JOURNAL OF APPLIED PHYSICS
VOLUME 94, NUMBER 10
15 NOVEMBER 2003
Ferromagnetic resonance experiments in an obliquely deposited
FeCo–Al2 O3 film system
N. A. Lesnik
Institute of Magnetism, NASU, 36b Vernadsky strase, 03142 Kiev, Ukraine
C. J. Oates, G. M. Smith, and P. C. Riedia)
School of Physics and Astronomy, University of St. Andrews, Fife, KY 169SS, Scotland, United Kingdom
G. N. Kakazei
Institute of Magnetism, NASU, 36b Vernadsky str., 03142 Kiev, Ukraine
and Department of Physics, Ohio State University, 174 West 18th Avenue, Columbus, Ohio 43210
A. F. Kravets
Institute of Magnetism, NASU, 36b Vernadsky strase, 03142 Kiev, Ukraine
P. E. Wigen
Department of Physics, Ohio State University, 174 West 18th Avenue, Columbus, Ohio 43210
共Received 26 March 2003; accepted 10 August 2003兲
Granular cermet films (Fe50Co50) x – (Al2 O3 ) 1⫺x fabricated using the electron-beam coevaporation
technique at oblique incidence of FeCo and alumina atom fluxes have been found to exhibit both
oblique and in-plane uniaxial magnetic anisotropy. This anisotropy first appears just below the
percolation threshold due to a magnetic coupling of particles taking place at a certain stage of their
growth and coalescence. The FeCo content x varied from 0.07 to 0.49. A simple model of the film
microstructure is presented based on the results of magnetization measurements and ferromagnetic
resonance at intermediate 共9.4 GHz兲 and high 共94 GHz兲 frequencies. At 94 GHz the concentration
dependence of the effective anisotropy field follows the solid solution law, since then the magnetic
field is sufficient to magnetize the films close to saturation. The 9.4 GHz data points deviate from
the solid solution line below the percolation threshold due to both modification of the resonance
fields by intergranular interactions in nonsaturated films and the reduction of the average
magnetization of granules, comparing to the saturation magnetization, at room temperature.
Different mechanisms of line broadening observed at frequencies used in experiments are also
discussed. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1615295兴
I. INTRODUCTION
Preparation and characterization of advanced recording
media such as granular and patterned films is now one of the
most active areas of research in magnetism 共see, e.g., Ref. 1兲.
Among the most important parameters of the material are the
values of anisotropy and saturation fields. Recently an interest in oblique deposition of films from one source has been
renewed as this technique allows the control of the film
microstructure2 and anisotropy.3
Granular cermet films 共GCF兲 constitute an insulator matrix containing dispersed magnetic metallic nanoparticles.
Being embedded in an alumina matrix, where they are immiscible and unwettable, magnetic granules have regular
shapes. They do not interact via an exchange mechanism. In
GCFs the particles interactions are provided by dipolar
forces.4 Below the structural/electric percolation threshold,
GCFs exhibit a magnetoresistance 共MR兲 effect 关e.g., 3.6% in
Fe–SiO2 , 5 4% to 5% in Fe–Al2 O3 , 6 8% in Fe–Al–O 共Ref.
7兲 and Refs. therein兴 at room temperature. The largest MR
effect is usually observed at magnetic fields of about 1 to 2 T
and above these values.
a兲
Electronic mail: [email protected]
0021-8979/2003/94(10)/6631/8/$20.00
6631
The sensing properties and the coercivity of granular
material are strongly influenced by the film microstructure
and magnetic local structure via the effect of sizes, shapes,
interactions among granules, and homogeneity of their distribution in the matrix. It is always important to know what
type of structural inhomogeneity is present.
Ferromagnetic resonance 共FMR兲 probes local film regions differing from each other in the magnetization and/or
anisotropy. They reveal themselves as separate signals in the
FMR spectrum. In the case of wide distribution of granule
sizes in the single ensemble, the appearance of a single resonance line is expected as the system can be characterized by
the average of both the magnetization and anisotropy field. If
the film has a ‘‘patch-like’’ structure, two or more FMR
peaks should occur. This means that local film regions, each
representing a separate ensemble, are characterized by different concentrations 共i.e., volume contents of magnetic material兲, corresponding average granule volumes, and magnetization. The structural origin of additional FMR signals, if
any, can be established at the high frequency and field ranges
where magnetic interactions among particles are greatly suppressed and will not produce unexpected resonance peaks in
the observed spectra. High field FMR investigation at hundreds of GHz gives an adequate picture of a homogeneous,
© 2003 American Institute of Physics
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
6632
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
as well as inhomogeneous, precession of the magnetization
that is either an average in the patches of the granular fraction or saturated in continuous film regions.
