360{\deg} Domain Walls: Stability, Magnetic Field and Electric Current Effects

The formation of 360{\deg} magnetic domain walls (360DWs) in Co and Ni80Fe20 thin film wires was demonstrated experimentally for different wire widths, by successively injecting two 180{\deg} domain walls (180DWs) into the wire. For narrow wires (less than 50 nm wide for Co), edge roughness prevented the combination of the 180DWs into a 360DW, and for wide wires (200 nm for Co) the 360DW collapsed, but over an intermediate range of wire widths, reproducible 360DW formation occurred. The annihilation and dissociation of 360DWs was demonstrated by applying a magnetic field parallel to the wire, showing that annihilation fields were several times higher than dissociation fields in agreement with micromagnetic modeling. The annihilation of a 360DW by current pulsing was demonstrated.

Magnetic domain walls (DWs) in narrow wires provide a data token for devices such as racetrack memory and logic gates [1][2][3]. DW devices maintain the traditional merits of magnetic data storage including non-volatility and high density, but offer new functionality including fully electrical operation by using spin torque transfer to manipulate the DWs and magnetoresistance to detect them. This can in principle enable faster switching speeds and lower energy consumption compared to DRAMs and other semiconductor devices [4]. Many proposed DW devices are made from nanowires containing 180DWs, where the orientation of magnetization rotates through 180° [5,6]. An essential requirement for DW devices is to be able to translate DWs within the device, which can be accomplished using a magnetic field or a current pulse due to spin transfer torque [7,8].
The 180DW in a wire with in-plane magnetization adopts a vortex or a transverse configuration, with transverse DWs favored in narrow or thin wires [6] as shown in the upper panel of figure 1(a). Closely spaced 180DWs in a nanowire interact magnetostatically, and the attraction between two 180DWs of opposite core magnetization can lead to the formation of a metastable 360°domain wall (360DW), as shown in the lower panel of figure 1(a). 360DWs are also known as 1D skyrmions [9], an example of a class of topologically protected structures which are under intense study due to their stability and device applications [10].
360DWs have been observed both in continuous ferromagnetic films [11] and in ferromagnetic nanostructures such as thin film rings or ellipses [12][13][14]. The orientation of magnetization rotates through 360°, and due to the opposite sense of core magnetization in the two component 180DWs, magnetic flux closure reduces the stray field around the 360DW in a thin film wire compared to that of a 180DW [15]. 360DWs are not expected to be translated by an applied field, but instead can be dissociated or annihilated. However, micromagnetic simulations predict that a current can translate the 360DW via spin torque transfer [15]. Moreover, instead of Walker Breakdown as observed in 180DWs, a 360DW is predicted to undergo annihilation at a sufficiently high spin current density. Simulations predict that 360DWs of different chirality can be filtered [16], and 360DWs have been proposed for use in magnetic sensors [17] and as an alternative to 180DWs in memory and logic.
360DWs in magnetic wires have been detected using magnetic force microscopy (MFM) [11], scanning electron microscopy (SEM) with polarization analysis [14], and anisotropic magnetoresistance (AMR) measurements [18][19][20][21], in which the formation of a 360DW results in a decrease of resistance. There has been considerable theoretical and modeling work on the behavior of 360DWs [22][23][24], but there have been no systematic experimental reports on the formation of 360DWs, their response to a field as a function of wire width, nor any observation of current-driven motion of a 360DW. In this article, we first demonstrate the formation and stability of 360DWs in specifically designed Co and Ni 80 Fe 20 nanostructures of different widths with in-plane magnetization. We then demonstrate the effect of applied magnetic fields or injected current pulses on 360DWs using AMR measurements for Ni 80 Fe 20 samples and MFM measurements for Co samples. Ni 80 Fe 20 has a relatively large AMR response so that individual DWs can be detected in situ, but its low switching field renders DWs vulnerable to perturbation by the stray field of an MFM tip. On the contrary, Co has a lower AMR but its higher switching field facilitates direct imaging of the stray field of DWs by MFM. Therefore studies of 360DWs in both NiFe and Co provide complementary information. We relate the experimental results to micromagnetic simulations.
