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Magnetic antivortex formation in pound-key-like nanostructuresArabinda Haldar and Kristen S. Buchanan Citation: Appl. Phys. Lett. 102, 112401 (2013); doi: 10.1063/1.4795521 View online: http://dx.doi.org/10.1063/1.4795521 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v102/i11 Published by the American Institute of Physics. Related ArticlesThe influence of individual lattice defects on the domain structure in magnetic antidot lattices J. Appl. Phys. 113, 103907 (2013) Magnetic properties and structure of Fe83.3–85.8B7.0–4.5P9Cu0.7 nanocrystalline alloys J. Appl. Phys. 113, 17A311 (2013) Lateral Interaction of transverse magnetic domain walls J. Appl. Phys. 113, 17B903 (2013) Magnetic structure of GdNiSn J. Appl. Phys. 113, 17E107 (2013) The effect of dissipation on the structure of quasi-solitonic states of nonlinear magnetically ordered media underhigh-frequency point influence Low Temp. Phys. 39, 140 (2013) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors
Magnetic antivortex formation in pound-key-like nanostructures
Arabinda Haldar and Kristen S. Buchanana)
Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
(Received 24 October 2012; accepted 4 March 2013; published online 18 March 2013)
Magnetic antivortices have potential for applications but they are considerably more difficult to
create than their topological counterpart, the vortex state. Here, we describe a method to generate
isolated magnetic antivortex (AV) states reliably in pound-key-like patterned structures. Magnetic
force microscopy images confirm that AV states are obtained after a simple two-step magnetic field
procedure that involves first a saturating field along the structure diagonal followed by a smaller field
applied in the opposing direction. Micromagnetic simulations show that the second field reverses
areas of the structure that have lower shape anisotropy first, which facilitates the subsequent
antivortex formation. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4795521]
Magnetic vortices have been studied extensively in
recent years because of their rich physics as well as their
potential for applications.1–7 Magnetic antivortices, the topo-
logical counterpart of the vortex state, have similar potential;
however, comparatively few experimental investigations
have been conducted because they are more difficult to cre-
ate as compared to vortices. A number of papers involving
micromagnetic simulations show that the magnetic antivor-
tex (AV) possesses similarly interesting dynamic properties
including gyrotropic motion and dynamic core reversal.8–14
Furthermore, micromagnetic simulations show that the AV
spin configuration may have advantages over vortices for
channeling spin waves emitted from the dynamic core rever-
sal.9 Although comparatively few experiments have been
done on the AV state, the experiments that have been done
on AV dynamics confirm that there is, indeed, interesting
physics to be studied.15 The main issue that impedes experi-
mental progress in this area is the difficulty associated with
designing a structure in which one can both reliably generate
and stabilize an isolated antivortex.
In confined magnetic structures with sub-micron length
scales, the magnetization reversal processes and remanent
spin configurations depend strongly on the shape of the
structure. The vortex (V) and AV spin configurations can be
described mathematically by the relation u ¼ nbþ cp=2,
where u is the angle of the in-plane magnetization at a given
position, b is the angular coordinate, and “c” is the chirality
which refers to the sense of curling of the magnetization.10
The two states differ only by the winding number “n” that
represents the sense of rotation of the spins, where n¼ 1 for
a circular vortex where the spins swirl around a central out-
of-plane core and n¼�1 for an AV state, a configuration
where the spins sweep in towards the central core from two
opposite sides and out at the other two. Since vortices are
flux closure states with minimal stray fields, they have low
magnetostatic energy and are often the ground state configu-
ration in sub-micron magnetically soft structures,16 whereas
the AV state generates stray fields and is consequently more
difficult to stabilize.17 An AV or set of AVs will form
naturally as part of a cross-tie wall or a V/AV/V chain in
thick rings18 or rectangular structures19 but only a few struc-
ture designs have been shown to reliably stabilize isolated
antivortices and, even then, they are obtained after some-
times complex magnetic field treatments.15,19–21 Figure-eight
and double figure-eight structures can be used to channel
flux lines and minimize stray fields, which help to stabilize
the AV state,9,15 but it is difficult to form the AV in these
structures.20 A more recent study on u-shaped structures
shows a reliable means to form an AV state through con-
trolled domain wall nucleation and propagation20 but the
field treatment requires either a vector magnet or rotation
stage and these designs cannot easily be incorporated into a
larger network. Shape anisotropy can be used as a means to
selectively reverse certain regions of a patterned structure to
assist the AV formation, as demonstrated in asymmetric
cross-like structures.21 Here, we demonstrate that this gen-
eral strategy can be extended to reliably generate AVs in sys-
tems interconnected by magnetic wires that may prove
useful for spin wave-based logic devices. New strategies for
reliable and reproducible AV formation will improve both
the experimental accessibility and technological potential of
this magnetic state.
