The magnetization dynamics of ε-Fe2O3 nanoparticles with an average size of about 9 nm is investigated. From comparison of the hysteresis loops obtained in quasi-static conditions and under pulse fields with amplitudes up to 200 kOe and pulse lengths 8–32 ms, it follows that the effective coercivity increases considerably with the variation rate of the imposed magnetic field. A theoretical explanation of this behavior is proposed. The model takes into account the superparamagnetic effects as well as the fact that magnetic anisotropy of the nanoparticles, along with the bulk term, includes a surface contribution. The latter, being of minor importance for the observed magnetic behavior of 25–100 nm particles, becomes essential when the particle size is below 10 nm. From the experimental data, a reference value of the surface anisotropy of nanodisperse ε-Fe2O3 is established, and evidence is presented to the effect that below 300 K this contribution does not significantly depend on temperature.

1.
E.
Tronc
,
C.
Chaneac
, and
J. P.
Jolivet
, “
Structural and magnetic characterization of ε-Fe2O3
,”
J. Solid State Chem.
139
,
93
104
(
1998
).
2.
M.
Popovici
,
M.
Gich
,
D.
Niznansky
,
A.
Roig
,
C.
Savii
,
L.
Casas
,
E.
Molins
,
K.
Zaveta
,
C.
Enache
,
J.
Sort
,
S.
de Brion
,
G.
Chouteau
, and
J.
Nogués
, “
Optimized synthesis of the elusive ε-Fe2O3 phase via sol-gel chemistry
,”
Chem. Mater.
16
,
5542
5548
(
2004
).
3.
M.
Kurmoo
,
J.-L.
Rehspringer
,
A.
Hutlova
,
C.
D'Orlans
,
S.
Vilminot
,
C.
Estournes
, and
D.
Niznansky
, “
Formation of nanoparticles of ε-Fe2O3 from yttrium iron garnet in a silica matrix: An unusually hard magnet with a Morin-like transition below 150 K
,”
Chem. Mater.
17
,
1106
1114
(
2005
).
4.
E.
Tronc
,
C.
Chaneac
,
J. P.
Jolivet
, and
J. M.
Greneche
, “
Spin collinearity and thermal disorder in ε-Fe2O3
,”
J. Appl. Phys.
98
,
053901
(
2005
).
5.
S.
Sakurai
,
J.
Jin
,
K.
Hashimoto
, and
S.
Ohkoshi
, “
Reorientation phenomenon in a magnetic phase of ε-Fe2O3 nanocrystal
,”
J. Phys. Soc. Japan
74
,
1946
1949
(
2005
).
6.
S.
Sakurai
,
S.
Kuroki
,
H.
Tokoro
,
K.
Hashimoto
, and
S.
Ohkoshi
, “
Synthesis, crystal structure, and magnetic properties of ε-InxFe2xO3 nanorod-shaped magnets
,”
Adv. Funct. Mater.
17
,
2278
2282
(
2007
).
7.
A.
Namai
,
S.
Sakurai
,
M.
Nakajima
,
T.
Suemoto
,
K.
Matsumoto
,
M.
Goto
,
S.
Sasaki
, and
S.
Ohkoshi
, “
Synthesis of an electromagnetic wave absorber for high-speed wireless communication
,”
J. Am. Chem. Soc.
131
,
1170
1173
(
2009
).
8.
S.
Sakurai
,
A.
Namai
,
K.
Hashimoto
, and
S.
Ohkoshi
, “
First observation of phase transformation of all four Fe2O3 phases (γ → ε → β → α-phase)
,”
J. Am. Chem. Soc.
131
,
18299
18303
(
2009
).
9.
L.
Machala
,
J.
Tucek
, and
R.
Zboril
, “
Polymorphous transformations of nanometric iron(III) oxide: A review
,”
Chem. Mater.
23
,
3255
3272
(
2011
).
10.
J.
Tucek
,
R.
Zboril
,
A.
Namai
, and
S.
Ohkoshi
, “
ε-Fe2O3: An advanced nanomaterial exhibiting giant coercive field, millimeter-wave ferromagnetic resonance, and magnetoelectric coupling
,”
Chem. Mater.
22
,
6483
6505
(
2010
).
11.
K.
Yamada
,
H.
Tokoro
,
M.
Yoshikiyo
,
T.
Yorinaga
,
A.
Namai
, and
S.
Ohkoshi
, “
The phase transition of ε-InxFe2xO3 nanomagnets with a large thermal hysteresis loop
,”
J. Appl. Phys.
111
,
07B506
(
2012
).
12.
M.
Gich
,
A.
Roig
,
C.
Frontera
,
E.
Molins
,
J.
Sort
,
M.
Popovici
,
G.
Chouteau
,
D. M.
y Marero
, and
J.
Nogués
, “
Large coercivity and low-temperature magnetic reorientation in ε-Fe2O3 nanoparticles
,”
J. Appl. Phys.
98
,
044307
(
2005
).
13.
S.
Ohkoshi
,
S.
Sakurai
,
J.
Jin
, and
K.
Hashimoto
, “
The addition effects of alkaline earth ions in the chemical synthesis of ε-Fe2O3 nanocrystals that exhibit a huge coercive field
,”
J. Appl. Phys.
97
,
10K312
(
2005
).
