Magnetic properties of ultrafine-grained cobalt samples obtained from consolidated nanopowders

Article abstract of DOI:10.1002/pssa.201026496

Co powders having nominal average particle size of 50 and 240 nm were synthesized using a polyol method and then consolidated by hot isostatic pressing (HIP) or the emerging spark plasma sintering (SPS) compaction processes. Bulk polycrystalline aggregates were obtained, having average grain sizes of about 200 and 300 nm, respectively. It is found that both nanoparticles and consolidated samples exhibit a soft ferromagnetic behavior. The magnetization reversal likely occurs by nucleation/propagation process. However, a curling process can be involved in the magnetization reversal for the smaller particles. The dynamic measurements provide for the consolidated samples magnetic parameters corresponding to bulk cobalt with vanishing anisotropy. The contribution of the intergranular region is found to be negligible. We can infer that the used consolidation routes insure a good magnetic interfacial contact between the particles.

Full text of DOI:10.1002/pssa.201026496

Phys. Status Solidi A 208, No. 8, 1942–1949 (2011) / DOI 10.1002/pssa.201026496
a
p s s
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applications and materials science
Magnetic properties of
ultrafine-grained cobalt samples
obtained from consolidated nanopowders
1
,
1
2
1
1
1
*
´
F. Fellah , S. M. Cherif , K. Bouziane , F. Schoenstein , N. Jouini , and G. Dirras
1
´
´
LSPM (CNRS-UPR 3407), Universite Paris 13, 99 av. J.B. Clement, 93430 Villetaneuse, France
2 Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khodh 123, Sultanate of Oman
Received 16 August 2010, revised 5 March 2011, accepted 11 March 2011
Published online 1 April 2011
Keywords cobalt, inelastic light scattering, magnetic properties, nanopowders
* Corresponding author: e-mail cherif@univ-paris13.fr, Phone: þ33 1 49 40 34 73, Fax: þ33 1 49 40 39 38
Co powders having nominal average particle size of 50 and nucleation/propagation process. However, a curling process
240 nm were synthesized using a polyol method and then can be involved in the magnetization reversal for the smaller
consolidated by hot isostatic pressing (HIP) or the emerging particles. The dynamic measurements provide for the con-
spark plasma sintering (SPS) compaction processes. Bulk solidated samples magnetic parameters corresponding to bulk
polycrystalline aggregates were obtained, having average grain cobalt with vanishing anisotropy. The contribution of the
sizes of about 200 and 300 nm, respectively. It is found that both intergranular region is found to be negligible. We can infer that
nanoparticles and consolidated samples exhibit a soft ferro- the used consolidation routes insure a good magnetic interfacial
magnetic behavior. The magnetization reversal likely occurs by contact between the particles.
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction With the reduction of the grain size, amorphous materials [9, 10] mainly dealing with the static
materials properties are enhanced in many fields of physics. behavior of magnetization. The study of the microstructure–
It is now established that the morphology, size of the property relationship in soft magnetic nanocrystalline Fe-
crystallites and the intercrystallite interactions greatly based materials pointed out the key role of the magneto-
influence various properties in nanostructured material [1, 2]. crystalline and exchange interaction [11]; the resulting
Two strategies to elaborate nanostructured materials are magnetic behavior is well described with the random
usually used and are refered to as ‘‘top down’’ and ‘‘bottom anisotropy model (RAM) [12] initially proposed by Alben
up.’’ The first one consists on reducing grains size by et al. [13]. The basic mechanism for the soft magnetic
introducing deformation in a bulk with techniques of so- behavior is that the local magnetocrystalline anisotropies are
called severe plastic deformation (SPD) [3, 4]. The second randomly averaged out for grain sizes smaller than the
one consists of elaborating a dense material by aggregation ferromagnetic exchange length, with the consequence that
of atoms such as electrodeposition [5] or by compacting the coercive field Hc decreases with decreasing the grain size
nanoparticles using powder metallurgy (PM) techniques.