FMR is a unique tool for the study of magnetic
anisotropy.8 –10 In the case of well-separated particles the
magnetocrystalline and shape anisotropies of the granules
themselves are only present. However, it is likely that below
the electric 共or structural兲 percolation threshold the uniaxial
film anisotropy may occur due to dipole-dipole coupling of
magnetic moments of evolved particles, if their growth is
oriented. This expectation is associated with a conclusion in
Ref. 11 that just below a structural percolation, interacting
granules, which are grown and stay close enough to each
other, are sensed as a ferromagnetic 共FM兲 continuum by dipolar forces. Due to film anisotropy, the high saturation field
that at present is a great deficiency of GCF for technical
applications should be reduced if the film is magnetized
along the easy axis. From this point of view the growth anisotropy known to occur in continuous films evaporated from
a single source at oblique incidence is worthy of attention. It
was studied long ago in divers crystalline films12 and its
origin was attributed to a film columnar structure. But we did
not find in the literature the information concerning the anisotropy of obliquely deposited double-component systems,
like GCF, although such films are often fabricated by a coevaporation technique resulting in an oblique deposition of
film components from different sources. A lack of publications on this subject can obviously account for the fact that
the oblique deposition effects are usually considered to be
undesirable and are excluded by deposition on a rotating
substrate. However, this may not be the case. As we reported
in Ref. 13, Co–Cu granular films fabricated by a coevaporation at oblique incidence possessed large in-plane anisotropy
providing a reduction in the saturation field when it was
applied along the easy axis.
This work is an extension of our previous studies on
granular films FeCo–Al2 O3 共Refs. 14 and 15兲 with the large
MR effect and specific magnetic and X-band resonance behavior indicating a formation of a patch-like film structure.
In the current work the previous data are verified using
higher frequency FMR techniques, at which the films are
closer to magnetic saturation. Using the data obtained by
FMR at 9.4 GHz and a superconducting quantum interference device 共SQUID兲, evidence will be given for the formation of oblique and in-plane uniaxial anisotropies. Peculiarities of the percolation process as well as a possible cause of
the local regions with increased FeCo content, occurring in
films deposited at oblique incidence, will be discussed.
II. FILM PREPARATION AND CHARACTERIZATION
A series of (Fe50 at. % Co50 at. % ) x – (Al2 O3 ) 1⫺x granular
films having a thickness of about 400 nm have been prepared
at room temperature in one run in a vacuum of 10⫺6 Torr
using the electron-beam coevaporation technique. The deposition rate was 0.1 to 0.2 nm/s. The films used in the experiments were deposited as stripes on to glass substrates as
shown in Fig. 1. Iron-cobalt and alumina were evaporated
from two sources at the fluxes inclination angles changing
Lesnik et al.
FIG. 1. Deposition scheme. Concentration gradient is along the x direction
共a兲. The flux inclination angles are shown for the samples with the corresponding FeCo contents indicated by points 共open and closed circles兲 共b兲.
from the film normal to 45° 关Figs. 1共a兲 and 1共b兲兴. The nominal volume content of the ferromagnetic component 共x兲 varied from 0.07 to 0.49 along the length of the stripe. The
individual FMR samples were small enough that the flux
angles were essentially unchanged within each one. A set of
separate samples, each indicated by a small open or closed
circle in the plots in Fig. 1共b兲, was obtained by subsequently
cutting the glass substrates. Each of the ten substrates was
divided into ten samples. The variation of the concentration x
across the individual samples was less than 0.01.
The nominal elemental contents of the films were determined using the energy disperse x-ray analysis 共EDAX兲.16
The magnetoresistance was maximal 共7.4% at 0.8 T兲 below
the anomalously low electrical percolation threshold x p
⬃0.18 estimated from the conductivity measurements.16,17
The magnetic measurements were made in a SQUID magnetometer. Room temperature X-band FMR spectra and angular
dependencies of the resonance field (H r ) were recorded at
9.4 GHz using a Radiopan electron paramagnetic resonance
共EPR兲 spectrometer. The angular out-of-plane dependencies
of H r were taken varying the angle ␪ from the film normal
␪ ⫽0 to the film plane ␪ ⫽90°. For in-plane dependencies of
H r the angle ␸ was changed between 0° and 360°. The values of the perpendicular resonance field were verified using a
Brucker EPR spectrometer having a field range sufficient to
measure the resonance of the films at the perpendicular orientation of the dc field. Room temperature spectra at the
perpendicular FMR configuration were recorded at 94.225
GHz using a high field 共HF兲 ESR spectrometer.18
At 9.4 GHz the effective fields (H eff) were calculated by
fitting experimental out-of plane angular dependencies of the
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
6633
resonance field (H r ) to the well-known Kittel’s formula for a
thin film given in the polar coordinates, ␪ m , and ␸ m , of the
magnetization 共M兲 vector:
冉冊
␻
␥
2
⫽ 关 H r cos共 ␪ m ⫺ ␪ 兲 ⫺H eff cos2 ␪ m 兴
⫻ 关 H r cos共 ␪ m ⫺ ␪ 兲 ⫺H eff cos 2 ␪ m 兴 ,
共1兲
where ␻/2␲ is the frequency of the microwave field, and ␥ is
the gyromagnetic ratio.