In this work, magnetic force microscopy and micromag-
netic simulations have been used to study the magnetic re-
versal process in pound-key-like structures. The results show
that AVs can be stabilized in these structures at remanence
reliably after a simple field treatment scheme that involves
first a saturating magnetic field applied along the structure
diagonal, followed by a lower field, the value of which can
be selected from hysteresis measurements, applied antiparal-
lel to the first. A degree of shape anisotropy is incorporated
into the structure design to select which areas of the structure
will lead the reversal process and drive the AV formation.
The pound-key-like structures investigated here are
illustrated in Fig. 1. The structure in Fig. 1(a) has a “circular”
hole inside and will be referred to as the AV-C structure.
The structure in Fig. 1(b) has unequal outer “leg” widths
hence it will be designated the AV-L structure. The critical
dimensions for each structure (widths w and b, radius R,
and sizes L) are labeled in Fig. 1; the total size for each is
2L � 2L. To understand the magnetic reversal process and to
a)Author to whom correspondence should be addressed. Electronic mail:
0003-6951/2013/102(11)/112401/4/$30.00 VC 2013 American Institute of Physics102, 112401-1
APPLIED PHYSICS LETTERS 102, 112401 (2013)
visualize the mechanism of the AV formation, the pound-
key-like designs were modeled numerically using the object
oriented micromagnetic framework (OOMMF) program.22
Material parameters appropriate for permalloy were used:
saturation magnetization Ms¼ 8� 105 A/m, exchange con-
stant Aex¼ 1:3� 10�11 J/m, and anisotropy was neglected.
Cells of 5 � 5 nm2 were used to represent the structures and
a damping coefficient of a¼ 1 was chosen to achieve rapid
convergence. The in-plane dimensions were varied in both
the experiments and simulations while the thickness was
held constant at 37 nm.
Figures 1(a) and 1(b) show micromagnetic simulations of
the spin configurations for the AV-C (w¼ 150 nm, R¼ 300 nm,
L¼ 1lm) and the AV-L (w¼ 150 nm, b¼ 300 nm, L¼ 1 lm)
structures, respectively. The field treatment used to achieve
reliable AV formation is as follows: (i) A high magnetic field
H1 is applied along the diagonal of the structure, which
causes the spins to align along the applied field. (ii) When
H1 is removed, the shape anisotropy of the legs causes the
spins to relax slightly so that they are aligned along each of
the legs with a net non-zero magnetization along H1. (iii)
Next, a lower field H2 (<H1) is applied antiparallel to H1.
The value of H2 is such that it does not overcome the large
shape anisotropy of the thin legs (w), but it is large enough
that the spins can reverse in the wider areas, which in turn
promotes further reversal. (iv) In both structures, two AVs
eventually form at opposing intersections along the diagonal
perpendicular to the magnetic field direction. (v) The field is
reduced to zero. Both of the structures retain the two AVs at
remanence. The AVs can be formed at either set of opposing
intersections for the AV-C structure depending on the choice
of diagonal, whereas the field must be applied along the di-
agonal that runs between the wider legs for the AV-L
structure.
Snapshots of the intermediate spin configurations (step
(iii) of Fig. 1) show that the reorientation of the moments
due to H2 begins near the central circular hole in the AV-C
structure, whereas in the AV-L structure, it begins within the
wider legs (width¼ b). These are the regions with lower
shape anisotropy. Several vortices are observed in the transi-
tional spin configurations but eventually these regions
become uniformly magnetized along H2. For the AV-C
structure, step (iv) shows that four of the eight outer legs
eventually relax such that their net direction is along H2.
After the initial spin reorientation in the inner (wider) region
(step iii), the reversal propagates through the legs that lie
along the diagonal parallel to H2 such that the local magnet-
ization varies smoothly through the central region in the
relaxed configuration. The remaining four legs retain their
initial orientation and AVs are stabilized at these intersec-
tions. For the AV-L structure, the mechanism is similar
except that the wide outer legs reverse first and then the re-
versal propagates through the central region. After removing
the field (step v), the spins along the diagonal remain aligned
along H2 and the AVs that have formed at the two other
intersections persist.
Figure 2 shows simulated hysteresis loops for an AV-C
structure with the same dimensions as the structure shown in
Fig. 1(a) (sample A: w¼ 150 nm, R¼ 300 nm, L¼ 1 lm) and
one that is a factor of 2.5 larger (sample 2.5 � A), both 37-
nm thick. The field H was applied in-plane along the struc-
ture diagonal (see inset of Fig. 2). The flat steps in the hyster-
esis loops are associated with the AV formation region and
hence represent the fields H2 that can be used for AV genera-
tion. H2 is smaller for the larger structure and the range of
fields that can be used to form the AVs (Dl0H2) also
becomes smaller. The field window Dl0H2 is 16.7 mT for
sample A, whereas for sample 2.5�A, it is only 2.7 mT.
