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Copyright © 2010 American Scientific Publishers
All rights reserved
Printed in the United States of America
Journal of
Nanoscience and Nanotechnology
Vol. 10, 7212–7216, 2010
Three-Dimensional Spin Configuration of
Ferromagnetic Nanocubes
H.-G. Piao
1 2
, D. Djuhana
1
, J.-H. Shim
1
, S.-H. Lee
1
, S.-H. Jun
1
,
S. K. Oh
1
, S.-C. Yu
1
, and D.-H. Kim
1 ∗
1
BK21 Physics Program and Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea
2
College of Science, Huaihai Institute of Technology, Lianyunguang 222005, China
We have systematically investigated three-dimensional spin configurations in ferromagnetic
nanocubes using micromagnetic simulation with variation of cube geometry. For thin cuboids, a spin
configuration exhibits a four-domain Landau state with a magnetic vortex structure at the center as in
the case of a thin film square. For a thick cube, a complex spin configuration with an S-type cylindri-
cally asymmetric vortex having two cores on a pair of surfaces while a leaf-like and a C-type states
are observed on the other two pairs of cube surfaces. Competition between the geometrical symme-
try and magnetic energy minimization condition in ferromagnetic nanocubes leads to the complex
spin structure with a spontaneously broken symmetry.
Keywords: Ferromagnetic Nanocube, Three Dimensional Spin Configuration.
1. INTRODUCTION
Recently, ferromagnetic nanomaterials such as particles,
disks, wires, and dots on nanometer scales have attracted
great interest for various potential applications in mag-
netoelectronics and magnetic recording technology.
1–8
In
the patterned ferromagnetic recording media, the ultimate
recording density is limited by the superparamagnetic
instability originated from the competition between ther-
mal fluctuation and ordering magnetization.
9–13
In order to
overcome the recording limit, numerous studies have been
proposed. For instance, data recording methods using vor-
tex core switching or core position in patterned ferromag-
netic elements have been proposed,
14–18
while the magnetic
vortex structure has been considered to be prevalent in
many patterned ferromagnetic system. The magnetic vor-
tex in a thin ferromagnetic pattern is composed of a cylin-
drically curling spin structure with a vortex core generating
the same magnetic surface charges on the patterned film
surfaces.
17
On the other hand, very few studies have been
addressed to the spin configuration of 3-D nanostructures.
One can easily expect that the magnetic vortex structure
with core magnetization perpendicular to the patterned film
plane will be frustrated, since the core direction is not
uniquely determined, for examples, in case of nanocubes
due to the unbroken x–y–z symmetry. Unfortunately, very
∗
Author to whom correspondence should be addressed.
little has been known for detailed spin configurations in
3-D ferromagnetic nanostructures.
In this work, we investigate 3-D spin configuration in fer-
romagnetic nanocubes with systematic variation of cuboids
thickness by means of micromagnetic simulation, where we
observe a transitional behavior of a ground spin configura-
tion from a two dimensional simple vortex spin structure
to a three dimensional complex spin structure. Full details
of 3-D spin configuration in ferromagnetic nanocubes are
explored.
2. MICROMAGNETIC SIMULATION
Using the object-oriented micromagnetic framework
(OOMMF)
19
based on the Landau–Lifshitz–Gilbert
equation,
20
3-D spin configurations of various ferromag-
netic nanocubes are investigated with systematical variation
of cube thickness under the zero external magnetic field.
Length and width of the nanocube are set to be 200 nm in
all cases. The geometry and dimension of the nanocube are
illustrated in Figure 1. The cube thickness d is varied from
5 to 200 nm. In all the micromagnetic simulations, the
unit cell dimension is 50 × 50 × 50 nm
3
and the Gilbert
damping constant is = 001. The material parameters of
Permalloy are chosen to neglect a contribution of magne-
tocrystalline anisotropy. The saturation magnetization of
M
S
= 80 × 10
5
A/m and the exchange stiffness coefficient
of A = 13 × 10
-11
J/m are used. Initial spin state of a
7212 J. Nanosci. Nanotechnol. 2010, Vol. 10, No. 11 1533-4880/2010/10/7212/005 doi:10.1166/jnn.2010.2760