The angles ␪ m were deduced from the condition for M
equilibrium given as
H sin共 ␪ m ⫺ ␪ 兲 ⫽H eff sin ␪ m cos ␪ m ,
共2兲
where H eff includes all the anisotropy fields H A of uniaxial
perpendicular symmetry, affecting a precession of magnetic
moments. In the general case this field can be expressed as
H eff⫽NM ⫺H A ,
共3兲
where N is the demagnetizing factor.
The fields of the oblique and in-plane anisotropy were
neglected, as they are of one to three orders of magnitude
smaller than the demagnetizing field, as it will be shown in
Sec. IV.
At 94 GHz Kittel’s formula for the perpendicular resonance field (H⬜r ) was used to calculate the effective fields:
H⬜r ⫽H 0 ⫹H eff ,
共4兲
where H 0 ⫽ ␻ / ␥ .
III. SPECTRA AND ANGULAR DEPENDENCIES OF
THE RESONANCE FIELD
Dependencies of absorbed microwave power derivative
versus applied dc field, i.e., resonance spectra, in three representative samples having different FeCo contents 共below,
close to, and above the percolation concentration, x⫽0.13,
0.18, and 0.31, respectively兲 are shown in Fig. 2. The inplane spectra ( ␪ ⫽90°) are plotted in the left panel for the
two orientations of applied field ␸ ⫽0° and 90°. In the
former case the field is applied along a direction of the concentration gradient 关Fig. 1共a兲兴. FMR signals recorded at 9.4
and 94 GHz in the perpendicular FMR configuration are
shown in the right panel in the second and third columns,
respectively.
According to the results of our studies on the considered
system,15 two FMR signals observed over the full range
90°⭓ ␪ ⭓0, come from two local regions in the film differing
in the FeCo content. A difference in the susceptibility 共␹兲 共a
steepness of lines slopes兲 of both regions is clearly seen in
Figs. 2共e兲, 2共f兲, 2共h兲, and 2共i兲, where ␹共1兲 共P1 resonance line兲
is always higher than ␹共2兲 共P2 line兲. This is in agreement
with the above-mentioned conclusion15 concerning concentrations of these regions: x(1)⬎x(2). As will be shown below, at the nominal percolation point and above this point,
the region 1 is structurally continuous while the region 2 is
still granular. The highest ␹ is inherent in a continuous
region.
In-plane spectra, measured at ␸ ⫽0° and 90° 关Figs. 2共a兲,
2共d兲, and 2共g兲兴, generally contain three signals which can be
FIG. 2. FMR spectra recorded at 9.4 and 94.2 GHz in representative films of
varying FeCo content: x⫽0.13 共a兲–共c兲; 0.18 共d兲–共f兲; 0.31 共g兲–共i兲. The inplane FMR spectra are shown at two orientations of the applied field ␸
⫽0°, 90°. Peak positions are indicated by the arrows.
either resolved or overlapped depending on the film concentration and the angle ␸. These peaks are indicated in Fig. 2
and all other figures as P0, P1, and P2. Unlike P1 and P2
being present in the case of perpendicular FMR at both frequencies 共Fig. 2, right panel兲, P0 is not detected.
The P0 in-plane resonance, positioning at zero-field at
9.4 GHz, changes slightly with the angle ␪, depends strongly
on the magnetization history of the film, and disappears near
␪ ⫽0. The line is extended toward a negative field region,
especially at ␸ ⫽0. The contribution of this signal to the
spectra decreases with increasing x. These features allow the
attribution of P0 to the fraction of very small particles, like
metal spray. Note that Fe and Co atoms may have enhanced
magnetic moments due to transition from band 共in metal兲 to
localized d-electrons in oxide, as these particles with the
large surface/volume ratio should mainly consist of the oxidized surface. For instance, we observed19 an enhancement
of the magnetic moments of the Co atoms, located near the
interfaces in FeCo/Al2 O3 discontinuous magnetic–insulator
multilayers 共DMIM兲, due to the formation of CoO. In such
systems discontinuous magnetic layers 共having a thickness
of 1–1.5 nm兲 are separated by continuous insulator spacer
layers.
The peaks P1 and P2 in Fig. 2, left panel, come from the
local regions 1 and 2 having different concentrations.15 Each
of them can be characterized by different anisotropies since
both the FMR signals are sensitive to the direction of the
applied magnetic field. The P2 signal is the strongest, dominating when the field is applied along the x gradient axis
( ␸ ⫽0). For region 1 the easy magnetization direction is
along ␸ ⫽90°, at which P1 dominates. The two signals for
the x⫽0.46 sample are clearly seen in Fig. 3 where the integrated resonance lines are decomposed by a Lorentzian
multipeak fit. There is no uniaxial anisotropy yet in region 2
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
6634
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
FIG. 3. The integrated in-plane FMR spectra 共solid lines兲 in the representative sample with x⫽0.46. A decomposition of the spectra using Lorentzian
multipeak fit is shown by the dashed lines.
FIG. 5. The concentration dependencies of the HF resonance fields of the
signals P1 共circles兲, P2 共squares兲, and S1, S2, S3 共stars兲.
as the FeCo flux inclination angle is low ( ␣ ⫽5°). However,
the P1 behavior demonstrates that this is present in region 1.