Simulations conducted for thicknesses of 25, 37, 50, and
60 nm for the AV-C structure (dimensions of A) show that
H2 also decreases with increasing thickness. Hysteresis simu-
lations performed for additional magnetic field angles show
that the AVs form in AV-C (A) structures even when the
field is misaligned with respect to the diagonal by as much
as 10�. Note that the total energy of the structure in the rema-
nent state directly after saturating (after H1) is consistently
lower than the energy of the AV state. The energy difference
is only �1%–4% for micron-sized structures but since the
FIG. 1. Micromagnetic simulations of the spin configurations in two pound-key-like structures. Rows (a) and (b) show spin distributions for an AV-C structure
with w¼ 150 nm, R¼ 300 nm, L¼ 1 lm and an AV-L structure with w¼ 150 nm, b¼ 300 nm, L¼ 1 lm, respectively. The critical dimensions w, b (>w), R(�L/2�w), and L are labeled in column (i). Columns (i) through (v) show the spin configurations at successively applied magnetic fields (l0H1¼ 150 mT and
l0H2¼�42.5 mT). All plots show equilibrium spin configurations except for panel (iii), which shows intermediate spin configurations as the structure relaxes
in field H2. In step (v), AV states are found in both structures at two out of the four crossing points at remanence. The color scale indicates the in-plane angle
of the magnetization.
112401-2 A. Haldar and K. S. Buchanan Appl. Phys. Lett. 102, 112401 (2013)
AV state is not the ground state it cannot be reached via a.c.
demagnetization. This energy difference is �1000kBT at
room temperature; the energy barrier between the two states
is likely larger, as evidenced by the finite fields required to
annihilate the AV (Fig. 2).
A series of AV-C and AV-L structures of different
dimensions were fabricated using electron-beam lithography
and lift-off on a Si wafer. Permalloy (Ni80Fe20) was sput-
tered in an Argon atmosphere at a pressure of 3:3� 10�3
Torr with a growth rate 1.22 nm/min after reaching a base
pressure of 1:9� 10�7 Torr. The thickness of all samples
was 37 nm. The dimensions of the AV-C structures presented
here are (w, R, L)¼ (300 nm, 1.15 lm, 3 lm) and (900 nm,
1.4 lm, 5.4 lm). For the AV-L structures, the dimensions are
(w, b, L)¼ (550 nm, 1.6 lm, 5.2 lm). The magnetic micro-
structures were imaged at remanence after a variety of field
treatments using magnetic force microscopy (MFM).
Commercial MFM tips that were magnetized along the tip
length prior to imaging were used. The phase shift of the
oscillating tip provides a measure of the gradient of the out-
of-plane component of the stray magnetic field. To visualize
the MFM contrast expected from the AV-C and AV-L struc-
tures in the antivortex state, we calculated the stray magnetic
field (out-of-plane component) of the spin configurations
shown in Fig. 1, columns (ii) and (v), at a lift height of
50 nm. The simulated structures are smaller than those used
in the experiments but the MFM images should be qualita-
tively the same independent of the scale.
Figure 3 shows the calculated and experimental MFM
images of the AV-C and AV-L structures at remanence after
various field treatments. Fig. 3(a) shows an MFM image of the
AV-C structure (w¼ 900 nm, R¼ 1.4 lm, L¼ 5.4 lm) after
saturating it with a large field l0H1¼ 130 mT then removing
the field. The bright (dark) regions in the image indicate that
the stray field of the sample and the magnetization direction of
the tip are in the same (opposite) directions. The bottom four
legs are dark and the upper four legs are bright, which indicate
that all of the moments are pointing along the legs such that
the net moment is along H1, as shown in the calculated image
in Fig. 3(c). Similar behavior is observed for AV-L structure
(Fig. 3(e)). We do not see bright/dark contrast experimentally
in the wide legs as the moments in these regions form closure
domains or Landau patterns. The Landau patterns do not form
in the smaller calculated structures (Fig. 3(g)) but the images
are otherwise in agreement.
