IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 11, NOVEMBER 2008 3063
Broadband Magnetic Response of Periodic Arrays of FeNi Dots
Juan Francisco Sierra , Ahmad A. Awad , Gleb N. Kakazei , Francisco Javier Palomares , and Farkhad G. Aliev
Departamento de Física de la Materia Condensada. C III, Universidad Autónoma de Madrid, Madrid 28049, Spain
IFIMUP-IN, Departamento do Física, Universidade do Porto, Porto, Portugal
ICMM-CSIC, Cantoblanco, Madrid 28049, Spain
We present a study of magnetization dynamics at room temperature in periodic arrays of 50 nm thick FeNi (Py) circular magnetic
dots of 500 nm radius and different center to center distance (1200 and 2500 nm), by using a broadband magnetometer based on Vector
Network Analyzer which works between 300 kHz and 8.5 GHz. We also present a comparison between the dynamic response, ferro-
magnetic resonance (FMR) and its linewidth, with static magnetic characteristics such as magnetization curves. The FMR peak appears
just above the nucleation field and is perfectly described by Kittel formula taking into account the demagnetizing factor of an individual
magnetic dot. In addition to FMR we observed a spin wave resonance below the uniform mode, which could be attributed to spin waves
in confined systems. The FMR linewidth shows a significant broadening close to the field region corresponding to nucleation of magnetic
vortex.
Index Terms—Magnetic devices, magnetic resonance, nanotechnology.
I. INTRODUCTION
M
AGNETIZATION dynamics in magnetic nanostructures
such as thin films, magnetic multilayers, magnetic
tunnel junctions and spin valves have attracted much attention
due to their technological applications in magnetic random
access memories (MRAM) [1] and patterned recording media
[2]. During last decade spin dynamics in magnetic dots with
different shapes and sizes have been intensively studied the-
oretically and experimentally. Spatial regularity of arrays of
magnetic elements permits the investigation of interdot interac-
tions [3] and collective excitations [4].
Depending on the aspect ratio where L is the thick-
ness and R is the dot radius, the circular element could have
in-plane or out-of-plane magnetization [5]. For all spins
trend to align in-plane to minimize both exchange and total
dipole energies. Reduction of the dot radius to micrometer or
submicrometer length scales induces therefore appearance of a
curling spin configuration in the dot and corresponding vortex
state formation where spins are aligned out-of-plane close to the
vortex core. This core has extension of the order of exchange
length which depends on the exchange stiffness A and
the saturation magnetization as: . Pres-
ence of such unusual topologic anomaly, the magnetic vortex,
is expected to give rise to a rich variety of interesting dynamic
properties including excitation of translational, radial (RM) and
azimuthal (AM) modes [6].
To study the dipolar interactions in the array of the mag-
netic dots in the saturated state, it is very important to examine
the magnetization dynamics at high frequencies (GHz range)
with the sample magnetized in plane. Different experimental
Digital Object Identifier 10.1109/TMAG.2008.2002527
Color versions of one or more of the figures in this paper are available online
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techniques have been used to probe high frequency magnetiza-
tion dynamics in Permalloy dots including Brillouin Light Scat-
tering (BLS) [7] and conventional Ferromagnetic Resonance
(FMR) [8]. Theoretical studies of saturated in-plane [9] and
out-of-plane [10] dots predict multiresonance eigenmodes. In
addition to the uniform Kittel resonance, the lateral confinement
of spins within each dot may cause a marked discretization of
the spin wave spectrum.
Here, we present broadband magnetization dynamics, both
above and below the vortex nucleation field, measured in arrays
of magnetic dots with 500 nm radius and 50 nm thickness. These
parameters (thickness of about 3 and aspect ratio of about
0.1) ensure vortex configuration in the ground state and uniform
magnetization along the dot thickness in the saturated state. In
order to investigate possible influence of dipolar coupling we
have measured response from the arrays with different center
to center (CTC) dots distance: the high density (HD) sample
had and the low density (LD) sample had
.
II. EXPERIMENTAL DETAILS
LD and HD arrays of polycrystalline Py dots were fabricated
on silicon wafers by using electron beam (EB) lithography and
lift-off techniques. A double layered resist spin coating and
highly directional EB evaporation were used to obtain circular
dots with sharp edges. This technique is very convenient to
fabricate arrays of submicron dots with different diameters and
periods, within area limited by substrate and with identical
properties of magnetic material: grain size, distribution, ori-
entation and film thickness over the whole sample (for more
details in sample preparation see [12]). The patterned area has
about with sufficient amount of magnetic material
for a good detection of magnetization dynamics of the samples
in our experimental set-up.
The measurements of high frequency magnetization dy-
namics were carried out by using Agilent E5071B Vector
Network Analyzer (VNA) working at frequencies up to 8.5
GHz. A VNA-FMR inductive technique was used to determine
the FMR frequency and the linewidth. Once the M-H loops
were measured, both samples were covered with a thin layer of
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