Magnetic properties of Fe-based nanoparticle assembly

Article abstract of DOI:10.1016/S0304-8853(02)01011-9

The magnetic properties of an assembly of very small Fe nanoparticles with an average diameter of the order of 3-5 nm are studied both experimentally and theoretically. The particles are dispersed in a polyethylene matrix with mass concentration 5%. The stray magnetic field of the samples with sizes 1 × 1 × 0.2 mm is measured by means of scanning SQUID microscope at 77 K as a function of external magnetic field. The presence of a weak remanent magnetization indicates a magnetic ordering in the samples studied at rather high temperatures. A distribution of the particle volumes or partial agglomeration of the particles within the assembly is suggested to be responsible for this unexpected behavior.

Full text of DOI:10.1016/S0304-8853(02)01011-9

Journal of Magnetism and Magnetic Materials 258–259 (2003) 54–56
Magnetic properties of Fe-based nanoparticle assembly
a,
S. Gudoshnikov *, B. Liubimov , L. Matveets , M. Ranchinski , N. Usov ,
a
a
a
a,d
b
b
c
S. Gubin , G. Yurkov , O. Snigirev , I. Volkov
c
a
Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, RAS (IZMIRAN), 142190 Troitsk,
Moscow region, Russia
N.S. Kurnakov Institute of General and Inorganic Chemistry RAS (IGIC), Leninski prospect, 31, Moscow 117907, Russia
b
c
Department of Physics, Moscow State University, Moscow 119899 GSP, Russia
d
Institute for Innovation and Fusion Research, 142190 Troitsk, Moscow region, Russia
Abstract
The magnetic properties of an assembly of very small Fe nanoparticles with an average diameter of the order of
–5 nm are studied both experimentally and theoretically. The particles are dispersed in a polyethylene matrix with mass
3
concentration 5%. The stray magnetic field of the samples with sizes 1 ꢀ 1 ꢀ 0.2 mm is measured by means of scanning
SQUID microscope at 77 K as a function of external magnetic field. The presence of a weak remanent magnetization
indicates a magnetic ordering in the samples studied at rather high temperatures. A distribution of the particle volumes
or partial agglomeration of the particles within the assembly is suggested to be responsible for this unexpected behavior.
r 2002 Elsevier Science B.V. All rights reserved.
Keywords: Superparamagnetism; Nanoparticles; Remanent magnetization
Magnetic properties of nanometer scale particles are
promising for various important technological applica-
tions [1]. In the present paper the magnetic behavior of
an assembly of Fe nanoparticles with an average
diameter of the order of 3–5 nm is studied both
experimentally and theoretically. The particles are
dispersed in polyethylene matrix with mass concentra-
tion 5%. To obtain very small Fe nanoparticles, a
field measurement. The cryostat is placed inside of two
m-metal shields with remanent magnetic field less than
0.1 mT. An external magnetic field is produced by the
Helmholtz coils situated inside of the shields. Small-
2
sized SQUID with an effective area of 800 mm and
1
/2
magnetic field sensitivity of about 100 pT/Hz
at
frequencies higher than 100 Hz was used as a sensor.
The SQUID measures a normal component of the stray
magnetic field of a sample at a distance of a few tens of
micrometers away from the sample surface.
5
decomposition of Fe(CO) is used in the polyethylene–
oil solution within the argon atmosphere at a tempera-
ture T¼ 2501C: For the magnetic measurement a sample
Fig. 1a shows a two-dimensional distribution of the
normal component of the magnetic induction measured
in a weak (less than 100 nT) residual magnetic field of
the shield at a distance h ¼ 150 mm above the sample
surface. The magnetic image clearly shows the magnetic
poles of different signs located at opposite edges of the
sample. The value of the z-component of magnetic
induction, Bz; varies within the range 73 mT. Maximal
value of Bz corresponds to the sample edges, as shown in
Fig. 1b, where the result of measurement along the
central line in Fig. 1a is presented. One can see that the
magnetic image and the distribution of the magnetic
is prepared as
a thin square platelet with size
Lx ¼ 0:1 cm and thickness Lz ¼ 0:02 cm. A contour of
the sample is shown by dashed line in the magnetic
images presented in Figs. 1 and 2.
The scanning SQUID microscope [2], in which a high-
temperature superconductor (HTS) DC SQUID and a
sample are cooled in a cryostat at the liquid nitrogen
temperature, T ¼ 77 K, was used for stray magnetic
*Corresponding author. Fax: +7-095-334-2401.
E-mail address: gudosh@izmiran.rssi.ru (S. Gudoshnikov).
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 1 0 1 1 - 9

S. Gudoshnikov et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 54–56
55
the maximal value of the stray magnetic field as
Hz;maxE2/MS ln½ðh þ LzÞ=hꢁ; where /MS is the aver-
age platelet magnetization and h5Lx is the elevation of
the point of the field measurement with respect to the
sample surface. Taking into account the experimental
2
2
value, Hz;maxE3 ꢀ 10 Oe, and using the values
2
2
22
Lz ¼ 2 ꢀ 10 cm and h ¼ 1:5 ꢀ 10 cm, one can esti-
mate the average platelet magnetization as
22
3
/
MS ¼ 2 ꢀ 10 emu/cm . Bearing in mind that the
mass concentration of the metal particles is only 5%,
the volume fraction of the metal within the platelet is
given by
4
3
0:05rP
0:95rFe þ 0:05rP
3
¼ 9 ꢀ 10ꢂ3
:
pR nFe ¼
Here R is the average particle radius, nFe is the
3
nanoparticle concentration, rFe ¼ 7:88 g/cm
and
3
r ¼ 1:4 g/cm are the densities of metal and polyethy-
P
lene matrix, respectively. Therefore, the average magne-
tization of the metal itself can be calculated as
3
3
/
MFeS ¼ 3/MS=4pR nFeE2 emu/cm .
At first glance, the estimated value of average
magnetization is very small with respect to the satura-
tion magnetization of pure Fe at the liquid nitrogen
3
temperature, Msð77 KÞEMsð0 KÞ ¼ 1740 emu/cm [3].
Fig. 1. (a) Grey-scale SSM image of the sample in residual
magnetic field of a magnetic shield (100 nT). (b) Single trace
along the central line shown in (a).
induction shown in Figs. 1a and b, respectively, corre-
spond to a sample more or less uniformly magnetized
along the square side.
Fig. 2a shows the magnetic image of the sample
obtained at the same distance, h ¼ 150 mm, from the
sample surface, but for the case when the sample was
previously magnetized perpendicular to its surface in a
strong magnetic field of a permanent magnet. A
distribution of the z-component of magnetic induction
measured across the middle part of the sample is shown
in Fig. 2b. One can see in Figs. 2a and b that the
magnetic field distribution corresponds to the sample
magnetized perpendicular to its surface. It should be
noted also that the magnetic images shown in Figs. 1
and 2 were stable and reproducible after application of
3
external magnetic field 71.2 ꢀ 10 A/m parallel to the
sample surface.
For theoretical interpretation of the experimental data
obtained, one should take into account that the
distribution of the perpendicular component of the
stray magnetic field shown in Fig. 1b is typical for
the middle plane, y ¼ 0; of a thin square platelet
uniformly magnetized along the square side. The
maximal value, Hz;max; of this magnetization component
corresponds to the platelet edge, x ¼ Lx=2: For a
platelet with the thickness Lz5Lx; one can calculate
Fig. 2. (a) The same as in Fig. 1a, but for the sample
magnetized perpendicular to its surface in a strong magnetic
field of a permanent magnet. (b) Single trace along the central
line shown in (a).

56
S. Gudoshnikov et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 54–56
On the other hand, one should take into account that
due to very small average radius of the nanoparticles,
R ¼ 2:5 nm, they should be in a superparamagetic state
even at liquid nitrogen temperature. Actually, the
relaxation time for spherical Fe nanoparticles can be
estimated by means of the relation [4]:
to explain the experimental data is to suppose certain
agglomeration of the particles within the assembly. Also,
the enhanced value of the effective anisotropy constant
of the particles related with our technological process
can be responsible for the increase in the relaxation time
of the assembly. Thus, further experiments are necessary
to study the experimental situation in detail.
ꢀ
ꢁ
1
t ¼ exp
f0
KV=4
kBT
;
In conclusion, it is shown that the scanning SQUID
microscope is a useful tool to study the properties of
nanoparticle assembly with a very small value of the
stray magnetic field. The weak remanent magnetization
is measured for the Fe-based nanoparticle assembly with
an average diameter of the order of 5 nm at T ¼ 77 K.
Possible reasons for this unexpected behavior are
discussed.
where K is the anisotropy constant, V is the particle
volume and kB is Boltzmann’s constant. The pre-
9
ꢂ1
exponential factor, f0; is of the order of 10 s , the
factor 1 in the exponent is due to cubic anisotropy of Fe
4
5
3
particles. Using the values K ¼ 5:8 ꢀ 10 erg/cm at
T ¼ 77 K [3], one can obtain the numerical relation for
the relaxation time t ¼ 10 exp(0.057R ) s, where R is
the particle radius in nm. Then, it is easy to see that for
R ¼ 7 nm the relaxation time tE0:3 s, whereas it
ꢂ9
3
This work was supported by means of ISTC Grant
No. 1991.
9
increases dramatically, tE10 s, for a particle with
slightly higher radius, R ¼ 9 nm. On the other hand,
the relaxation time turns out to be negligibly small,
tE2 ꢀ 10ꢂ9 s, for R ¼ 2:5 nm. One can see, therefore,
References
that for the particle assembly with average diameter
R ¼ 2:5 nm, practically all particles should be in the
superparamagnetic state even at the liquid nitrogen
temperature, the remanent assembly magneti-
[
[
1] R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 339.
2] S.A. Gudoshnikov, L.V. Matveets, K.A. Andreev, et al.,
Appl. Supercond. 5 (1998) 313.
[
[
3] C. Kittel, Introduction to Solid State Physics, Wiley, New
York, 1963.
zation being strictly zero. The surprising result,
3
/
assumes that at least 0.1% of the particles of the given
MFeSE2 emu/cm , can be explained, however, if one
4] A. Aharoni, in: J.L. Dormann, D. Fiorani (Eds.), Magnetic
Properties of Fine Particles, North-Holland, Amsterdam,
1992, pp. 3–11.
assembly have the radius R > 8 nm. Another possibility