The method used to generate a 360DW is similar to previous work [14]. The structures consist of a magnetic thin film wire in the shape of an arc, with width varying from 50 to 200 nm, connected to a round injection pad of 1 μm diameter. The structures were made from a thin film stack of Ta (5 nm)/Ni 80 Fe 20 (10 nm)/Au (5 nm) or Ta (5 nm)/Co (10 nm)/Au (5 nm) which was deposited by magnetron sputtering (5 cm diameter target, 100 W, and growth rates of 0.15-0.30 nm s −1 for different materials) on a Si substrate with native oxide, at an Ar pressure of 1 mTorr and a base pressure better than 5×10 −8 Torr. A bilayer resist [25] consisting of 4% polymethyl-methacrylate (PMMA) of thickness 30 nm and 2% hydrogen silsesquioxane (HSQ) of thickness 40 nm was spin coated on the magnetic film then exposed using an Elionix F-125 e-beam lithography tool with a dose of 38 mC cm −2 . The HSQ layer was developed using 4% NaCl+1% NaOH in water solution for 20 s, washed with DI water and carefully dried by a nitrogen blow gun. The underlying PMMA layer was then removed with O 2 plasma at a pressure of 6×10 −3 Torr at 90 W power for 2 min. Using these patterned bilayer resists as an etch mask, the metal film was then etched using an Ar ion beam with a beam current of 10 mA and pressure of 2×10 −4 Torr. The etching was monitored using an end-point detector. Since the PMMA acts as a sacrificial layer, the resist stack could then be removed with hot 1165 solvent [MicroChem Corp.] and sonication after the ion beam etching. An AFM image of a typical structure is shown in the upper panel of figure 1(b). For AMR measurements of Ni 80 Fe 20 samples, four electrodes made of Ta (7 nm)/Au (100 nm) were patterned using liftoff over the pad-wire structure in a second lithography step to enable a four-point measurement of resistance. For MFM characterization, we used low moment magnetic tips (Bruker MESP-LM) in order to reduce the interaction between the sample and the stray field of the tip. Lift height was set to 50 nm during the second MFM pass to ensure relatively small interaction between sample and tip as well as to obtain clear phase information. The scale for the MFM phase images shown in this paper is   3 . Micromagnetic simulations were performed using the OOMMF package [26]. respectively. The cell size was (5 nm) 3 in most simulations, though (2 nm) 3 cells were used for comparison: this predicted a critical field and a critical current for annihilation that were higher by about 15%, but the results were qualitatively the same. We describe first the formation and stability of 360DWs in Co arcs. In order to generate a 360DW, an inplane field sequence was applied perpendicular to the arc.
= + H 3000 Oe y was applied to fully saturate the magnetization and form the first 180DW with its core magnetized along +y at the center of the arc at remanence.
= -H 300 Oe y was then applied, a field sufficient to reverse the magnetization in the round pad but not high enough to reverse the magnetization in the arc due to its higher shape anisotropy. A second 180DW with opposite sense to the first 180DW was formed at the interface between the round pad and the arc. The two 180DWs combine to form a 360DW aided by their magnetostatic attraction [14]. AFM and MFM images of a Co sample of width 120 nm are shown in figure 1(b). The dark and bright contrast observed at the center of the arc qualitatively resembles the calculated stray field around the 360DW in figure 1(a) and confirmed the presence of a 360DW.
Co samples with different arc widths of 50, 80, 120, 150 and 200 nm were tested to study the 360DW stability as a function of arc width. We expect TWs to be energetically preferable within the width range according to micromagnetic simulations in Co nanowires. The 80, 120 and 150 nm samples successfully formed a 360DW in the arc. In the sample with 50 nm wire width, two 180DWs of opposite sense were formed but remained separate in the arc without combining into a 360DW (the bright contrast originates from the second 180DW). This is attributed to pinning: the amplitude of line edge roughness is expected to be independent of wire width [25], but the resulting changes in wire width are proportionately larger for narrower wires. The length of a 180DW also decreases with decreasing wire width [2], making it more sensitive to high frequency edge roughness. These factors lead to stronger pinning of the 180DWs in narrower wires, which impedes their combination into a 360DW.
