0021-3640/02/7506- $22.00 © 2002 MAIK “Nauka/Interperiodica” 0268
JETP Letters, Vol. 75, No. 6, 2002, pp. 268–272. Translated from Pis’ma v Zhurnal Éksperimental’noœ i Teoreticheskoœ Fiziki, Vol. 75, No. 6, 2002, pp. 318–322.
Original Russian Text Copyright © 2002 by Alekseev, Bykov, Popkov, Polushkin, Korneev.
1. It is known that nonuniform vortex magnetization
configurations arise in small (ferro)magnetic particles with
a low magnetic crystalline anisotropy and sizes exceeding
the absolute single-domain threshold (~0.05 μ) [1, 2]. The
distribution of magnetic moments observed in the
remanent state depends essentially on the magnetiza-
tion prehistory and on the particle shape and size.
Recently, new, primarily lithographic technologies
have evolved for obtaining thin-film elements with pla-
nar sizes down to several tens of nanometers and regu-
lar lattices with a given geometry [3, 4]. Progress in the
field of nanotechnology has stimulated the study of
micromagnetism in small particles based on thin-film
magnetic elements (see, for example, [5–8]). These
works are devoted to both the occurrence of vortex con-
figurations primarily in elements rectangular in shape
and states of a new type, the so-called C and S configu-
rations, that are characterized by edge spin pinning due
to the magnetostatic effect of element edges. The edge
pinning effect is manifested in the multimode character
of magnetization reversal, which can be the reason for
the giant instability of switching fields associated with
the thermally activated change of the magnetization
reversal near the saturation state [8]. The use of ele-
ments with a nonrectangular, in particular, ellipsoidal
shape, in which the formation of alternative magnetiza-
tion configurations associated with spin pinning in the
vicinity of narrow poles of the magnetized element is
not highly probable, is one of the ways for suppressing
this instability. It is these elements that are formed, for
example, under the irradiation of a finely dispersed
superparamagnetic Fe–Cr medium by interfering laser
beams [9]. A regular lattice of ferromagnetic elements
is formed at interference maxima as a result of the mod-
ification of magnetic properties. The technology of
obtaining such a structured medium was described pre-
viously in [9]. The goal of this work was (1) to simulate
possible remanent magnetization states in submicron
elements with an ellipsoidal shape and (2) to compare
the results of simulation with experimental data for
magnetic lattices obtained in studying thin-film Fe–Cr
alloys using a magnetic force microscope (MFM).
2. Magnetization of ellipsoidal particles. The
magnetization reversal processes in flat microparticles
were analyzed theoretically by numerically integrating
the Landau–Lifshitz equations with free boundary con-
ditions. The scheme of numerical integration and exam-
ples of modeling rectangular particles were described
previously in our works [7, 8, 10]. It was possible to
vary the element sizes and the magnetic anisotropy
parameters in the calculations. In this work, we will
report the results of modeling an elliptic flat element
0.6 × 0.3 × 0.015 μ in size with zero magnetic anisot-
ropy. The magnetic parameters adopted in the calcula-
tion, namely, the saturation magnetization M = 1300 G
and the exchange constant A = 10
–6
erg/cm
3
, corre-
sponded to experimental data for Fe–Cr films.
Modeling the process of magnetization along the
long element axis (easy direction of magnetization)
showed that the main magnetic hysteresis loop has a
rectangular shape for a particle of a specified size and
that a uniformly magnetized particle is switched in the
field H
c1
= 300 Oe. The magnitude of this field grows as
the film thickness and the element aspect ratio increase.
Observation of Remanent States of Small Magnetic Particles:
Micromagnetic Simulation and Experiment
A. M. Alekseev
1
, V. A. Bykov
1
, A. F. Popkov
1,
*, N. I. Polushkin
2
, and V. I. Korneev
3
1
State Research Center of Russian Federation–State Research Institute for Problems in Physics, NT MDT,
Moscow, 103460 Russia
2
Institute of Microstructure Physics, Russian Academy of Science, Nizhni Novgorod, 603950 Russia
3
Moscow Institute of Electronic Engineering (Technological University), Moscow, 103482 Russia
*e-mail: popkov@nonlin.msk.ru
Received February 10, 2002
Abstract—Micromagnetic properties of submicron ferromagnetic elements ellipsoidal in shape are studied
theoretically and experimentally. By numerically solving the equations of magnetodynamics, it is found that
different remanent magnetization states can be obtained, depending on the manner of magnetization reversal in
such elements: one-vortex states, two-vortex states, and vortex-free states with skew-symmetric spin pinning.
The magnetization configurations predicted in the calculations have been observed experimentally using mag-
netic force microscopy in regular lattices of microstructures formed in thin-film samples of Fe–Cr alloys under
irradiation by interfering laser beams. © 2002 MAIK “Nauka/Interperiodica”.
PACS numbers: 75.60.Ej; 75.60.Jk; 75.70Ak