Uniform magnetic excitations in NiO nanoparticles

Article abstract of DOI:10.1016/j.physb.2006.05.234

A sample of isolated disc shaped NiO nanoparticles was studied at the RITA-II triple axis spectrometer at SINQ (PSI) using the newly implemented multi-analyser blade imaging mode. The particles were 13 nm in diameter and had a thickness of about 2.5 nm. A non-dispersive spin excitation was observed at the antiferromagnetic (frac(1, 2) frac(1, 2) frac(1, 2)) reflection at a scattering vector of κ = 1.30 A?^{- 1}, at an energy of 0.51 ± 0.02 meV. This is shown to be due to uniform magnetic excitations in the nanoparticles.

Full text of DOI:10.1016/j.physb.2006.05.234

ARTICLE IN PRESS
Physica B 385–386 (2006) 398–400
www.elsevier.com/locate/physb
Uniform magnetic excitations in NiO nanoparticles
Ã
C.R.H. Bahla,b, ,1, L. Theil Kuhna, K. Lefmanna, P.-A. Lindgarda, S. Mørupb
˚
aMaterials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark
bDepartment of Physics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Abstract
A sample of isolated disc shaped NiO nanoparticles was studied at the RITA-II triple axis spectrometer at SINQ (PSI) using the newly
implemented multi-analyser blade imaging mode. The particles were 13 nm in diameter and had a thickness of about 2.5 nm. A non-
1 1 1
dispersive spin excitation was observed at the antiferromagnetic ð2 2 2Þ reflection at a scattering vector of k ¼ 1:30 Aꢀ1, at an energy of
˚
0:51 ꢁ 0:02 meV. This is shown to be due to uniform magnetic excitations in the nanoparticles.
r 2006 Elsevier B.V. All rights reserved.
PACS: 75.75.+a; 75.50.Ee; 78.70.Nx
Keywords: Nanomagnetism; Uniform magnetic excitations; Uncompensated spins
1. Introduction
where the spins within the particle coherently reverse
between the magnetic easy axes.
Antiferromagnetism was first observed by neutron
scattering in the antiferromagnets MnO and NiO [1].
In bulk NiO the spins were found to be stacked in
alternating layers perpendicular to the (1 1 1) direction and
Early theoretical work on perfect uniaxial two-sublattice
bulk antiferromagnets in zero applied field, with an
exchange field, HE, and an anisotropy field, HA, predicted
the presence of two degenerate resonance modes, i.e., q ¼ 0
spin waves with precession energies given at low tempera-
tures by Ref. [3]
1 1 1
an antiferromagnetic ð2 2 2Þ reflection was observed at
ꢀ1
˚
k ¼ 1:30 A
.
In antiferromagnetic nanoparticles the spin dynamics
deviates from that observed in bulk. The spin wave
spectrum will be quantised, due to the finite size of the
particles. q ¼ 0 spin waves are thermally activated, and
are the dominant excitations in nanoparticles [2]. In the
NiO nanoparticles presented here, there is a large gap
ðꢂ20 meVÞ to the first qa0 spin wave. Further thermal
excitation may induce superparamagnetic relaxation,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ ¼ _o ¼ gmB ð2HE þ HAÞHA,
(1)
where g is the g-factor and mB is the Bohr magneton.
The anisotropy of bulk NiO is dominated by an ‘‘out of
plane’’ term confining the spins to the (1 1 1) planes, and a
significantly weaker ‘‘in plane’’ term aligning the spins
to a certain direction within that plane. This anisotropy
structure splits the two resonance modes into one low
energy mode with an anisotropy field purely from the
‘‘in plane’’ anisotropy term, and one with a higher
energy having an anisotropy field from both the ‘‘in plane’’
and ‘‘out of plane’’ anisotropy terms [4]. Hutchings
and Samuelsen measured the spin wave gap of the low
energy mode in bulk NiO at 78 K, finding a value of 1:0 ꢁ
0:5 meV [5]. Using the quoted value of the exchange
field, HE ¼ 987 T, this gives an anisotropy field of
HA ¼ 0:038þꢀ00::002479 T.