D. For amorphous materials or for nanocrystalline materials
The magnetic response of a material is highly influenced (up to D ¼ 100 nm), a D6 dependence of Hc is observed [11].
by its microstructure in addition to its shape and size. These The nanocrystalline materials fill in the gap between
factors depend on the processing route [6]. The elaboration amorphous and conventional polycrystalline materials that
of bulk nanostructured metal via a bottom-up strategy exhibit large grain size, for which Hc follows a 1/D
combining sol-gel method and consolidation by hot isostatic dependence [11]. The RAM has also been successfully
pressing (HIP) [7] or the emerging spark plasma sintering applied to nanostructured transition metals [14, 15] and
(SPS) [8] has proved recently to be a promising approach in coarse-grained polycrystalline alloys [16]. The 1/D behavior
order to obtain ultrafine-grained materials showing specific of the coercive field is usually explained by domain-wall
interesting properties. Some interesting papers report studies pinning at grain boundaries. For large grain size and for bulk
of magnetic properties of powdered and consolidated soft magnetic materials, a magnetization reversal taking place
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Original
Paper
Phys. Status Solidi A 208, No. 8 (2011)
1943
through a process of nucleation of small reversed domains temperature of 500 8C and a pressure of 200 MPa for 2 h. The
(usually on inhomogeneities or defects) and a subsequent studied samples are finally prepared in the form of thin
propagation of magnetic domain walls is rather reported plates.
[17]. The magnetic properties may also be affected by local
The crystalline phase assemblies present in the pow-
structural features in the grain boundaries [18, 19]. On the dered and in the compacted materials were determined by
other hand, the exchange coupling between the grains also X-ray powder diffraction [X-ray diffraction (XRD)]
´
˚
depends on the magnetic nature of the intergranular region, using CoKa1 radiation whose wavelength is 1.78896 A.
as observed in multiphase systems [11].
Microstructural investigations of the as-prepared powders
In this work, we mainly report on the study of both the and of as-consolidated specimens were conducted on a JEOL
static and dynamic magnetic properties of synthesized Co 2011-EFTEM transmission electron microscope, operated at
nanoparticles and the corresponding ultrafine-grained aggre- 200 kV. The grain sizes of these materials were determined
gates, with sizes lying in an intermediate range between from TEM micrographs by measuring and averaging the
nanocrystalline and microcrystalline materials, namely diameters of more than 150 grains. The magnetization of the
between 200 and 300 nm, obtained by the nonconventional consolidated samples was measured with a DMS 1660 VSM
consolidation SPS and HIP techniques. The first objective is in a magnetic field up to 13.5 kOe applied in-plane
to verify the variation of magnetic properties, if any, upon (longitudinal configuration) and out-of-plane (polar con-
consolidation of Co nanoparticles and to point out the role of figuration). The VSM was calibrated using pure nickel
the intergranular region. The elaboration processes, the (Ms ¼ 54.9 emu/g). The dynamic properties of the consoli-
structural and morphological properties are briefly presented dated films were studied by means of the BLS technique that
and commented on. Details are presented elsewhere [20, 21]. constitutes a powerful tool to investigate the magnetic
The hysteresis loops for the Co nanoparticles were obtained properties of magnetic films [23, 24]. In a BLS experiment, a
using a magnetic balance of the Faraday type. Vibrating beam of Arþ laser light operated on a single mode of the
sample magnetometry (VSM) and Brillouin light scattering 514.5 nm line, is used as a probe to reveal spin waves that are
(BLS) spectroscopy techniques have been used in order to naturally present in the medium under investigation in the
investigate, respectively, the static and dynamic magnetic 3–300 GHz spectral frequency range. A 300-mW p-polar-
behavior of the Co consolidated materials.
ized light was focused on the surface of the sample and the
scattered light was analyzed by means of a Sandercok-type
´
2 Samples and experimental tools Co nanoparti- 3 þ 3 pass tandem Fabry–Perot interferometer. In the present
cles have been synthesized by the polyol method using work, we used the backscattering geometry so that the value
nucleant agent [22]. Depending on the nature and the of the wave vector of the spin waves probed is fixed
concentration of the nucleant agent, two cobalt particle experimentally to the value k ¼ (4p/l)sinu, where l denotes
average sizes were obtained: 50 and 240 nm. The exper- the wavelength in air of the laser light and u the angle of
imental procedure is as follows: first, ionic salts, cobalt (II) incidence. Moreover, the excited spin waves are studied
acetate tetrahydrate (0.02 and 0.08 mol/L, respectively), versus the amplitude of the in-plane applied magnetic field
sodium hydroxide (0.05 and 0.2 mol/L, respectively) and up to 5 kOe.