The anisotropy in both regions will be discussed in more
detail in Sec. IV.
These two signals are also observed in the angular ␪
dependencies of the resonance fields 关 H r (1) and H r (2) for
P1 and P2, respectively兴 as it is seen in Fig. 4. Experimental
data 共points兲 have been obtained at ␸ ⫽0 共the left slopes of
the curves兲 and at ␸ ⫽90° 共the right sides兲. At low angles ␪
both peaks are resolved 关Figs. 4共a兲 and 4共b兲兴. They are also
resolved if the film having the low x is magnetized in the
plane. In the sample with the higher nominal FeCo content
关Fig. 4共b兲兴 the value of average magnetization in the granular
region 2 has approached the saturation magnetization value
in the continuous region 1. Thus the signals P1 and P2 stay
closer to each other than in films with lower x. They overlap
at 90°⭓ ␪ ⭓20°. At ␸ ⫽0 P2 dominates whereas at ␸ ⫽90°
only P1 is seen. Such a behavior is rather due to the presence
in these regions of the uniaxial in-plane anisotropies with
mutually perpendicular easy axes.
FIG. 4. Angular out-of-plane dependencies of the resonance field in samples
with x⫽0.16 共a兲 and 0.31 共b兲. The plots in 共a兲 and 共b兲 were measured at
␸ ⫽0° and 90°, respectively, that are shown by arrows. The experimental
data are indicated by closed circles for P1 and open squares for P2. Solid
共for P1兲 and dashed 共for P2兲 lines were computed using Kittel’s formulas 共1兲
and 共2兲.
In addition to P1 and P2, one or more peaks S1, S2, and
S3 appear near the film normal at 6°⭓ ␪ ⭓0. They are indicated by arrows in the right panel of Fig. 2. Figure 5 shows
the concentration dependencies of the perpendicular resonance field of the additional peaks together with those of the
peaks P1 and P2, all obtained using HF FMR. The origin of
the S signals is not clear, as the low number of peaks does
not allow for a detailed analysis. But taking into account the
fact of their presence in saturated samples, they cannot be
attributed to granule interactions and should be rather connected with the inhomogeneous precession like a spin-wave
resonance.
IV. ANISOTROPY
Figure 6 shows the angular dependencies of the X-band
FMR fields H r ( ␪ ) and H r ( ␾ ) in a representative film with
x⫽0.24. They demonstrate an evolution of the periodicity of
H r ( ␸ ) from 180° to 360° for the two signals as ␪ decreases
from 90° to 0° 关Fig. 6共a兲兴. A shift of the maximum of H r ( ␪ )
from ␪ ⫽0 at ␸ ⫽90° 关Fig. 6共d兲兴 to ␪ ⬃6° at ␸ ⫽0 关Fig. 6共c兲兴
is also observed. According to Ref. 10, such behavior is typical of samples with a uniaxial oblique anisotropy. The content x⫽0.24 of this film lies within the concentration range
where region 1 is structurally continuous while region 2 is
still granular.15 The easy out-of-plane magnetization directions are parallel in both regions as can be seen in Fig. 6共a兲,
at ␪ ⫽0° and 3° where the curves for P1 and P2 are similar.
An asymmetry of the plots is connected with the slight obliquity of the sample-holder. The maximum value of the oblique
anisotropy field is estimated to be 0.03 T for region 1 and
about three times smaller for region 2. The inclination angle
is ⬃6° for P1 and P2 peaks. It is likely that the oblique
anisotropy occurs in the granular region 2 due to the coupling of evolved granules elongated in the direction of FeCo
flux.
In the film plane the easy axes of the uniaxial anisotropy
in the regions 1 and 2 are perpendicular to each other as seen
in Fig. 6共a兲 at ␪ ⫽90° and ␸ ⫽0°, 180° where the minimum
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
FIG. 6. Angular ␸ and ␪ dependencies of the resonance field 共a兲, 共c兲, 共d兲 and
a variation of the in-plane anisotropy field depending on concentration 共b兲 in
the representative sample with x⫽0.24. In-plane curves 共a兲 were measured
at ␪ ⫽0°, 3°, 20°, and 90°. Out-of-plane dependencies were recorded at ␸
⫽0° 共c兲 and 90° 共d兲; the solid lines represent the fit of the experimental data
共symbols兲 with Kittel’s formulas. In each graph the closed circles and solid
lines and the open squares and dashed lines indicate the P1 and P2 peaks,
respectively.
resonance field H r (2) corresponds to maximum H r (1). P2 is
not seen at ␸ ⫽90° 共the hard direction for this region兲. This
is detected at higher fields, e.g., at ␪ ⫽20°.
Composition dependencies of the in-plane anisotropy
fields H a (1) 共closed circles兲 and H a (2) 共open squares兲 are
presented in Fig. 6共b兲, where the former is shown by negative values as the corresponding easy axis is perpendicular to
the x gradient line. The anisotropy field values were estimated using experimental ␸ dependencies together with
simulated ␪ dependencies of the resonance fields and the
spectra decomposed by Lorentzian multipeak fit 共the representative spectra are shown in Fig. 3兲. The estimated values
of the maximum anisotropy energies (K⬃104 to
105 erg/cm3 ) are not too high.