For the sample with wire width of 200 nm, no 360DW was observed. MFM images of the sample after applying the initial saturation field of = + H 3000 Oe y showed a 180DW with transverse configuration as illustrated by dark contrast at the arc center. This result shows that a 180DW could be formed but the second 180DW is assumed to annihilate the first one instead of forming a 360DW. The reduced influence of edge roughness may have enabled the second 180DW to approach the first at a higher velocity, which promotes annihilation.
The experimental results for 360DW formation under transverse field cycling agree with the prediction of micromagnetic modeling, figure 2(a), for Co arcs. Simulations were performed with the same field sequence of H y =+3000 Oe followed by H y =−200 Oe, for wire widths of 50, 100, 200 and 300 nm. The arc shape in the model leads to edge roughness due to the finite cell size. The 50 nm wide model wire was unable to form a 360DW because the second 180DW did not propagate far enough to combine with the first 180DW. The 100 and 200 nm arcs did produce 360DWs, but in the 300 nm wide model wire the 360DW spontaneously annihilated.
The effect of magnetic field on 360DWs was studied experimentally in both Ni 80 Fe 20 and Co samples and characterized by AMR and MFM, respectively. A SEM image of a Ni 80 Fe 20 sample is shown in figure 3(a), which was 200 nm wide and 10 nm thick. Vortex DWs are energetically favorable in this material and geometry compared to TWs, according to micromagnetic simulations. A small DC current was applied between the outer two electrodes and the voltage between the inner two electrodes was measured in order to obtain the resistance. This reference DC current was lower than 5 μA, corresponding to an average current density of <2 10 9 A m −2 in the arc, which was 0.001-0.01 times the current density reported to move a DW in Ni 80 Fe 20 nanowires [8,[27][28][29][30]. Therefore the effect of the measurement current on the wall was neglected.
As shown in the round dot line in figure 3(b), a head-to head 180DW was formed by applying = + H 3000 Oe, y then a field in the +x direction was applied, starting from zero and increasing with a step size of 1 Oe. The resistance was measured after each field step. A change of D =  W R 0.055 0.005 was observed at 5 Oe based on ten repeated measurements, indicating movement of the 180DW to the right, out of the area between the inner two electrodes. The increase of the resistance is due to the AMR effect from the 180DW: the resistance is lower at the DW because the magnetization is locally perpendicular to the electron flow. The AMR follows the relation in which ( ) r D H is the change of resistivity and q is the angle between magnetization and electron flow [31]. If a field was applied in the -x direction, a similar resistance jump of D =  W R 0.053 0.005 was observed at −6 Oe based on ten repeated measurements, shown in the square dot line in figure 3(b). This indicated the 180DW moving to the left, out of the area between the inner two electrodes. Out of 20 total measurements, the resistance jump was very similar for eight and nine of the measurements for fields along +x and −x, respectively. The other three tests gave either no resistance change or a change of » W 0.03 which may have indicated differences in the DW structure or location. Other groups have also shown DW AMR in large numbers of repeated tests [18]. We used the eight and nine measurements to calculate DR.
A field sequence of = + H 3000 Oe y followed by = -H 300 Oe y was then used to form a 360DW in the 200 nm wide Ni 80 Fe 20 wire, followed by a field in the +x or −x direction as shown in figures 3(c) and (d), respectively. In figure 3(c), a resistance jump of D =  W R 0.078 0.007 based on ten measurements was observed at @ + H 14 Oe.