K2PtCl4 (0.08 mmol/L), and AgNO3 (0.04 mmol Lꢀ1) were
dissolved in 1.2-propanediol. Then the solution was heated
up at boiling point (186 8C) for 6 h under mechanical stirring
3 Results and discussion
3.1 Structure and morphology For simplicity, the
and distillation. After cooling to room temperature, Co consolidated samples were labeled according to the initial
nanoparticles were separated from the supernatant by size of particles and the compression method used, namely
centrifugation and washed with ethanol and acetone. SPS50, SPS240, and HIP240 (see Table 1).
Finally, dense nanostructured materials were obtained using
Figure 1 shows typical XRD patterns corresponding to
SPS (model 515S of Syntex society) and HIP techniques. The the 50-nm powder (a) and SPS50 consolidated sample (b).
SPS sintering was carried out under a pressure of about The quantitative analysis of the crystalline phases showed
50 MPa and at a temperature of 500 8C for 150 s at the that the 50-nm powder XRD pattern exhibits mainly
sintering temperature. HIP sintering was processed at a (ꢁ100%) a face-centered cubic (fcc) structure while a
Table 1 Grain size: D, saturation magnetization Ms, remanent magnetization Mr, squareness S, and coercive field: Hc, measured on
nanoparticles and ultrafine grains consolidated samples.
samples
D (nm)
Ms (emu/g)
Mr (emu/g)
S ¼ Mr/Ms
Hc (Oe)
50-nm particles
240-nm particles
SPS50
SPS240
HIP240
145
165
165
165
165
8
4
5
21
25
0.055
0.024
0.03
0.13
0.15
100
50
40
70
235
280
310
100
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F. Fellah et al.: Magnetic properties of ultrafine-grained cobalt samples
fcc
hcp
(b)
(a)
50
60
70
80
90
100
Angle 2θ (degree) / (Co K )
α1
Figure 1 XRD spectra of 50 nm Co powders (a) and SPS50 con-
solidated sample (b).
hexagonal close-packed (hcp) structured phase (ꢁ15%) is
also observed for the 240-nm particles (not shown). After
compaction we notice an increase of the hcp structured
phase (until 35%) as observed on Fig. 1b. Figure 2 shows the
TEM microstructures of the 50-nm powder (a) and the
corresponding size distribution of the particles (b).
Figure 2 TEM photomicrographs of 50-nm Co powders (a) and
corresponding size-distribution histogram (b).
One can observe that the powder consists of spherical
particles with a narrow size distribution. For the correspond-
ing consolidated sample (Fig. 3a), the average grain size D
is larger, namely D ¼ 235 nm (Fig. 3b). For the investigated instance, see Fig. 3a) composed of an intricate mixture of
consolidated samples, D scales in the range of 200–300 nm: fcc, hcp structures, and nanotwins. More details can be found
235, 280 and 310 nm for the SPS50, SPS240, and HIP240, in Ref. [20]. It is possible that these thin microstructures, of
respectively (Table 1). It is noticed here that the grain growth less than 10 nm thickness, might induce a local preferential
strongly depends on both the initial particle size and the direction of the magnetocrystalline anisotropy axis within
processing route. For the SPS processing the grain sizes in each grain, thus influencing magnetic properties.