Ã
Corresponding author. Risø National Laboratory, Frederiksborgvej
399, DK-4000 Roskilde, Denmark. Tel.: +45 4677 5491;
fax: +45 4677 5758.
E-mail address: christian.bahl@risoe.dk (C.R.H. Bahl).
1This work was supported by the Danish Natural Sciences Council
through the Danish Neutron Scattering Centre (DANSCATT). CRHB
has been supported by the Danish Technical Research Council. The
experimental work was performed at the SINQ neutron source at the Paul
Scherrer Institut (PSI). We thank Lis Lilleballe for preparation of the
sample.
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2006.05.234

ARTICLE IN PRESS
C.R.H. Bahl et al. / Physica B 385–386 (2006) 398–400
399
In nanoparticles the level splittings of the uniform
excitations are given by Eq. (1) [6]. The anisotropy
structure of nanoscale NiO has not previously been
reported. However, in nanoscale hematite (a-Fe2O3), as
in bulk, the anisotropy has a strong ‘‘out of plane’’ and a
much weaker ‘‘in plane’’ component [7]. It would seem
likely that this is also the case for NiO. Indeed, a high
energy resonance mode has been observed in nanoparticles
of NiO [8] by far infra-red absorption spectroscopy and we
shall show evidence of a low energy resonance mode,
measured by inelastic neutron scattering.
2. Results
Isolated NiO nanoparticles were prepared by heating
chemically precipitated Ni(OH)2 for 3 h at 300 ꢃC. The
sample was subsequently ball-milled, suspended in water
and coated with phosphate, to avoid contact between the
particles, before being freeze dried. The particles have been
studied by transmission electron microscopy and X-ray
diffraction. They were found to be disc shaped with a
thickness of about 2.5 nm and a diameter of about 13 nm.
Inelastic neutron scattering was performed at the RITA-
II triple axis spectrometer at SINQ (PSI). The sample was
measured at 200 K, as the inelastic intensity was large at
this temperature. Energy scans were measured centred
ꢀ1
˚
Fig. 1. Energy scans of the antiferromagnetic reflection at k ¼ 1:30 A ðꢃÞ
and
a
background scan combined from scans at k ¼ 1:00 and
ꢀ1
˚
1:60 A ð’Þ. In all the scans the signals from each of the seven analyser
blades have been added. The data was measured at 200 s/point, except in
the range ꢁ0:2 meV, where it was 50 s/point.
1.2
-4.5
1
-4.0
1 1 1
around the antiferromagnetic ð2 2 2Þ reflection at a scattering
vector of k ¼ 1:30 Aꢀ1. The final energy was 5.0 meV and a
˚
0.8
-3.5
Be filter was placed between the sample and the analyser.
To establish the instrumental resolution and asymmetry
induced by the filter, two energy scans wꢀer1e measured at
0.6
-3
˚
background values of k ¼ 1:00 and 1:60 A and averaged
0.4
to one background scan.
The RITA-II spectrometer was run in the newly
implemented multi-blade analyser imaging mode as de-
scribed in Ref. [9]. The seven analyser blades are situated at
slightly different scattering angles (about 1ꢃ apart), each
scattering neutrons into different channels of a collimator,
situated in front of a position sensitive detector. Due to the
small size of the particles the scattering reflections are very
broad in k. Thus an energy ꢀsc1an of the full antiferromag-
-2.5
0.2
1
1.1 1.2 1.3 1.4 1.5 1.6
κ [Å-1]
Fig. 2. Colour ðk; ꢀÞ-map showing the signal from uniform magnetic
ꢀ1
˚
excitations at k ¼ 1:30 A and ꢀ0 ¼ 0:51 meV. The map is constructed
from five adjacent energy scans, each measuring with seven analyser
blades.