x The higher resistance change confirmed the presence of a 360DW instead of 180DW and the higher value of H x represents the critical field to dissociate a 360DW, overcoming the magnetostatic attraction between the two component 180DWs and separating them to form a reverse domain. In comparison, in figure 3(d), a resistance jump of D =  W R 0.075 0.007 was observed at @ -H 84 Oe, x much higher than the critical field in figure 3(c). This represents the critical field to annihilate the 360DW, in which the field compresses the 360DW, eventually eliminating it. The ratio of AMR change expected between a 180DW and a 360DW was calculated by exporting the magnetization distribution from OOMMF into MATLAB and determining the resistance based on equation ( . Simulations in Ni 80 Fe 20 nanowires were carried out to calculate the critical fields for annihilation and dissociation of a 360DW versus wire width, figure 2(b). We first initiated a 360DW at the center of the wire, allowed it to relax, then applied a field in either the +x or −x direction along the wire to dissociate or annihilate the 360DW, respectively. We increased the field from 0 with a step size of 10 Oe in order to find the critical value. As shown in figure 2(b), the critical fields for annihilation and dissociation decreased by about 40% and 80%, respectively with an increase of wire width from 50 to 300 nm. The 360DW became less symmetrical as the width increased, with the two component 180DWs tilting towards each other at one side of the wire, making the 360DW less stable. It has also been shown in [18] that the 360DW forms a much less stable vortex structure with increasing wire width.
For a model Ni 80 Fe 20 nanowire of width w=200 nm and thickness t=10 nm, the critical field to dissociate a 360DW is = + H 75 Oe x and to annihilate it is = -H 310 Oe.
x The modeling predicted much higher absolute values of the annihilation and dissociation fields than were measured experimentally, which may be a result of the zero temperature of the model and the lack of extrinsic defects that could initiate annihilation and dissociation. However, both model and experiment agree in showing annihilation field several times larger in magnitude than dissociation fields.
The effect of a magnetic field on 360DWs in Co nanowires were examined using MFM. As shown in figure 4(a) x the component 180DWs moved further such that the left-hand bright-contrast wall moved into the injection pad and the right dark-contrast wall moved to the end of the wire. The reversal of the wire is evident from the change in contrast from bright to dark at the tip of the wire, labeled by the black circles in figure 4. A similar dissociation process was observed in a Co sample with 150 nm wire width, figure 4(b), except that the field steps did not capture the presence of two separate 180DWs in the wire. In the 150 nm wide wire, dissociation occurred at a field between 125 and 150 Oe.
360DW annihilation in a Co sample was demonstrated by applying a field in the -x direction. The same field sequence as in figure 4 was applied initially to form a 360DW at the center of the arc. The MFM measurements are shown in the supplement (figure S1). The 360DW remained stable in the arc for  -H 500 Oe.
x The 360DW disappeared after applying a field of = -H 700 Oe, x but different from the dissociation results in figure 4, the right-hand end of the wire retained its bright contrast before and after the annihilation. This proves that the magnetization direction remained the same in the arc, indicating annihilation instead of dissociation of the 360DW. The field for annihilation (−700 Oe) was also much larger than that for dissociation (+150 Oe) in the 150 nm wide Co wire, confirming the same trend as seen in the Ni 80 Fe 20 samples and in micromagnetic simulations.
The effects of current on 360DWs were examined in 150 nm wide Co samples. Two electrodes were placed on top of the sample as shown in figure 5(a), labeled I + and I − , and the conventional current flowed from the right electrode to the left electrode. Figure 5(b) is an MFM image of the sample initiated with a 360DW at the arc center. Current pulses of +2 V, +4 V or +6 V amplitude and 200 ns duration were then injected into the sample, corresponding to current densities of approximately 1.2, 2.4 or3. 6 10 12 A m −2 respectively in the arc, averaged over the Ta/Co/Au stack. A delay of 3 s was inserted between each pulse to minimize Joule heating [32]. From MFM imaging there was no observed effect of current pulses with amplitude of 2 V. Figure 5(c) shows the 360DW after two pulses of 4 V, which moved ∼200 nm to the right, indicating a small current-driven 360DW motion. We did not see any further translation after two additional pulses of 4 V, but after ten additional pulses of 4 V the 360DW disappeared as shown in figure 5(d). Since the current is limited to the region of the arc between the two electrodes, the current-driven 360DW will not be able to move further than the electrode. Moreover, from our tests the phase contrast of a 360DW can still be observed at 150 nm lift height, which means that even if the 360DW is beneath the arc, we should still be able to see the phase contrast. As shown in figure 5(d), MFM did not reveal the 360DW remaining under the Au contact, implying that the 360DW was annihilated.