According to the data in Fig. 6共b兲, the in-plane anisotropy H a (1) occurs at the nominal x⫽0.13 in region 1, being
still granular, and reaches its maximum value at x⫽0.24
共continuous region 1兲. In region 2 关P2 plot in Fig. 6共b兲兴,
H a (2) was detected first at x⫽0.24 where it is a maximum.
Then both the in-plane and oblique anisotropy values decrease with x. This is contrary to a change of the inclination
angle of the alumina flux, which increases with x, but corresponds to a decrease of the FeCo flux angle 关Fig. 1共b兲兴.
Therefore the granule shape and spatial orientation are controlled by the FeCo flux, i.e., the particle growth and coalescence are flux oriented.
The concentration range where the main region 2 possesses the in-plane anisotropy is narrower (0.18⬍x⬍0.39)
than for region 1 (0.13⬍x⬍0.46). At x⫽0.07 and 0.09 only
one line is detected at any angle and the perpendicular resonance field is almost the same as the parallel one. Therefore,
here granules are spherical and noncorrelated. In region 2
this state takes place up to x⫽0.18.
6635
FIG. 7. The concentration dependence of the effective field plotted for the
FMR signals observed at 94 GHz: P1 at nominal x 共closed circles兲, P1 at
estimated x 共crossed circles兲, P2 共open squares兲. The dashed line shows a
solid solution law. Similar dependencies for P1 and P2 at 9.4 GHz are
shown in the inset. The nominal percolation point x p is indicated by the
arrow.
V. EFFECTIVE ANISOTROPY FIELDS
The effective anisotropy field (H eff) was deduced for
each signal by fitting the experimental ␪ dependencies of the
resonance field to Eqs. 共1兲–共4兲 at 9.4 and Eq. 共4兲 at 94 GHz.
In the former case the best fit was obtained for g⫽2.2 for all
films. This is consistent with the results reported in Ref. 20
where measurements of the g-factor, performed in saturated
samples Fe–SiO2, have shown that the value of g is independent of the film concentration.
At 94 GHz the H eff(x) curves are linear for both signals
共Fig. 7兲 unlike similar dependencies plotted for 9.4 GHz
shown in the inset in this figure. The results obtained at 9.4
GHz, are discussed in Ref. 15. In accordance with the
conclusion,15 the FeCo content of region 2 is nearly equal to
the nominal x in each sample 共this is the main region occupying the bulk of the film area兲. Meanwhile region 1 is enriched with FeCo, i.e., x(1)⫽x⫹⌬x. Since above the percolation point x p the composition dependence of H eff(1) is
parallel to the line showing the solid solution law, the additional FeCo amount ⌬x⫽const. The electric percolation in
this region begins earlier and determines the x p value in the
investigated film series. In fact x p ⫽x p (1). Considering the
solid solution line to be an upper limit for x, the true content
of region 1 can be estimated by shifting the P1 plot to higher
concentrations. This curve is shown in Fig. 7 共inset兲 by
crossed circles. A break in the P1 plot should occur at the
magnetic percolation since at room temperature the average
magnetization of the granule fraction differs from the saturation magnetization.11 In region 1 the H eff(x) curve actually
consists of two linear parts, demonstrating either Langevinlike behavior of the average magnetization of superparamagnetic 共SP兲 granules below x p (1) or the variation of saturation
magnetization according to the solid solution law above the
percolation threshold. Using this estimation procedure, the
value of the percolation point in region 1 is found to be
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
6636
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
FIG. 8. The concentration dependencies of the FMR linewidth in the
FeCo–Al2 O3 films magnetized perpendicularly to the film plane at 9.4 共left
panel兲 and 94 GHz 共right panel兲 for the signals: P1 at nominal x 共closed
circles兲, P1 at estimated x 共open circles and dashed lines兲, and P2 共solid
squares兲. The lines are guides to the eye.
x p (1)⬇0.4. This is in agreement with the values 0.4⬍x p
⬍0.7 usually observed in cermet films, e.g., Refs. 20 and 21.
At 94 GHz all films are nearly saturated: there is no
break in the H eff(x) dependence for P1 共Fig. 7, closed
circles兲. The P2 data points 共open squares兲 lie on the solid
solution line and the P1 data fall on this line by using x(1)
⫽x nominal⫹⌬x 共crossed circles兲. The value of ⌬x⬇0.17 is in
good agreement with the value obtained from X-band FMR
measurements.
The appearance of the uniaxial anisotropy at x⫽0.24
共see the previous section兲 in region 2 indicates the concentration at which SP granules are already correlated. In the
next section the concentration dependencies of the linewidth
will support this conclusion.