˚
netic reflection at k ¼ 1:30 A can be measured with good
statistics by adding the data normalised to the scattering
efficiency of the analyser blades in each of the seven
channels. This is presented in Fig. 1 along with the
background scan added in the same way. Alternatively the
data in each channel can be plotted separately giving a
ðk; ꢀÞ map. Five such scans adjacent to each other have
been used to create the ðk; ꢀÞ map covering k ¼ 0:92 ꢀ
spectrum of these, as expected, has no dispersion. The first
qa0 level is far beyond the energy range of the data.
The corresponding inelastic neutron signal from hema-
tite nanoparticles has previously been successfully fitted
with a damped harmonic oscillator model [6]. This model is
a convolution of the resolution function, consisting of a
Gaussian and a broad Lorentzian, and terms describing
the Bragg peak, the incoherent elastic background, a
quasielastic signal from superparamagnetic relaxation and
finally the damped harmonic oscillator term describing the
inelastic signal
ꢀ1
˚
1:68 A shown in Fig. 2.
3. Discussion
It is seen in Fig. 2 that there is a localised inelastic signal
at the antiferromagnetic reflection at k ¼ 1:30 Aꢀ1. This is
2gꢀ20
˚
IðꢀÞ / DðꢀÞ
.
(2)
2
ðꢀ2 ꢀ ꢀ20Þ þ 4g2ꢀ2
due to the uniform excitations and shows that the energy

ARTICLE IN PRESS
C.R.H. Bahl et al. / Physica B 385–386 (2006) 398–400
400
Here DðꢀÞ is the detailed balance factor, g is the HWHM of
the inelastic peaks and ꢁꢀ0 are the centre positions of these.
Applying this model to the data presented in Fig. 1, the
parameters of the inelastic signal have been determined.
We find values of ꢀ0 ¼ 0:51 ꢁ 0:02 meV and g ¼ 0:42ꢁ
0:09 meV. Although the measurement was performed at
200 K, this is still well below the reported Neel temperature
of 460 K [10]. Assuming the bulk value of the exchange
field, the anisotropy field is calculated from Eq. (1) yielding
a value of HA ¼ 0:0098 ꢁ 0:0008 T.
4. Conclusion
The new seven blade analyser imaging mode of the
RITA-II spectrometer has been used to study non-
dispersive uniform magnetic excitations in disc-shaped
NiO nanoparticles. An estimate of the ‘‘in plane’’
anisotropy field within the nanoparticles is given taking
into account the uncompensated magnetic moment of the
particles.
Although NiO has a similar anisotropy structure to
hematite we do not observe the dramatic increase of
anisotropy in nanoparticles compared to bulk which has
previously been observed in hematite [13]. However, the
‘‘in plane’’ anisotropy of bulk hematite is extremely small
giving HA ꢄ 0:001 T compared to HA ꢄ 0:026 T in hema-
tite nanoparticles of a similar size as the present NiO
particles. We observe comparable values of the ‘‘in plane’’
anisotropy in bulk and nanoscale NiO. This may be due to
the bulk value being larger than in hematite.
However, due to the small size of nanoparticles, there
will be a number of uncompensated spins on one of the
sublattices and thus the particles may be considered as
being weakly ferrimagnetic. This uncompensated moment
in NiO nanoparticles has been observed in numerous
papers, e.g., Ref. [11]. The surplus of spins on one
sublattice will change the precession frequency of the
resonance mode, splitting it into two modes. Assuming
uniaxial anisotropy the energies of these are given by
Ref. [3]
2
References
HE DS
4
_o ¼ gm
ꢁ
2
ꢁ
B
S
[1] C.G. Shull, W.A. Strauser, E.O. Wollan, Phys. Rev. 83 (1951) 333.
[2] S. Mørup, B.R. Hansen, Phys. Rev. B 72 (2005) 24418.