the bulk samples are about 340 and 16% for the 50 and 240-
nm powders, respectively. For the HIP processing of the 240-
nm powder the grain size is about 22%, i.e., 4% higher than
observed for the SPS counterpart. Nevertheless, in this case,
3.2 Static magnetic measurements
3.2.1 Nanoparticles Figure 4 displays hysteresis
the temperature, the pressure and time are important loops, magnetization M versus applied field H, at RT for
parameters. More generally, grain growth during sintering the 50- and 240-nm size Co particles. The related values of
happens due to motion of atoms across a grain boundary. coercive field Hc and of squareness S, defined as the ratio of
Convex surfaces have a higher chemical potential than the remanent magnetization Mr to the saturation magnetiza-
concave surfaces, therefore grain boundaries will move tion Ms, are reported in Table 1. The coarser particles exhibit
toward their center of curvature. This is the situation of a weaker Hc (ꢁ50 Oe) than the smaller ones (ꢁ100 Oe) and a
relatively smaller particles that are characterized by a higher higher Ms (165 vs. 145 emu/g) typical of bulk characteristics
radius of curvature and then a larger grains growth is [26]. Surface oxidation or, as previously observed, residual
expected. The relative densities measured by the solvent molecules adsorbed on the surface [27, 28] could
Archimedes method are 91.4, 74.5, and 91.3% for the explain the observed reduction of Ms for the small particles
SPS50, SPS240, and HIP240 samples, respectively. Indeed, relative to the bulk value. Note that the in-plane Hc values are
all compacted materials are still porous. This difficulty to sensitively higher than those reported for thick cobalt films
obtain fully dense materials starting from nanopowder is (few Oe) [29]. On the other hand, the enhancement of the
frequently reported in literature [25]. As shown by the TEM coercivity for the smaller nanoparticles is in agreement with
micrographs the core of each individual grain exhibits a the results reported for Ni nanoparticles [30] and those of
highly faulted nanoscaled lamellar microstructure (for Leslie-Peleckly and Rieke [31] linking the maximum of Hc
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Phys. Status Solidi A 208, No. 8 (2011)
1945
The mechanisms responsible for the magnetization
reversal can correspond to coherent rotation, curling or
domain-wall motion. In the case of a spherical nanoparticle
of diameter D, Aharoni has shown that the process of
magnetization reversal by coherent rotation is ensured for
up to a diameter such that D < dc ¼ 7.21L, L being the
exchange length given by (A/2pMs2)1/2; with A the exchange
stiffness constant [32]. Namely, using the cobalt material
parameters determined from our BLS measurements as
discussed in Section 3.3 (A ¼ 1.8 ꢂ 10ꢀ6 erg/cm and
4pMs ¼ 17.6 kOe, i.e., 165 emu/g), one finds L ꢁ 4 nm, in
good agreement with the literature [33]. We can conclude
that the homogeneous rotation is then operative up to
approximately a particle diameter of about 30 nm. Since the
diameters of our particles are above the critical size dc for
coherent rotation, it is most likely that reversal occurs by
curling or nucleation followed by propagation of domain
walls. The curling process is effective if the diameter D is
larger than L but lower than the width of a Bloch wall
D ¼ (A/K)1/2, where K is the magnetic in-plane anisotropy
constant. Its order of magnitude for cobalt is usually about
105 erg/cm3, one then obtains a value D ꢁ 50 nm. Thus, this
process can be involved in the magnetization reversal for the
50-nm size particles. In the case of the coarser particles,
multidomains may form and the magnetization reversal may
be determined by the domain-wall motion. This behavior is
in agreement with the phase diagram for small magnetic
spheres reported by Skomski et al. [34]. It is also noticed that
for Fe nanoparticles, transition from coherent to incoherent
mode reversal was observed around at dc ¼ 20 nm [35]; one
consequence is then the lowering of Hc in comparison with
that expected from coherent rotation model.
The low values of S, 0.055 and 0.024 for the 50 and 240-
nm particles, respectively, illustrate their soft magnetic
behavior. Lower saturation magnetization (55–100 emu/g)
and higher coercive fields (up to 460 Oe) were reported for
Co particles of sizes lying between 8 and 200 nm,
synthesized by a sol–gel technique [36] while fcc Co
microparticles and a mixture of fcc–hcp Co microparticles
[37], exhibited similar coercive fields and squareness values
to those obtained in our study. The results obtained on our
50-nm Co particles are comparable to those obtained, at low
temperature (3 K), on 7-nm hcp Co nanoparticles (Ms ¼
145 emu/g and Hc ¼ 130 Oe) [37]. However, a lower
saturation field Hs ¼ 1 kOe and a higher squareness
S ¼ 0.45 were reported. Indeed, the magnetic behavior
depends on different parameters such as synthesis technique,
temperature, particle size, and crystalline structure.
Figure 3 SPS50 consolidated sample (a) and corresponding size
distribution histogram (b).