VI. FMR LINEWIDTH
Figure 8 shows the composition dependence of the linewidth (⌬H⬜ ) measured at the perpendicular configuration in
the film series for both the P1 共closed circles兲 and the P2
共solid squares兲 signals. The data in the left and right panels
were taken at 9.4 and 94 GHz, respectively. At 9.4 GHz ⌬H⬜
peaks at x⫽x m 共1 or 2兲 共Fig. 8, left兲. A mechanism of line
broadening was discussed in Ref. 16 where it is explained by
static fluctuations of random internal fields (H i ) on granules,
reaching a maximum at the concentration x m ⬍x p , at which
interacting granules stay close enough to each other to exhibit ferromagnetic behavior even without direct contact between them. For x⬎x m , H i should mainly fluctuate due to
relatively rare ‘‘holes’’ in the ferromagnetic background,
which are only removed well above the structural 共or electric兲 percolation point x p (1 or 2) where ⌬H⬜ reduces to a
small value for the continuous film.
However, at 94 GHz, the perpendicular linewidth continues to widen with decreasing x. This suggests that inhomogeneous line broadening is due to another mechanism. In
fact, the granule interactions are suppressed by high fields
共about 3–5 T兲. Thus line broadening can be provided by the
distribution of SP granule sizes, magnetocrystalline anisotropy energies, and directions of magnetic moments, as in the
case of FM particles. At very short times (⬃10⫺11 s at 90
GHz兲 it is sufficient to realize rf absorption by SP granules in
the metastable state. In other words, the measurement time is
equal to or shorter than the oscillation period (⬃10⫺11 to
10⫺12 s) of small superparamagnetic granules 共less than 3
nm in diameter兲; hence for HF FMR they are ferromagnetic
at room temperature. For these films the average granule
diameter has been estimated in Ref. 16 to be about 3 nm for
x⬃x p ⫽0.18.
At 9.4 GHz the maxima of P1 and P2 plots in Fig. 8
indicate the magnetic percolation point x m . 16 In region 1
x m (1) is close to nominal x⫽0.18, i.e., x m (1)⬃0.35 as estimated, and x m (2) is also found at about 0.35 in region 2
共Fig. 8, left panel兲. Note that in this region the anisotropy
appears at x⫽0.24 at which the resonance line is broadened
due to granule interactions.
Performing the x estimation procedure for the P1 linewidth curves like for the effective fields of region 1 described above 共Fig. 7兲, an extrapolation of the curves P2 in
Fig. 8, left and right panels, toward higher FeCo contents
was obtained. This demonstrates that region 1 is formed in a
manner similar to that of the main region 2. The value ⌬x
⫽0.17 determined above, was again used.
VII. SQUID DATA ANALYSIS
SQUID data of the film series becomes clear only when
taken together with the picture of the magnetic local structure obtained by FMR. Figure 9 shows the temperature dependencies of the magnetic moments measured in fieldcooled 共FC兲 and zero-field-cooled 共ZFC兲 regimes for films of
different FeCo contents. The upper curves correspond to the
FC regime. ZFC data relate to the lower curves of these
plots. The four curves for each sample shown in Fig. 9 were
obtained at the applied field 共H兲 of 0.001 T 共closed squares兲,
0.002 T 共open squares兲, 0.005 T 共closed triangles兲, and 0.01
T 共open triangles兲. The field was applied perpendicular to the
direction of the x gradient, which is parallel to the anisotropy
easy axis in region 1: H⬜H a (2) 储 H a (1) in each sample in
Figs. 9共a兲–9共c兲 and H 储 H a (2)⬜H a (1) in Fig. 9共d兲. The recorded total signal is a sum of the signals coming from each
region of the sample, namely: 共i兲 the main region 2 having
the largest area, lower x, than in region 1, and consequently
smaller in both the average granules size and magnetization;
共ii兲 the region 1 of larger granules 共or continuous at x
⭓0.18) with the higher susceptibility ␹ (1)⬎ ␹ (2); and 共iii兲
a fraction of the smallest particles yielding the lowest average magnetization.
In region 1 ZFC and FC curves should be identical for
the cases 共a兲–共c兲 as granules have been frozen by the strong
anisotropy field: H a (1)⭓H. The form of the ZFC curves
共a兲–共c兲 is mainly determined by the behavior of M in region
2 as the inherent easy magnetization direction is perpendicular to H. The curve shapes should also depend on the ratio of
the signal intensities I(1)/I(2) in each sample.
An increase of the FC curves with a decrease of the
temperature in the low range and at highest H come from the
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
6637
FIG. 9. The temperature dependencies of magnetic moments measured in FC and ZFC films with x⫽0.13 共a兲;
0.31 共b兲; and 0.24 共c兲 and 共d兲 at different fields: 0.001 T
共closed squares兲; 0.002 T 共open squares兲; 0.005 T
共closed triangles兲; and 0.01 T 共open triangles兲. Applied
field H ⬜H a (2) 共a兲–共c兲, H 储 H a (2) 共d兲.
fraction of the smallest granules revealing themselves as the
P0 peak in FMR spectra. This is slower for increasing x
关Figs. 9共a兲, 9共c兲, and 9共b兲兴 that denotes a reduction of the
fraction amount at the higher FeCo content to be in agreement with FMR data.
