnetic materials
for electromagnetic waves can be negative in the vicinity of
the ferromagnetic resonance 共FMR兲 frequency, which is usually in the microwave region.8,9 In order to realize LHMs by
this approach, detailed knowledge of FMR conditions in the
nanogranular films is necessary.
In this paper, we have reported the results of FMR studies of diluted Fe nanogranular films with small values for the

II. EXPERIMENTAL

Nanogranular Fe-SiO2 films were prepared by a cosputtering technique. Fe chips were placed on a SiO2 target.
They were simultaneously sputtered in 2.7 Pa Ar gas using a
rf magnetron sputtering apparatus. This technique enables asmall volume fraction of Fe in the films to be controlled by
the areal ratio of Fe and SiO2 on the sputtering target. Films
about 10 ␮m in thickness were deposited onto quartz substrates for FMR studies. The substrates were not heated during the deposition. The as-deposited films were studied.
The volume fraction in the films was estimated by using
electron probe microanalyses 共EPMA兲. The EPMA were carried out on films 1 ␮m in thickness deposited on Al plates. A
cross section of the samples was observed using a transmission electron microscope 共TEM兲 operated at 800 kV. The
specimens for the TEM observations were prepared according to standard procedures including mechanical and Ar-ion
thinning techniques.
FMR studies were performed using a conventional
X-band ( ␯ ⫽9.1 GHz) ESR spectrometer equipped with a cylindrical TE011 cavity. The samples 共about 3 mm⫻3 mm)
were placed onto a quartz sample holder, put into the cavity,and held in either parallel or perpendicular orientation to thesample plane of the applied magnetic field. FMR spectra
were obtained by sweeping the magnetic field from 0 to 10a兲Electronic mail: s-tomita@riken.go.jp

0021-8979/2004/95(12)/8194/5/$22.00

8194© 2004 American Institute of Physics

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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004

Tomita et al.

8195

kOe. The magnetic field was calibrated using a ␣,␣-diphenyl-␤-picryl hydrazyl 共DPPH兲 sample (g⫽2.0036).
A standard field modulation technique was used so that thedetected signal corresponded to the first field derivative of
the absorbed microwave power. A He gas-flow cryostat combined with a temperature controller allowed us to vary the
sample temperature continuously in the range of 3–300 K. In
addition to FMR studies, the magnetization of the samples
on various temperatures and magnetic fields was investigatedusing a superconducting quantum interference device
共SQUID兲 magnetometer.

III. RESULTS AND DISCUSSION
A. Film composition and structure

In this study, EPMA was used to determine the ratio of
the atomic concentrations of Fe to Si (X Fe /X Si). The volume
fraction of Fe 关v 共%兲兴 was then calculated from the atomic
Fe:Si ratio using v /(100⫺ v )⫽0.260(X Fe /X Si). 10 This relation assumes that the material is completely phase-separated
into SiO2 and crystalline ␣-Fe. On the other hand, Fe nanoparticles have amorphous structures in the present samples,as will become obvious later. Therefore, v calculated in thismanner does not give a strictly correct volume fraction of Fe
in the films. Since this slight difference was not thought toseriously affect the conclusions, the calculated v was used tokeep our notation consistent with that used by others.
Though Fe nanogranular films have been prepared with v⫽1, 5, 15, 20, and 24%, the v ⫽5% and 15% films are thefocus of this study.
Figure 1 shows a cross-sectional TEM image of a filmwith v ⫽15%. Spherical dark patches about 2 nm in diametercan be seen. These patches correspond to Fe nanoparticles inamorphous SiO2 matrices. The micrograph shows no obvious evidence of physically connected particles. As shown in
the inset, the size distribution of the particles is narrow. The
average diameter (d ave) and standard deviation 共␴兲 are 2.01
nm and 0.42 nm, respectively. Debye–Scherrer rings in a
selected-area electron diffraction 共SAED兲 pattern are quite
broad 共not shown here兲. Almost all of the rings were assigned to amorphous Fe,11 although a few dim rings could
not be identified. Based on these findings, the v ⫽15% film
was characterized by isolated, roughly spherical, and amorphous Fe nanoparticles with d ave⫽2.01 nm embedded in
SiO2 glass matrices. TEM observation of another film withv ⫽5% also revealed that amorphous Fe nanoparticles about
1 nm in diameter were dispersed in the SiO2 glass matrices.
TEM studies have indicated that Fe nanoparticles in thefilms possess amorphous rather than crystalline structures.
The formation of amorphous Fe nanoparticles in asdeposited Fe–SiO2 films prepared by a co-sputtering method
was previously reported by Holtz et al.10 They reported thatsputtered films had an excess of silicon; the O:Si atomic ratio
was less than 2.0. The excess silicon atoms incorporated into
the Fe particles were considered responsible for the amorphous phase of Fe. It was also reported that post-deposition
annealing between 480– 700 °C under vacuum converts theparticles from amorphous to crystalline.