50 nm particles
240 nm particles
150
100
50
0
-50
-100
-150
-15
-10
-5
0
5
10
15
H (kOe)
Figure 4 (online colour at: www.pss-a.com) Hysteresis loops of
240-nm (*) and 50-nm (&) cobalt nanopowders obtained at room
temperature (T ¼ 300 K).
value to the critical diameter dc. It is worth noting that for
3.2.2 Consolidated samples When the magnetic
both Co particles the magnetization saturation is achieved field is applied normal to the sample plane (Fig. 5), the
with a high applied field Hs ꢁ 5 kOe, which approximately magnetization loops look like those we can expect from the
corresponds to the demagnetizing field of a single supposed usual scheme of a coherent rotation in the hard axis-
spherical particle: 4pMs/3, with 4pMs ¼ 17.6 kOe (i.e., geometry. The effective anisotropy field is defined as
165 emu/g) the saturation magnetization of bulk cobalt. Heff ¼ 4pMeff ¼ 4pMs ꢀ Ha?, where Ha? is the perpendicu-
This emphasizes the role of the dipolar interactions between lar anisotropy field and 4pMs is the magnetization at
particles.
saturation. However, because of the grain sizes, the coherent
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F. Fellah et al.: Magnetic properties of ultrafine-grained cobalt samples
200
150
100
50
HIP240 shifted by - 30 emu/g
SPS240
SPS50 shifted by + 30 emu/g
200
150
100
50
HIP240 shifted by -30 emu/g
SPS240
SPS50 shifted by +30 emu/g
0
0
150
-50
-100
-150
100
50
-50
0
-100
-150
-200
-50
-100
-150
-15
-10
-5
0
5
10
15
-15 -10 -5
0
5
10 15
H (kOe)
H (kOe)
-3
-2
-1
0
1
2
3
Figure 5 (online colour at: www.pss-a.com) Hysteresis loops of
Co consolidated samples with the applied field H perpendicular to
H (kOe)
the sample plane obtained at room temperature (T ¼ 300 K). The Figure 6 (online colour at: www.pss-a.com) Hysteresis loops of
loops corresponding to HIP240 and SPS50 have been shifted by the consolidated samples obtained at room temperature (T ¼ 300 K)
ꢀ30 emu/g and þ30 emu/g, respectively.
with the applied field H parallel to the sample plane displayed in the
[ꢀ2.5 kOe; þ2.5 kOe] field range. The loops corresponding to
HIP240 and SPS50 have been shifted by ꢀ30 emu/g and
þ30 emu/g, respectively. The insert shows the global hysteresis
loops.
rotation is certainly not the mechanism of magnetization
reversal, but, in order to just obtain an order of magnitude of
the magnetic anisotropy, one can assume a coherent reversal
scheme. In this case, the slope at the origin [Ms/
(4pMs ꢀ Ha?)] equal to 0.085 for HIP240, 0.089 for
SPS50, and 0.093 for SPS240, leads to this information. characterized by relatively large S values; the largest value,
Such a rough estimation gives the following values of Ha?
1.1, 1.67, and 2.2 kOe for the HIP240, SPS50, and SPS240 value close to 0.75 was also reported for cobalt films
samples, respectively. obtained by chemical vapor deposition [38]. Our measured
:
0.754, was observed for a 195-nm thick sample [28] while a
These values are, as expected, weak compared to the values of Hc are, however, still higher than those reported for
saturation magnetization. In fact, the crystal structure is amorphous materials or for nanocrystalline materials (up to
dominated by the fcc cubic phase; the contribution of the hcp D ¼ 100 nm). In the latter case, a D6 dependence of Hc was
phase being relatively modest, as revealed by XRD observed [11] and successfully described within the RAM
measurements. On the other hand, pole figures (not shown) model [12]. The nanocrystalline materials fill in the gap
revealed that the samples exhibit no marked fiber texture; between amorphous and conventional polycrystalline
those elaborated by SPS exhibiting a very small 00.2 texture. materials that exhibit large grain size, for which Hc follows
From the observed crystallographic features of the samples a 1/D dependence [11]. This relation is generally ascribed to
one then expects weak perpendicular anisotropy whose the pinning of domain walls at interfaces or grain boundaries.
origin is probably related to magnetocrystalline and
The observed magnetization behavior in our samples
magnetoelastic contributions. It is, however, interesting to seems to rule out pinning at the grain boundaries as the origin
note that the samples obtained by SPS consolidation actually for the coercivity (the so-called ‘‘pinning coercivity’’ [39]).