A minimum in the ZFC curves in Fig. 9共a兲 is the result
of the superposition of two signals coming from granular
regions of different content, hence different T b 共below this
temperature SP particle oscillations are blocked兲. In this case
there is no in-plane anisotropy in region 2. The M 2 (T) signal
was observed on the strong background of M 1 (T). Qualitatively, these plots are similar to ZFC-FC curves obtained in
Ref. 22 by the Monte Carlo simulation of M (T) dependencies for an assembly of noninteracting granules. In fact the
authors of Ref. 22 assumed the existence of two local regions
having different blocking temperatures T b .
A gap between FC and ZFC curves above T b 关Figs. 9共b兲
and 9共c兲兴 is assumed to be due to the anisotropy. ZFC particles have been frozen at the field H a (2)⬎H and the additional energy (kT col) is needed for a transition to the superparamagnetic state.23 The gap collapses at T col when the
thermal energy kT col is high enough to switch the magnetization into the H direction. If H a (2)⭐H, then T col⭐T b (2)
and the two curves merge in the vicinity of T b . This is the
case for the top curves 共open triangles兲 in Fig. 9. They do not
display any gap and T b (2) can be estimated using these
plots. Thus the fields H a (2)⬍0.01 T in all the samples are in
agreement with the anisotropy values obtained by FMR. The
largest gap occurs at x⫽0.24 and H⫽0.005 T 关Fig. 9共c兲兴. In
this case H and H a (2) values should be nearly equal. Indeed
the in-plane anisotropy field H a (2)⫽0.005 T according to
FMR data. The plot in Fig. 9共d兲 obtained at 0.005 T and
H 储 H a (2) does not show a gap that confirms the abovementioned assumption.
The central parts of the magnetization curves obtained in
SQUID are shown in Fig. 10 for representative samples of
different FeCo content. Apparently the hysteresis loops of
high squareness originate from the region 1 as the field was
applied along its anisotropy easy axis. The high-field edges
of the loops come from the granules in region 2. At x
⫽0.23 关Fig. 10共b兲兴 the double-loop is observed revealing the
presence of two local regions.
Note that a similar film series deposited on polymeric
substrates14 exhibits the same FMR and SQUID behavior as
has been described above for the films deposited on glass
substrates.
SQUID data agree well with the idea of the inhomogeneous film structure consisting of two regions differing in
FeCo contents and each possessing an in-plane anisotropy
with the easy axis directed perpendicular to that of its counterpart.
VIII. CONCLUSIONS
(Fe50Co50) x – (Al2 O3 ) 1⫺x granular films deposited by
electron-beam coevaporation at oblique incidence in a
FIG. 10. The magnetization curves obtained from a SQUID magnetometer
at T⫽300 K in representative samples of different FeCo content. The nominal percolation point x p ⬃0.18.
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
6638
Lesnik et al.
J. Appl. Phys., Vol. 94, No. 10, 15 November 2003
vacuum ⬃10⫺6 Torr are characterized of a patch-like microstructure. They contain local regions of two types revealing
themselves as two signals in FMR spectra and differing in
both concentrations and areas they occupy. Films deposited
at incidence angles more than 5° possess uniaxial oblique
and in-plane anisotropies.
The FMR and SQUID studies show that an evolution of
the film structure depending on the concentration takes place
in three stages as follows: at x⬍0.18 the films present an
array of noncorrelated FeCo granules in the alumina matrix;
at 0.18⬍x⬍0.46 they contain chains of granules which are
elongated in the direction of FeCo atom flux and coupled by
dipolar forces producing the uniaxial anisotropies in the film;
at x⬎0.46 the films are continuous. This evolution scheme
共except of anisotropy occurring兲 is similar to that observed in
DMIM.19
The simplest model of the films microstructure as it
emerged in the course of FMR and SQUID studies is as
follows.
The deposition of films at the oblique incidence onto
unheated substrates at a pressure no less than 10⫺6 Torr provides a slowing down of the surface diffusion and selfshadowing that can lead to the formation of a specific microstructure, such as columnar in crystalline material.12 In
amorphous films 共e.g., CoP兲 oriented chains of elongated
pores were considered to give rise to anisometric structural
elements of the film, like columns.24
In the films under study the columnar-like structure may
be rather inherent in the amorphous matrix because of the
higher content of alumina (0.5⬍Al2 O3 ⬍0.93) while the
shape and orientation of growing particles 共hence the
uniaxial anisotropy兲 is controlled by the FeCo atom flux. In
the alumina matrix such a structure may occur due to the
presence of counterpart atoms evaporated simultaneously
with alumina but at the opposite angles relative to the film
normal. The majority of ferromagnetic atoms are dispersed
in the matrix. They form the main granular region 2. But
some amount of the Fe/Co, together with oxygen atoms, may
occupy void sites occurring due to self-shadowing of alumina molecules. They remain at these sites since the surface
diffusion is reduced under conditions available in our experiment. As a result, a network of parallel chains of FeCo may
divide the matrix onto column-like regions. Alumina columns should be nearly parallel to Al2 O3 incident flux. In
addition, some part of Fe and Co atoms can accumulate near
the column boundaries by diffusion mechanism. Thus region
1 presents a network of similar patches positioned near the
boundaries where the FeCo content is higher. A difference
between FeCo contents in the two regions ⌬x is constant
since the time of deposition determining the diffusion is the
same for all samples. Both the oblique and in-plane anisotropy fields decrease with a decrease of the inclination angle
␣ of FeCo atom flux while the alumina flux is inclined maximally from the film normal and canted columns keep forming. Patches of region 1 are confined by columns’ boundaries
in the plane section. Here the granules are oblate along the X
axis and the anisotropy is present even if ␣ is close to zero.