FIG. 1. A cross-sectional TEM image of a film with v ⫽15%. The inset
shows the size distribution of the particles.

B. Ferromagnetic resonance studies

Figures 2共a兲 and 2共b兲 show the FMR spectra obtained atroom temperature for films with v ⫽5 and 15%, respectively.
Note that the spectra correspond to the field derivative of theabsorbed microwave power. The inset of Fig. 2共a兲 illustrates
the configuration of a sample in an applied magnetic field(H). The ␪ was defined as the angle between H and the film
plane; ␪ ⫽0° and ␪ ⫽90° correspond to H in the directions
parallel and perpendicular to the film plane, respectively.
In Fig. 2共a兲, a broad resonance at about 3000 Oe could
be clearly observed. The g value of this resonance is about
2.20. This resonance signal is referred to as the main resonance signal in the following. In addition to the main resonance signal, a weak signal around 500 Oe was observed.
The origin of this weak signal has yet to be elucidated. Figure 2共a兲 shows that the position and width of the main resonance signal for the v ⫽5% film are independent of ␪. On theother hand, the resonance signal for the film with v ⫽15%
was influenced by ␪ 关Fig. 2共b兲兴. At ␪ ⫽0°, the signal appeared around 2900 Oe 共solid line兲, whereas the signal appeared upfield at 3500 Oe for ␪ ⫽90° 共dashed line兲.
More detailed FMR studies were carried out by changing
the temperature in the range of 4 –300 K. It should be first
noted that the position of the signal in the film with v⫽5% was almost entirely independent of the temperature.
Thus, only the results for the film with v ⫽15% are shown in
Fig. 3. Figure 3共a兲 shows the temperature dependence of the

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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004

FIG. 4. The resonance field of the main-resonance (H 0 ) in films with v⫽5% 共䊊,䊉兲 and in v ⫽15% 共䊐,䊏兲 are plotted as a function of temperature
down to 50 K. The open and solid marks correspond to the H 0 in the paralleland perpendicular configurations, respectively.

FIG. 2. Room temperature FMR spectra of films with 共a兲 v ⫽5% and 共b兲
v ⫽15%. The inset illustrates the configuration of a sample and an appliedmagnetic field.

FMR spectrum at ␪ ⫽0°. Suppression of the signal intensity
in the vicinity of the zero field at low temperatures is an
artifact caused by a magnet power supply. The main resonance signal appeared around 2900 Oe at room temperature.
As the temperature decreased, the resonance signal was ob-

served to broaden and shift to a lower magnetic field. Figure
3共b兲 shows the temperature variation of the spectra at ␪
⫽90°. The main resonance signal shifted towards a higher
field and broadened with decreasing temperature.
In addition to the main resonance signal in Fig. 3共a兲
below 150 K, another signal was observed at a lower field,
around 1000 Oe, and was remarkable at around 30 K. Also at␪ ⫽90° 关Fig. 3共b兲兴, a broad signal around 2000 Oe was observed at low temperatures. The position of the signal in bothconfigurations shifted to a slightly lower field as the temperature decreased. A similar feature was observed by Sharma
and Baiker12 in FMR spectra for a silica-supported Ni catalyst 共Ni content 8%兲. One of the possible origins of thissubsidiary feature is unsaturation of the magnetization of thefilms.13 The deformation of the main resonance signal due tothe appearance of this subsidiary feature is thus believed to
be prevented in a high field, in other words, in a high frequency FMR study.
C. Main resonance signal in FMR spectra

FIG. 3. The temperature dependence of FMR spectra for a film with v⫽15% at 共a兲 ␪ ⫽0° 共the parallel configuration兲 and 共b兲 ␪ ⫽90° 共the perpendicular configuration兲.