Figure 3(b) shows the experimental MFM phase contrast
for the same AV-C structure after the full field treatment
(l0H1¼ 130 mT, then l0H2¼�6.6 mT, then return to
l0H¼ 0). The alternating bright and dark contrasts in the
pair of legs in Fig. 3(b) as well as the details of the contrast
near the intersection are in agreement with the calculated
results shown in Fig. 3(d), indicating that two AVs have
formed. Figs. 3(f) and 3(h) show that two AV states form at
remanence in the AV-L structure, as well. Figure 4 shows a
scanning electron micrograph and corresponding MFM
images of an array of identical AV-C (w¼ 300 nm,
R¼ 1.15 lm, L¼ 3 lm) structures. After the full field
FIG. 2. Simulated hysteresis loops for AV-C structures with dimensions of
w¼ 150 nm, R¼ 300 nm, L¼ 1 lm (A), and w¼ 375 nm, R¼ 750 nm,
L¼ 2.5 lm (2.5 � A). The inset shows the direction of H.
FIG. 3. Experimentally measured ((a) and (b)) and calculated ((c) and (d))
MFM images of an AV-C structure (w¼ 900 nm, R¼ 1.4 lm, L¼ 5.4 lm)
and an AV-L structure (w¼ 550 nm, b¼ 1.6 lm, L¼ 5.2 lm) (experimental:
(e) and (f); calculated: (g) and (h)). Images were obtained at remanence after
applying l0H1¼ 130 mT (first column, saturated configuration) and after
applying first H1 then l0H2¼�6.6 mT (second column, AV state). The
arrows in (c), (d), (g), and (h) show the local in-plane direction of the spins
for scaled down structures (same dimensions as in Fig. 1), while the contrast
shows the magnitude of the out-of-plane component of the stray magnetic
field 50 nm above the structure, where white is positive and black is nega-
tive. The insets to the right show enlarged versions of the AV regions.
112401-3 A. Haldar and K. S. Buchanan Appl. Phys. Lett. 102, 112401 (2013)
treatment (l0H1¼ 130 mT followed by l0H2¼�11.4 mT),
the MFM phase contrast in the legs is consistent with the for-
mation of two AVs (see Fig. 3(b)) for all of the imaged struc-
tures. The AVs, once formed, are stable at room
temperature; MFM imaging repeated three weeks after the
field treatment shows that the AV states persist for at least
this long.
The antivortex state, like the vortex state, possess a cen-
tral out-of-plane magnetic core, the polarity of which can
also be observed using MFM.19,23 In the simulated spin dis-
tributions shown in Fig. 3(d), both of the cores are oriented
upwards (positive polarities). The central regions of the AVs
show a subtle central bright feature in the calculated MFM
contrast that is due to the positive core polarities. The cores
in Fig. 3(h) have positive and negative polarities in the
upper/left and bottom/right, respectively, which lead to cen-
tral AV regions that are predominantly bright and dark,
respectively. By comparing these calculated images with the
experimental MFM results, the core polarizations in Fig.
3(b) are identified as negative on the left and positive on the
right, whereas both polarities are positive in Fig. 3(f). A vari-
ety of core polarity combinations were observed experimen-
tally, suggesting that direct core-core interactions are
minimal at the time of formation, which is expected since
the cores are separated by >5 lm.
In conclusion, MFM images of two variations of a pound-
key-like design show that these structures can be used to stabi-
lize isolated antivortices using a simple field treatment scheme
that involves first saturating the structure along its diagonal,
then applying a smaller field in the opposing direction.
Micromagnetic simulations of the magnetization reversal pro-
cess show that the AV formation relies on shape anisotropy—
the second magnetic field reverses only selected areas of the
magnetic structure initially, which subsequently facilitates the
AV formation. The range of fields that leads to the AV forma-
tion can be readily identified from steps in the hysteresis
curves, providing a means to select the correct field for a given
structure. This simple structure design can be used to reliably
form isolated AV states that, furthermore, can be extended nat-
urally to form a larger network. These findings will facilitate
further experimental investigations on the properties of AVs
including AV dynamics and spin wave generation.
We thank M. Wu for access to sputtering and MFM
facilities, Y. Sun and H. Chang for assistance with sputtering,
and M. Asmat-Uceda for useful discussions. This research
was funded in part by the National Institute of Standards and
Technology Grant No. 60NANB10D011 and the National
Science Foundation Award No. 0907706.
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FIG. 4. (a) Scanning electron micrograph (SEM)
of an array of AV-C structures (w¼ 300 nm,
R¼ 1.15 lm, L¼ 3 lm). (b) Experimental MFM
phase image of this array at remanence after first
applying external magnetic fields l0H1¼ 130 mT
followed by l0H2¼�11.4 mT along the directions
indicated by the arrows. The contrast at the ends of
the legs is the same as in Fig. 3(d), which indicates
that each structure contains two AVs.
112401-4 A. Haldar and K. S. Buchanan Appl. Phys. Lett. 102, 112401 (2013)