14.
Y. C.
Tseng
,
N. M.
Souza-Neto
,
D.
Haskel
,
M.
Gich
,
C.
Frontera
,
A.
Roig
,
M.
van Veenendaal
, and
J.
Nogués
, “
Nonzero orbital moment in high coercivity ε-Fe2O3 and low-temperature collapse of the magnetocrystalline anisotropy
,”
Phys. Rev. B
79
,
094404
(
2009
).
15.
A.
Namai
,
M.
Yoshikiyo
,
K.
Yamada
,
S.
Sakurai
,
T.
Goto
,
T.
Yoshida
,
T.
Miyazaki
,
M.
Nakajima
,
T.
Suemoto
,
H.
Tokoro
, and
S.
Ohkoshi
, “
Hard magnetic ferrite with a gigantic coercivity and high frequency millimetre wave rotation
,”
Nat. Commun.
3
,
1035
(
2012
).
16.
G. A.
Bukhtiyarova
,
O. N.
Martyanov
,
S. S.
Yakushkin
,
M. A.
Shuvaeva
, and
O. A.
Bayukov
, “
State of iron in nanoparticles prepared by impregnation of silica gel and aluminum oxide with FeSO4 solutions
,”
Phys. Solid State
52
,
826
837
(
2010
).
17.
G. A.
Bukhtiyarova
,
M. A.
Shuvaeva
,
O. A.
Bayukov
,
S. S.
Yakushkin
, and
O. N.
Martyanov
, “
Facile synthesis of nanosized ε-Fe2O3 particles on the silica support
,”
J. Nanopart. Res.
13
,
5527
5534
(
2011
).
18.
S. S.
Yakushkin
,
A. A.
Dubrovskiy
,
D. A.
Balaev
,
K. A.
Shaykhutdinov
,
G. A.
Bukhtiyarova
, and
O. N.
Martyanov
, “
Magnetic proper ties of few nanometers ε-Fe2O3 nanoparticles supported on the silica
,”
J. Appl. Phys.
111
,
044312
(
2012
).
19.
D. A.
Balaev
,
A. A.
Dubrovskiy
,
K. A.
Shaykhutdinov
,
O. A.
Bayukov
,
S. S.
Yakushkin
,
G. A.
Bukhtiyarova
, and
O. N.
Martyanov
, “
Surface effects and magnetic ordering in few-nanometer-sized ε-Fe2O3 particles
,”
J. Appl. Phys.
114
,
163911
(
2013
).
20.
I. S.
Poperechny
,
Yu. L.
Raikher
, and
V. I.
Stepanov
, “
Dynamic magnetic hysteresis in single-domain particles with uniaxial anisotropy
,”
Phys. Rev. B
82
,
174423
(
2010
).
21.
I. S.
Poperechny
and
Yu. L.
Raikher
, “
Dynamic hysteresis of a uniaxial superparamagnet: Semi-adiabatic approximation
,”
Physica B
435
,
58
61
(
2014
).
22.
C.
Chen
,
O.
Kitakami
, and
Y.
Shimada
, “
Particle size effects and surface anisotropy in fe-based granular films
,”
J. Appl. Phys.
84
,
2184
2188
(
1998
).
23.
V. P.
Shilov
,
J.-C.
Bacri
,
F.
Gazeau
,
F.
Gendron
,
R.
Perzynski
, and
Y. L.
Raikher
, “
Ferromagnetic resonance in ferrite nanoparticles with uniaxial surface anisotropy
,”
J. Appl. Phys.
85
,
6642
6647
(
1999
).
24.
A.
Aharoni
, “
Surface anisotropy in micromagnetics
,”
J. Appl. Phys.
61
,
3302
3304
(
1987
).
25.
X.
Batlle
and
A.
Labarta
, “
Finite-size effects in fine particles: Magnetic and transport properties
,”
J. Phys. D: Appl. Phys.
35
,
R15
R42
(
2002
).
26.
M.
Jamet
,
W.
Wernsdorfer
,
C.
Thirion
,
V.
Dupuis
,
P.
Mélinon
,
A.
Pérez
, and
D.
Mailly
, “
Magnetic anisotropy in single clusters
,”
Phys. Rev. B
69
,
024401
(
2004
).
27.
F.
Bødker
,
S.
Mørup
, and
S.
Linderoth
, “
Surface effect in metallic iron nanoparticles
,”
Phys. Rev. Lett.
72
,
282
285
(
1994
).
28.
W. F.
Brown
, “
Thermal fluctuations of a single-domain particle
,”
Phys. Rev.
130
,
1677
1686
(
1963
).
29.
Y. L.
Raikher
and
M. I.
Shliomis
, “
The effective field method in the orientational kinetics of magnetic fluids and liquid crystals
,”
Adv. Chem. Phys.
87
,
595
751
(
2007
).
30.
N.
Pérez
,
P.
Guardia
,
A. G.
Roca
,
M. P.
Morales
,
C. J.
Serna
,
O.
Iglesias
,
F.
Bartolomé
,
L. M.
Garcia
,
X.
Batlle
, and
F.
Labarta
, “
Surface anisotropy broadening of the energy barrier distribution in magnetic nanoparticles
,”
Nanotechnology
19
,
475704
(
2008
).
You do not currently have access to this content.