exhibit larger anisotropy values than the one consolidated Moreover, small grains may favor nucleation of reverse
under HIP conditions. In the first case, the nanoparticles are domains. This will tend to lower the coercivity. Based on this
submitted to a uniaxial pressure that may favor anisotropy, correlation between values of coercive fields and grain size,
while the effect is less marked in the second case where the we believe that in our case the coercivity is mainly associated
pressure is isostatic.
with nucleation of reverse domains rather than with pinning
Figure 6 displays the hysteresis curves obtained for the of domain walls. Note that for bulk magnetic materials, a
consolidated samples in the longitudinal configuration in an magnetization reversal taking place through a process of
applied field up to 2.5 kOe. The insert shows the cycles for nucleation of small reversed domains (usually on inhomo-
the complete field range. The coercive field Hc is found to be geneities or defects) and a subsequent propagation of
of same order of magnitude as for nanoparticles and to magnetic domain walls is rather reported [17]. Thus, the
increase with the grain size, while S decreases (see Table 1). lamellar microstructure within grains, combined to the
The M–H loops show a linear-like decrease of the dipolar interactions, probably also contribute to the fast
magnetization. Consequently, the values of Hc and of the reversal mechanism observed and may induce a supple-
squareness S are weak, characteristic of a soft magnetic mentary local anisotropy within each grain. The exact role of
behavior. For comparison, thick cobalt samples obtained by the observed thin microstructures needs to be clearly
thermal deposition on silicon or glass substrate were evidenced for further investigations.
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Original
Paper
Phys. Status Solidi A 208, No. 8 (2011)
1947
75
45
40
35
30
25
20
15
10
5
stokes
anti-stokes
DE
50
DE
B
B
B
DE from simulation
B from simulation
DE
25
0
DE from eq. (1)
B from eq. (2)
0
0
1
2
3
4
5
6
H (kOe)
-80
-40
0
40
80
Figure 8 Variation of the DE and B modes frequency f versus
the applied magnetic field H for SPS240 sample with an angle
of incidence u ¼ 458 (i.e., k ¼ 1.73 ꢂ 105 cmꢀ1). Symbols are the
experimental data; the continuous lines are best fits obtained using
Eq. (1) for the DE mode and (2) for the B mode with a saturation
magnetization 4pMs ¼ 17.6 kOe and a gyromagnetic factor:
g ¼ 1.9 ꢂ 107 Hz/Oe. The dashed lines are the fits obtained from
the complete simulation of the BLS spectra (see text).
Frequency shiꢀ (GHz)
Figure 7 Typical Brillouin spectrum obtained from the sample
SPS240 with an angle of incidence q ¼ 458 (i.e., k ¼
1.73 ꢂ 105 cmꢀ1) and an applied field H ¼ 3.5 kOe. DE and B set
for the surface-like-mode and bulk-like-mode spin waves lines,
respectively. Continuous line: calculated spectrum.
3.3 Dynamic magnetic measurements Figure 7 for the DE and B modes, respectively, taking g fixed at its
shows a typical Brillouin spectrum obtained in the case of the value for bulk cobalt: g ¼ 1.95 ꢂ 107 Hz/Oe, i.e., g ¼ 2.16,
SPS240 sample with an angle of incidence u ¼ 458 and an and surprisingly by adjusting the saturation magnetization to
applied magnetic field H ¼ 3.5 kOe. It exhibits two magnetic its value for cobalt bulk material 4pMs ¼ 17.6 kOe, indicat-
lines in both the Stokes (left side) and anti-Stokes (right ing a vanishing magnetic anisotropy in the consolidated
side), namely Damon–Eshbach (DE) and B, respectively. films. Note that the bulk B mode exhibits a less marked
The large Stokes/anti-Stokes intensity ratio of the DE line agreement using Eq. (2), that provides the frequency of the
identifies it as a DE surface-mode-like spin wave [40]. On the uniform mode. The bulk mode is sensitive to the magnetic
other hand, the broad line B exhibits the behavior of a bulk- exchange (neglected here) and then Eq. (2) represents a
like-mode line, regrouping a high number of standing spin rough approximation of its frequency. In order to provide a
waves (SSW), which is very sensitive to the magnetic better agreement between experiment and theory, a complete
exchange within the material.
