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:

kristen.buchanan@colostate.edu

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)