In Fig. 4, the resonance field for the main resonance(H 0 ) in the film with v ⫽15% is plotted as a function oftemperature. The open and solid squares correspond to H 0 at␪ ⫽0° and ␪ ⫽90°, respectively. In an effort to derive H 0 ,data analyses were conducted. The derivative FMR spectrum
was integrated to obtain a spectrum of absorbed microwave
power, and the spectrum was then decomposed into two signals with Lorentzian lineshapes. The H 0 was derived fromthe decomposed signal at a higher field. It was very difficult
to decompose the spectra well at low temperatures due to thebroadness and deformation, thus only the data from room
temperature to 50 K were presented.
The H 0 of the signal for the v ⫽15% film at ␪ ⫽90° 共thesolid squares in Fig. 4兲 appeared at about 3700 Oe at room
temperature and shifted upfield upon cooling. It finallyDownloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

Tomita et al.

J. Appl. Phys., Vol. 95, No. 12, 15 June 2004

reached about 5000 Oe at 50 K. On the other hand, the H 0 at␪ ⫽0° 共open squares兲 shifted from about 3000 Oe to thedownfield as the temperature decreased. The results for thev ⫽5% film at ␪ ⫽0° 共open circles兲 and at ␪ ⫽90° 共solid
circles兲 are also shown in the same figure for comparison.
The H 0 of the v ⫽5% film was observed to be independentof both the angle and the temperature.
It should be mentioned here that both the v ⫽5% and
15% films showed spontaneous magnetization in the M–Hcurves obtained by the SQUID magnetometer, although thedata is not shown here. The spontaneous magnetization isbelieved to originate from ferromagnetic amorphous Fe
nanoparticles in the films.14 It is thus reasonable to interpretthe main resonance signals as due to a FMR uniform mode
共the Kittel mode9兲, which corresponds to a uniform precession of all of the magnetic moments coupled in the Fe nanoparticles with the angular frequency ␻ 0 . The FMR condition
for an ellipsoidal ferromagnet, to which the external field isapplied along the z axis, is given by the Kittel equation,9

␻ 20 ⫽ ␥ 2 关 H 0 ⫹ 共 N x ⫺N z 兲 M z 兴关 H 0 ⫹ 共 N y ⫺N z 兲 M z 兴 ,共1兲

where H 0 is the applied magnetic field for the uniform mode
resonance; M z is the magnetization in the z direction; and ␥
is the gyromagnetic ratio, which is related to the g value by␥ ⫽⫺g ␮ B /ប. The Bohr magneton is represented by ␮ B ,and ប is the Planck constant divided by 2␲. The N x , N y ,and N z are the demagnetization factors along the x, y, and z
directions, respectively, which vary with the shape of theferromagnet and satisfy the relation N x ⫹N y ⫹N z ⫽4 ␲ . For anoninteracting uniform sphere, the shape effect can be neglected because N x ⫽N y ⫽N z , and␻ 0 / 兩 ␥ 兩 ⫽H 0 .

共2兲Equation 共2兲 indicates that the H 0 for magnetically isolated
spherical magnets is independent of the magnetic field direction and temperatures below the Curie temperature. This
clearly explains the angular and temperature dependence ofthe main resonance signal for v ⫽5%. Furthermore, the gfactor of the signal (g⫽2.20) is close to that of a uniform
mode in bulk ferromagnetic Fe material, the value of which,obtained from the literature, is g⫽2.14⫾0.08. 15 The main
resonance in v ⫽5% film can thus be assigned to a FMR
uniform precession mode in the individual spherical Fe
nanoparticle about 1 nm in diameter. This indicates that, in afilm with v ⫽5%, the very small Fe nanoparticles are magnetically isolated and show superparamagnetism, in which
the magnetic moment of each single domain nanomagnet is
randomly oriented by thermal fluctuations.
An increase in v is followed by an increase in the sizeand density of Fe nanoparticles, as shown by the TEM observation. Superparamagnetic spherical Fe nanoparticles thenbegin to magnetically couple with each other at the magnetic
percolation threshold ( v m ), resulting in the formation ofmagnetic networks in the films. Given that the ensemble ofthe coupled superparamagnetic moments above v m behaves
macroscopically as a thin magnetic film, a shape effect must
be considered for FMR conditions. The Kittel equation 关Eq.
共1兲兴 for ferromagnetic disks is expressed as

8197

FIG. 5. Magnetization in v ⫽15% film at ␪ ⫽90° during the zero-fieldcooled 共dashed line兲 and field-cooled 共solid line兲 procedures under 3000 Oe.