An estimation of the temperature increase from Joule heating at the end of a current pulse was made based on the calculation in [33]: Previous simulation results [15] predicted that in a smooth-edged nanowire with zero anisotropy, a spin current will translate a 360DW, and at high enough spin current density will annihilate it. However, our experiments showed annihilation after only a small translation. The limited current-driven motion of the 360DW is attributed to the anisotropy from Co and extrinsic pinning from edge roughness. This was confirmed by measurements of current-driven motion of 180DWs in the same sample. Ten identical 200 ns current pulses were injected at voltages of +2 to +6 V (the highest voltage led to damage to the sample), but the 180DW was not translated. This suggests that DWs are pinned in the Co nanowires [34], and the current therefore annihilated the 360DW without moving it.
To assess the role of edge roughness, simulations (at zero temperature) were performed for Co nanowires with the same random anisotropy as described above as well as with an edge roughness amplitude 3% of the average wire width, produced by removing cells from the side of the wire randomly. Both 360DWs and 180DWs were only able to move by < 100 nm when a current density of5.3 10 12 A m −2 was applied. On increasing the current density to7.1 10 12 A m −2 , the 180DW translated further while the 360DW was annihilated after an initial »100 nm motion. This shows the importance of the edge properties on the motion of the DWs.
The experimental results show that current pulses provided an effective method for annihilating the 360DW. It required −700 Oe to annihilate a 360DW in the 80 nm wide Co sample but only +150 Oe to move a 180DW. For the current pulsing, annihilation of the 360DW occurred at 4 V pulse amplitude but moving a 180DW required at least 6 V. The joule heating during current pulsing may contribute to destabilizing the wall, but the temperature decreased too quickly to enable an accurate measurement [32]. We estimated above that the temperature increase would be ∼36 K based on the results in [33,35], which is also consistent with a measurement based on resistance change [36].
The modeling illustrates the different 360DW annihilation mechanism between using current pulses and using external field, making current pulses particularly effective in 360DW annihilation. Figures 6(a) and (b) show snapshots of the simulated 360DW annihilation processes driven by field and current in a 100 nm wide and 10 nm thick wire, using the same parameters as in figure 2. A cell size of (2 nm) 3 was used in this set of simulations. In figure 6 the 360DW develops a trapezoidal shape with the narrower side at the bottom of the figure. In the field-driven annihilation process, the field pushes the two component 180DWs together and when they are close enough the 360DW is annihilated starting from its narrower edge. On the contrary, in the currentdriven annihilation process, the current translates the 360DW, which moves with an oscillatory motion and becomes unstable, eventually closing up from the narrower edge. During the annihilation process, the exchange energy provides a barrier for annihilation. At the critical annihilation field of 320 Oe, the maximum exchange energy was´-1.24 10 J, 17 while at the critical annihilation spin current velocity of = u 180 m s −1 (corresponding to a current density of =J 6.3 10 12 A m −2 ), the maximum exchange energy was onlý -0.78 10 J. 17 The difference points to the instability of the 360DW under current as a contributing factor to the annihilation process.
In summary, 360DWs were formed in both Ni 80 Fe 20 and Co wires with a range of widths. 360DW dissociation and annihilation were experimentally observed by AMR measurements in Ni 80 Fe 20 and by MFM measurements in Co nanowires, and the critical fields were determined. The experimental results were compared with micromagnetic simulations, both of which showed that field-driven annihilation requires several times larger field than field-driven dissociation, though the magnitude of the critical fields was higher in the simulations. The effects of current on 360DWs in Co were examined using MFM. Current produced a small translation of the 360DW then led to its annihilation at2.2 10 12 A m −2 , a current smaller than that required to translate a 180DW in a Co nanowire of the same width. The high fields required for translation are attributed to edge pinning in the Co, but the relatively low current required for annihilation is consistent with the lower energy barrier for current-driven annihilation compared to field-driven annihilation predicted by micromagnetic modeling. The modeling also predicts a different annihilation mechanism for current and field. These results provide experimental evidence for the formation and manipulation of 360DWs, which are important in the study of memory and logic devices based on both 180DWs and 360DWs.