numerical simulation of the spectra, taking into account the
For a magnetic material of large thickness, in the dipolar magnetic exchange, has been achieved [41]. This allows the
approximation (absence of exchange) and neglecting fitting of the spectra with appropriate parameters, namely, in
anisotropy, the expression for the DE spin waves frequencies our case, g coefficient (2.16), the magnetization at saturation
f approximates to the value [40]:
4pMs (17.6 kOe) and the exchange stiffness constant A
(1.8 ꢂ 10ꢀ6 erg/cm i.e., Dech ¼ 2.6 ꢂ 10ꢀ9 Oe cm2 with
Dech ¼ MsA/2 being the spin wave exchange constant),
which corresponds to the values reported for polycrystalline
thick cobalt films [29, 42]. For comparison, the Dech value
derived from our BLS measurements is 32% smaller than
that obtained from a neutron-scattering study of single-
crystal cobalt [43]. The polycrystalline character of our
samples combined with the fact that inelastic light
measurements only provide an average value for Dech can
explain such a discrepancy. It is indeed noteworthy that BLS
measurements on single-crystalline Co films [44] have
2pf
¼ ðH þ 2pMsÞ;
(1)
g
where Ms is the saturation magnetization, g the gyromag-
netic factor, and H is the applied magnetic field. In the limit
of a null wave vector, the surface-wave frequency decreases
and reaches the frequency of the bulk mode:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2pf
¼
HðH þ 4pMsÞ:
(2)
g
The study of the frequency dependence of the DE and B produced results closer to those obtained by the neutron-
modes on the magnetic field strength has been carried out for scattering study of Ref. [43]; the difference being about 13%.
all the consolidated materials. Experimental and calculated
Figure 8 shows the experimental frequency variations
curves are reported in Fig. 8 for the representative case of the versus the applied field compared to our best fits (dashed
SPS240 sample. The best fits of the calculated curves to the lines), obtained using the above-determined values of the
experimental points have been obtained from Eqs. (1) and (2) magnetic parameters.
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a
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F. Fellah et al.: Magnetic properties of ultrafine-grained cobalt samples
The fitted value of the saturation magnetization confirms the obtained values of the magnetization at saturation and of
the assumption of a negligible magnetic anisotropy. On the the exchange stiffness constant.
other hand, it indicates that the contribution of a nonferro-
Acknowledgements This work was conducted in the
framework of an interdisciplinary research program at LPMTM.
K. B. is very grateful to the University of Paris 13 for the stay as a
visiting Professor.
magnetic phase, if it exists in the grain-boundaries region, is
negligible. This is also confirmed by the value of the
exchange stiffness constant A that we have determined that is
a strong indication that the magnetic ‘‘contact’’ between the
particles after the consolidation process is not significantly
altered, eventually, by the presence of a secondary crystal-
line phase (antiferromagnetic CoO phase, cobalt oxide,
amorphous phase, etc.) at the grain boundaries, which could
lower A. A similar feature has been recently reported on Co
polycrystalline nanomaterials with an average grain size of
10 nm where no reduction in exchange stiffness has been
observed despite the presence of a high volume of grain
boundaries [45]. It is interesting to note that XRD
measurements showed that the sample consolidated by HIP
presents a more or less noticeable amount of cobalt oxide
CoO (6%), whereas those consolidated by SPS are pure
cobalt phases. This can be due to the difference in the
elaboration protocol [21]. However, no significant variation
of the fitted magnetic parameters was noticed in the case of
the HIP240 sample. The CoO contribution remains negli-
gible. As pointed out in the introduction, indeed the
exchange coupling between the grains depends on the
magnetic nature of the intergranular region, as observed in
multiphase systems [11]. Studies of collective spin waves in
Co100–xCrx alloy films by means of BLS at room temperature
[46, 47] reported a strong reduction of the magnetic
exchange constant when the Cr content increases, a value
of Dech ¼ 0.75 ꢂ 10ꢀ9 erg cm2 has been obtained for
example for x ¼ 15.7 at%, almost four times lower than
the bulk value [46] while a reduction by an order of
magnitude was found for Cr content reaching 50 at% [47].
The segregation of nonmagnetic Cr along grain boundaries
was discussed as the possible origin of this drastic reduction.
Thus, we can infer that the consolidation routes used in this
work insure a good magnetic interfacial contact between the
particles.
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