␻ 0 / 兩 ␥ 兩 ⫽ 冑H 0 共 H 0 ⫹4 ␲ M z 兲 ,␻ 0 / 兩 ␥ 兩 ⫽H 0 ⫺4 ␲ M z ,␪ ⫽0°,

␪ ⫽90°,

共3a兲
共3b兲

where the term 4 ␲ M z represents the demagnetization effect.
These equations suggest that the H 0 in the parallel 共perpendicular兲 configuration appears at a lower 共higher兲 magnetic
field than the resonance field without the demagnetization
effect. The predicted angular dependence of the uniform
mode signal is in good agreement with the present FMR
results for v ⫽15% at room temperature; as shown in Fig. 4,
H 0 appeared around 3000 Oe at ␪ ⫽0° and around 3700 Oe
at ␪ ⫽90°. These results clearly indicate that a film with v⫽15% is beyond the magnetic percolation threshold v m ,and the amorphous Fe nanoparticles in the film are magnetically coupled despite the fact that v is low compared to thatof the structural percolation threshold ( v p ⫽50– 60%). It isthus concluded that a slight difference in v affects the FMR
conditions of diluted ferromagnetic-metal nanogranularfilms, and the permeability ␮ of a film with v ⬎ v m would
exhibit anisotropy under a given magnetic field and microwave frequency.
Equations 共3a兲 and 共3b兲 also point out that the temperature dependence of H 0 in a film with v ⫽15% is attributed tothat of the 4 ␲ M z . The temperature dependence of M z forv ⫽15% was investigated using a SQUID magnetometer.
Figure 5 shows M z versus temperature during zero-fieldcooled 共ZFC兲 and field-cooled 共FC兲 procedures under a magnetic field of 3000 Oe. The dashed and solid lines correspondto ZFC and FC curves, respectively. The magnetic field wasapplied in the direction perpendicular to the film plane ( ␪⫽90°). The ZFC curve indicates that the M z has a peak at 6
K. This is attributed to the blocking phenomena of superparamagnetic particles.1 As the temperature decreases, superparamagnetic particles of smaller and smaller size become
successively blocked until the blocking temperature T B of 6K, where the ZFC curve shows a maximum. This blocking
process leads to an increase in the M z as the temperature

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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004

FIG. 6. The H 0 ⫺3726 for v ⫽15% film at ␪ ⫽90° derived from Fig. 4 andthe 4 ␲ M z under 3000 Oe at ␪ ⫽90° derived from the FC curve in Fig. 5 aresimultaneously plotted as a function of temperature.

decreases. Figure 6 shows the temperature dependence of the
4 ␲ M z derived from a FC curve in Fig. 5. In the same figure,the amount of the shift of the uniform mode signal for v⫽15% at ␪ ⫽90° (H 0 ⫺3726) is plotted as a function oftemperature 共solid squares兲. The temperature dependence ofthe 4 ␲ M z is successful in qualitatively reproducing a shift of
the resonance field H 0 . This allows us to point out that the ␮of the film above v m depends on the temperature at a given
magnetic field and microwave frequency.
IV. CONCLUSIONSFMR in diluted Fe nanogranular films with low volume
fractions of Fe ( v ) has been studied in detail as a function of
the v , the temperature, and the angle between an appliedmagnetic field and the film plane. The results of v ⫽5 and
15% films prepared by a co-sputtering method were presented. A clear resonance signal corresponding to the FMR
uniform mode 共the Kittel mode兲 was observed in both films.
The two films showed completely different angular and temperature dependence of the resonance field. The uniform
mode signal of the v ⫽5% film was not affected by either theangle or the temperature of the film. On the other hand, thesignal of the v ⫽15% film was found to strongly depend on
the both these parameters. Even though the v ⫽15% is far
below the v value of the structural percolation threshold( v p ⫽50– 60%), this dependence can be explained by the
Kittel equations for ferromagnetic disks, indicating that afilm with v ⫽15% is beyond the magnetic percolation threshold v m and the ferromagnetic Fe nanoparticles in the film aremagnetically coupled. The results suggest that a difference inv , the angle, and the temperature strongly affect the FMR
conditions of diluted ferromagnetic-metal nanogranularfilms, i.e., these factors affect the permeability ␮ of films
under a given magnetic field and microwave frequency. In
addition, the lower field side of the resonance signal with v⫽15% film was deformed probably due to unsaturation of
the magnetization of the film. The unsaturation of the magnetization can be prevented by using a high magnetic field, inother words, in a high frequency FMR study above 10 GHz.
The present study enables us to suggest that the v , angle,
temperature, and operation frequency should be carefully selected in order to realize LHMs using diluted ferromagneticmetal nanogranular films.
ACKNOWLEDGMENTS

The authors would like to acknowledge K. Toshikiyo, H.
Yashiro, K. Katsumata, K. Takeuchi, and S. Ushioda for contributing a valuable discussion of this work.
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