[3] C. Kittel, Phys. Rev. 82 (1951) 565.
3
5
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ
ꢁ
2 þ HEHA
þ ð2HE þ HAÞHA
.
HE DS
DS
S
þ
˚
[4] P.-A. Lindgard, A. Kowalska, P. Laut, J. Phys. Chem. Solids 28
(1967) 1357.
2
S
[5] M.T. Hutchings, E.J. Samuelsen, Phys. Rev. B 6 (1972) 3447.
[6] M.F. Hansen, F. Bødker, S. Mørup, K. Lefmann, K.N. Clausen,
ð3Þ
P.-A. Lindga
M.F. Hansen, F. Bødker, S. Mørup, K. Lefmann, K.N. Clausen,
P.-A. Lindgard, J. Magn. Magn. Mater. 221 (2000) 10;
S.N. Klausen, K. Lefmann, P.-A. Lindgard, K.N. Clausen, M.F.
˚
rd, Phys. Rev. Lett. 79 (1997) 4910;
Here DS=S is the fraction of uncompensated spins relative
to the number of spins in one sublattice. In a similar sample
of NiO nanoparticles the uncompensated moment has been
measured by high-field Mossbauer spectroscopy and
magnetometry to be 0.6% [12]. Assuming that we are
˚
˚
Hansen, F. Bødker, S. Mørup, M. Telling, J. Magn. Magn. Mater.
266 (2003) 68.
[7] S.N. Klausen, K. Lefmann, P.-A. Lindgard, L. Theil Kuhn,
˚
measuring the mode with the lowest energy, o , Eq. (3)
ꢀ
C.R.H. Bahl, C. Frandsen, S. Mørup, B. Roessli, N. Cavadini,
C. Niedermayer, Phys. Rev. B 70 (2004) 214411.
gives HA ¼ 0:023 T and thus a splitting between the two
modes of Do ¼ o ꢀ o ¼ 0:68 meV. As we do not know
þ
ꢀ
[8] V.V. Pishko, S.L. Gnatcheko, V.V. Tsapenko, R.H. Kodama,
S.A. Makhlouf, J. Appl. Phys. 93 (2003) 7382.
the error on DS=S we cannot calculate the error on HA.
Due to the decrease of scattering cross-section with
increasing energy transfer, it is likely that we observe
[9] C.R.H. Bahl, P. Andersen, S.N. Klausen, K. Lefmann, Nucl. Instr.
and Meth. B 226 (2004) 667;
C.R.H. Bahl, K. Lefmann, A.B. Abrahamsen, H.M. Rønnow,
F. Saxild, T.B.S. Jensen, L. Udby, N.H. Andersen, N.B. Christensen,
H.S. Jakobsen, T. Larsen, P.S. Hafliger, S. Streule, Ch. Niedermayer,
Nucl. Instr. and Meth. B 246 (2006) 452.
the o mode as the o mode is found at a higher energy,
ꢀ
with much less intensity. Furthermore, the tails of the
þ
o
peak may obscure the signal from the o mode as g is
ꢀ
þ
comparable to Do.
˚
[10] S.N. Klausen, P.-A. Lindgard, F. Bødker, S. Mørup, Phys. Stat. Sol.
(A) 189 (2002) 1039.
Assuming the bulk value of the exchange field may be an
overestimate as the many spins at the surface of a particle
will have broken bonds. However, a reasonably smaller
value of the exchange field would only give a slight increase
of the anisotropy field.
[11] J.T. Richardson, D.I. Yiagas, B. Turk, K. Forster, M.V. Twigg,
J. Appl. Phys. 70 (1991) 6977.
[12] C.R.H. Bahl, M.F. Hansen, T. Pedersen, S. Saadi, K.H. Nielsen,
B. Lebech, S. Mørup J. Phys.: Condens. Matter. 18 (2006) 4161.
[13] F. Bødker, S. Mørup, Europhys. Lett. 52 (2000) 217.