In the main region 2, which is located in the bulk of the
column, the granules are oblate along the Y axis The latter
provides the corresponding in-plane anisotropy axis, which
is perpendicular to that in region 1. In this case the anisotropy is not observed since ␣ ⫽10°.
According to this structural model a patch-like structure
may be prevented by improving the vacuum and/or the deposition time. This is expected to stop the occurrence of both
the alumina columns and the associated patches with an
FeCo concentration higher than the nominal one.
Cermet films evaporated at oblique incidence in a high
vacuum may provide advantages over conventional GCF. A
presence of the anisotropy while the films are granular
should lead to a decrease in the MR saturation field if the
film is magnetized along the easy axis. The anisotropy can be
controlled by changing the inclination angle of FeCo atoms
flux.
ACKNOWLEDGMENTS
The authors are grateful to Professor J. Walton 共the University of St. Andrews兲, who provided an opportunity for
X-band FMR test measurements. N.A.L. acknowledges the
Royal Society of UK for support of the research via a travel
grant.
1
The Physics of Ultra-High-Density Magnetic Recording, Springer Series
in Surface Sciences, edited by M. L. Plumer, J. van Ek, and D. Weller
共Springer, New York, 2001兲.
2
B. Dick et al., J. Vac. Sci. Technol. B 19, 1813 共2001兲.
3
A. Lisfi et al., Phys. Rev. B 66, 174420 共2002兲.
4
G. N. Kakazei et al., in Processing of Advanced Magnetic Materials, edited by Y. Liu, D. J. Sellmyer, and G. C. Hadjipanayis 共Kluwer Academic
and Tsinghua University Press, in press兲.
5
S. Honda, T. Okada, and M. Nawate, Phys. Rev. B 56, 14 566 共1997兲.
6
Y. H. Huang, J. H. Hsu, and J. W. Chen, IEEE Trans. Magn. 33, 3556
共1997兲.
7
S. Mitani et al., J. Magn. Magn. Mater. 198-199, 179 共1999兲.
8
B. Heinrich et al., J. Appl. Phys. 70, 5769 共1991兲.
9
C. J. Oates et al., J. Appl. Phys. 91, 1417 共2002兲.
10
V. O. Golub, G. N. Kakazei, and N. A. Lesnik, in Frontiers in Magnetism
of Reduced Dimension Systems, NATO ASI Series 3. High Technology,
Vol. 49, edited by V. G. Bar’yakhtar, P. E. Wigen, and N. A. Lesnik
共Kluwer, Dordrecht, 1998兲, pp. 211–216.
11
G. N. Kakazei et al., J. Appl. Phys. 85, 5654 共1999兲.
12
D. O. Smith, J. Appl. Phys. 30, 264 共1959兲; K. Hara, T. Hashimoto, and E.
Tatsumoto, J. Phys. Soc. Jpn. 28, 254 共1970兲; A. G. Lesnik, Induced
Magnetic Anisotropy 共Naukova Dumka, Kiev, 1976兲, pp. 130–138.
13
G. N. Kakazei et al., J. Magn. Magn. Mater. 196–197, 29 共1999兲.
14
A. F. Kravets, N. A. Lesnik, M. Rokhlin, and P. E. Wigen, IEEE Trans.
Magn. 37, 2219 共2001兲.
15
N. A. Lesnik et al., Phys. Status Solidi A 196, 157 共2003兲.
16
V. O. Golub et al., Mater. Sci. Forum 373–376, 197 共2001兲.
17
A. Ya. Vovk et al., J. Appl. Phys. 92, 1 共2002兲.
18
G. M. Smith, J. C. G. Lesurf, R. H. Mitchell, and P. C. Riedi, Rev. Sci.
Instrum. 69, 3924 共1998兲.
19
N. A. Lesnik et al., J. Magn. Magn. Mater. 242–245, 943 共2002兲.
20
A. Butera, J. N. Zhou, and J. A. Barnard, Phys. Rev. B 60, 12 270 共1999兲.
21
S. Sankar, A. E. Berkowitz, and D. J. Smith, Phys. Rev. B 62, 14 273
共2000兲.
22
E. De Biasi, C. A. Ramos, R. D. Zysler, and H. Romero, Phys. Rev. B 65,
144416 共2002兲.
23
R. W. Chantrell et al., Phys. Rev. B 63, 024410 共2000兲.
24
L. S. Palatnik et al., Fiz. Met. Metalloved. 10, 68 共1990兲 关Phys. Met.
Metallogr. 70, 63 共1990兲兴.
Downloaded 23 Jun 2009 to 138.251.105.135. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp