Structure and dynamics of magnetic nanoparticles

Article abstract of DOI:10.1016/S0921-4526(99)01620-8

In this paper we present X-ray and neutron diffraction data illustrating aspects of crystal and magnetic structures of ferromagnetic α-Fe and antiferromagnetic NiO nanoparticles, as well as inelastic neutron scattering studies of the magnetic fluctuations

Full text of DOI:10.1016/S0921-4526(99)01620-8

Physica B 276}278 (2000) 830}832
Structure and dynamics of magnetic nanoparticles
K.N. Clausen!ꢀ*, F. B+dker", M.F. Hansen", L. Theil Kuhn#ꢀ!, K. Lefmann!,
P.-A. Lindgard!, S. M+rup", M. Telling$
!Condensed Matter Physics and Chemistry Department, Ris~ National Laboratory, Frederiksborgrej 399, DK-4000 Roskilde, Denmark
"Department of Physics, Bld. 307, Technical University of Denmark, DK-2800 Lyngby, Denmark
#Lab. of Solid State Phys. and Magn., Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
$Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK
Abstract
In this paper we present X-ray and neutron di!raction data illustrating aspects of crystal and magnetic structures of
ferromagnetic a-Fe and antiferromagnetic NiO nanoparticles, as well as inelastic neutron scattering studies of the
magnetic #uctuations in NiO and in canted antiferromagnetic a-Fe O . In the inelastic case we make use of the fact that
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we can study both the superparamagnetic relaxation and collective magnetic excitations of the whole particle moment at
the antiferromagnetic Bragg positions. ( 2000 Elsevier Science B.V. All rights reserved.
Keywords: Magnetic #uctuations; Magnetic order; Nanoscale objects
vapor [2], and they are covered by a thin layer of 2.0}2.5
nm protective oxide. This method of nanoparticle pro-
1. Introduction
duction is slow, but we have obtained a su$cient amount
of powder to perform X-ray powder di!raction. The
Nanometer-sized magnetic particles often display
properties, which are very di!erent from the bulk proper-
X-ray spectrum (Fig. 1a) shows that the main part of the
ties. This intriguing fact is a challenge both for the basic
nanoparticles is in the BCC form, a-Fe, and the width of
understanding and for the industrial applications of mag-
netic nanoparticles (see, e.g. Ref. [1]). In this paper, we
the peaks corresponds to an average (volume weighted)
particle size of 24$1 nm, but a broader contribution
from a layer consisting of strained iron oxide with spinel
structure is also visible. The magnetic properties of these
particles will later be studied using small-angle neutron
scattering.
present a few examples, showing how X-ray and neutron
scattering can shed light on some of the open questions in
this "eld.
Our NiO nanoparticle sample was produced by an-
2. Structural studies of magnetic nanoparticles
nealing of Ni(OH) for 3 h at 3003C. Transmission
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electron microscopy revealed that the particles were disk-
Metallic nanoparticles will in general oxidize if ex-
posed to oxygen, and it is therefore crucial to protect the
nanoparticles by coating. The a-Fe nanoparticles pre-
sented here are fabricated in a hollow cathode cluster
source from condensation of a super-saturated metal
shaped with a thickness of about 2 nm and an average
diameter of about 13 nm. For comparison, we studied
a sample of lm-sized particles, produced by annealing
a commercial NiO powder for 6 h at 11003C. Fig. 1b
shows the neutron powder di!raction spectra for the
two NiO samples. The sample annealed at 11003C shows
resolution-limited peaks, whereas the sample annealed at
3003C shows peak broadening corresponding to a par-
ticle size of about 5 nm. NiO is an antiferromagnet
(AFM), and the nuclear and magnetic peaks are well
*Corresponding author. Tel.: #45-4677-4704; fax: #45-
4677-4790.
E-mail address: kurt.clausen@risoe.dk (K.N. Clausen)
0921-4526/00/$- see front matter ( 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 2 0 - 8

K.N. Clausen et al. / Physica B 276}278 (2000) 830}832
831
Fig. 2. Results from a neutron time-of-#ight experiment on
hematite at temperatures of 10 K (top) and 295 K (bottom). The
momentum transfer, q is along the vertical axis, while the energy
transfer, e, is along the horizontal axis. The intensity is marked
as a grey-scale code, so that the black (quasielastic) vertical
stripe denotes the largest signal, its light surroundings represents
somewhat lower intensity, the larger grey area means low values,
and the white background is close to zero signal. The arrow
marked `Na shows the position of the "rst nuclear peak, while
the two arrows marked `Ma show the positions of the "rst AFM
peaks.
Fig. 1. (a) X-ray di!raction spectrum of a-Fe nanoparticles at
room temperature. The underlying spikes show the normalised
results of a crystal structure simulation of a-Fe and c-Fe O
(solid lines). (b) Indexed neutron di!raction data on NiO
nanoparticles ("lled circles) and NiO lm-sized particles (open
circles) at 10 K.
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separated. The magnetic peaks are broader than the
nuclear peaks, and correspond to a magnetic correlation
length which is approximately 1 nm shorter than the
particle size. A detailed analysis of the entire powder
pattern is in progress in order to see whether this di!er-
ence in magnetic and structural size is due to magnetic
disorder over the entire particle or to a disordered or
non-magnetic surface layer.
tivated, transverse oscillations around the easy directions
(collective magnetic excitations, CME) [5,6].
Our a-Fe O (hematite) sample was prepared by
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thermal decomposition of Fe(NO ) ) 9H O [7]. Using
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electron microscopy, the nanoparticles were found to be
almost spherical, with an average diameter of about
15 nm. Hematite nanoparticles have a canted AFM
structure at least down to 5 K [7,8]. In a neutron time-
of-#ight experiment at IRIS (ISIS), we were able to map
out the scattering intensity in the (q, e) plane for various
temperatures of this sample, as shown in Fig. 2. At 10 K,
the elastic (mostly incoherent) signal is prominent as
a thick, vertical stripe, and the magnetic Bragg peaks
show up as an increase of this signal at the indicated
positions. At room temperature, the scattering extends
signi"cantly into the inelastic regime; especially around
the AFM re#ections. This is a clear indication of thermal-
ly activated magnetic dynamics, where the two sublatti-
ces #uctuate out of phase [9,8].
3. Magnetic 6uctuations in nanosized particles
The Neel}Brown theory [3,4] considers a single-do-
main ferromagnetic particle, but may be used also for
AFM particles. The (sublattice) magnetisation is sup-
posed to be subject to a uniaxial anisotropy, given by
E "K < sinꢁ h, where h is the angle between the mag-
!
%&&
netisation and the easy axis, K is the e!ective magnetic
%&&
anisotropy constant, and < is the particle volume. Ther-
mal #uctuations may cause the magnetisation direction
to #ip between the two energy minima (superparamag-
netic relaxation) with a characteristic longitudinal relax-
ation time
q"q exp(K </k ¹),
%&&
(1)
ꢃ
Triple-axis neutron measurements on nanoparticles
were "rst performed by Hennion et al. [10]. In Ref. [8],
we presented the "rst nanoparticle data obtained by the
where q (+10\ꢄ}10\ꢅꢁ s) is a characteristic attempt
ꢃ
time. The magnetisation also performs thermally ac-

832
K.N. Clausen et al. / Physica B 276}278 (2000) 830}832
so far triple-axis spectroscopy has only barely resolved
the longitudinal #uctuations in a-Fe O . Recently,
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Casalta et al. [12] used neutron spin-echo spectroscopy
to achieve more than two orders of magnitude better
energy resolution than by the triple-axis method. They
used spin-echo spectroscopy at small scattering angles to
study 2 nm single-domain ferromagnetic a-Fe particles in
an insulating matrix of Al O . They were able to deter-
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mine the temperature- and q-dependence of the super-
paramagnetic relaxation time spanning four orders of
magnitude from 0.01 to 160 ns. At high temperatures, the
relaxation followed the Neel}Brown expression (1), but
below 40 K the relaxation time was modi"ed by inter-
particle interactions.
4. Conclusion
Neutrons can provide essential information about
both the crystal and magnetic structure and of the mag-
netic dynamics of small magnetic particles of nanometer
size. Triple-axis spectroscopy is sensitive to dynamics of
time scales of 10\ꢄ}10\ꢅꢁ s, comparable to q in Eq. (1),
ꢃ
while neutron spin-echo spectroscopy is sensitive to dy-
Fig. 3. Inelastic neutron scattering data of nanoparticles.
(a) Constant-q scan on hematite around the "rst AFM peak,
q"1.37 A\ꢅ and ¹"240 K. The upper solid line shows a "t to
a model with a sum of a Lorentzian central peak and a damped
harmonic oscillator, convoluted with the experimental resolu-
tion [8]. The dashed line shows the damped harmonic oscillator
contribution only. (b). Constant-q scan on NiO around the "rst
AFM peak, q"1.31 A\ꢅ and ¹"295 K. The upper solid line
shows a "t to a model with the sum of one d-function and one
Lorentzian peak convoluted with the experimental resolution,
while the lower line shows the Lorentz contribution only.
namics a few orders of magnitude slower, covering a wide
interval of superparamagnetic relaxation times, q in
Eq. (1). Neutron techniques are thus able to provide
unique information about the magnetic dynamics of
nanoparticles.
Acknowledgements
The work was supported by the Danish Natural
Sciences Research Council and the Danish Technical
Research Council. We appreciate support from the
EU-TMR Access to Large Scale Facilities Programme at
ISIS. LTK thanks the Niels Bohr Institute for use of their
hollow cathode cluster source.
conventional triple-axis method near an AFM re#ection.
Fig. 3a shows a constant-q scan for 15 nm hematite par-
ticles taken at the RITA spectrometer at Ris+ [11]. Clear
`shouldersa are seen on the central quasi-elastic peak,
corresponding to transverse #uctuations (CME) of the
sublattice magnetisation in the nanoparticles; their am-
plitudes increase with temperature [8]. The longitudinal
#uctuations are just visible as a small broadening of the
central peak; the temperature behaviour is in agreement
with the Neel}Brown theory, viz. Eq. (1) [8].
Fig. 3b shows a constant-q scan for NiO nanoparticles
taken at the conventional triple-axis spectrometer TAS7,
Ris+. The NiO data show a much larger broadening of
the inelastic signal, but no obvious `shouldersa. As a pre-
liminary model, we have chosen one resolution limited
central line from the magnetic structure plus one broad
Lorentzian line arising from strongly damped CME. As
for hematite, the amplitude of the broader component
increases with temperature.
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NiO and a-Fe O are both AFM structures, where the
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nuclear and magnetic scattering are well separated, and