Exploring characteristics of the corner sections of a domain wall trap nanostructure with the two-field direction method

A 2D polycrystalline permalloy domain wall trap nanostructure with a thickness of 20 nm was studied. The structure was alternatively designed and patterned using QCAD/L-Edit software and focused-ion beam technique. With this design, a magnetic domain wall can be created and propagated with a sequence of two-field directions in a Lorentz microscopy. The trap consists of two horizontal nanowires and three 90°-tilted ones. Each nanowire has an in-plane dimension of 200 × 1000 nm2. The trap corners were curved to allow a created domain wall that easily moves through the structure. A head-to-head domain-wall aims to create using a continuous field, this created wall can be propagated in the trap using a sequence of two-field directions. The designed trap was simulated using the Object Oriented Micro-Magnetic Framework software. Lorentz microscopy and simulation results indicate that the propagation of a domain wall is strongly affected by the precise roughness behavior of the trap elements. Domain wall pinning and transformation of wall chirality are sensitively correlated to the corner sections of the trap structure and field directions at a certain regime. Using the two-field direction method enables us to explore characteristics of the corner sections of the patterned trap nanostructure. This study is vital to fabricate an optimal nano-trap which supports a reproducible domain wall motion. This also suggests a useful method for the domain wall propagation using sequences of two-field directions. This work provides a better understanding of wall creation and propagation in polycrystalline permalloy curved nanowires which are of interest for concepts of nonvolatile data storage devices.


Introduction
Propagation of a magnetic domain wall (DW) in ferromagnetic nanostructures has attracted much attention in recent years. [1][2][3][4][5][6][7][8] The concepts of DW propagation are mainly integrated in various potential applications, i.e. magnetic logic gates and memory devices. 1,3,7,8 A number of parameters which directly affect the DW propagation/stability in such applications, i.e. temperature, structural dimension/geometry, DW propagation methods, wall types/chiralities. 2,[4][5][6][7][8][9][10][11][12] These parameters can be engineered to either allow or pin DW movements in those structures. 2,[4][5][6][7][9][10][11][12][13][14] To fabricate such devices for the real life applications, a further understanding of relative parameters that link to characteristics of DW motion is really important. As mentioned in our previous work and by other authors, a domain wall trap (DWT) structure and its characteristics were mainly studied. 2,4,[13][14][15] Among a number of DWT-like nanostructures which were investigated, a new geometry has been created in our previous work. 14 With this design, a single DW can be created at a certain location in the given structure, i.e. corners and/or nanowires, the created DW is then propagated in the structure using a two-eld direction method. 14 The composed geometry consists of two horizontal nanowires and three other 90 -tilted ones. Each nanowire has an in-plane dimension of 200 Â 1000 nm 2 . This structure partly proved that it has an ability to support a headto-head (H2H) DW that could be reproducibly moved in the alternative 90 -switching of two-eld directions, represented as a combination of blue and violet arrows in Fig. 1. Using this propagation method, the structure required small elds to propagate a created transverse DW (TDW) through the structure, i.e. 250 Oe (simulation) or from 12 Oe to 25 Oe (experiment). 14 Despite the trap thickness of 20 nm, 2 TDWs are oen found in the simulated structure using the Object Orientated Micro-Magnetic Framework (OOMMF) soware, 16 whilst vortex DWs (VDWs) are more oen appeared in the patterned structure. Hence, this work aims to discuss on experimental results observed from the given structure using the two-eld direction method with a variation of eld angle (AEq) around the two in-plane magnetization components (M x and M y ), also indicated in the inset of Fig. 1. The structure was directly fabricated and characterized using focused-ion-beam (FIB) and Lorentz transmission electron microscopy (LTEM) techniques, respectively. 14,17,18 Prior to each DW propagation, a continuous biased-eld or creation eld was applied with an unchanged angle of u ¼ 60 to the two horizontal nanowires, as shown in the inset of Fig. 1. This procedure aims to create a DW at the rst corner of the structure (C 1 ). A question remained from this structure is, why de-pinning elds (H depin ) required at the trap corners are different, particularly in the patterned structure. In other words, the potential energy landscapes at those trap corners can be experimentally explored with the two eld direction method, results of which will be discussed in the following sections.

Structural designs and simulations
A number of experimental methods have been used to create DWs in various nanostructures with different geometries. [19][20][21][22][23][24][25] Magnetic elds or electric currents with either continuities or pulses, were usually used to create/propagate DWs in such structures with/without protrusions. [26][27][28] One of those methods is, an injection pad was attached to one end of a nanowire. Using such injection pads, a single DW was successfully created. The nucleated DW however does not propagate uniformly due to the edge roughness behaviour of those structures. Such characteristics come from those restricted geometries which act as potential barriers/wells, a combination effect of those energy landscapes resists/allows the domain wall propagation to a certain degree. Some few structures with restricted dimension geometries were modied and investigated in our previous work. 14 Among those structures, a single DW has created and propagated quasi-uniformly through the DWT structure, as given in Fig. 1. To gain a better understanding of a correlation between structural properties and propagation eld directions, the DWT structure was designed and patterned using the QCAD/L-EDIT soware and FIB technique, respectively. 14 This tilting eld method is available in the modied eld emission gun LTEM (FEG LTEM-CM20). 18,29,30 This technique might provide a DW propagation eld range for each DWT corner, i.e. particularly at the trap curvatures linking the horizontal nanowires and the vertical ones, denoted as the 1st and 2nd nanowires, and the 1st, 2nd and 3rd legs, respectively. Domain wall pinning, de-pinning and transformation of wall chirality are also characterized. Fig. 1 and 2 show that a T/VDW can be created at the C 1 corner of the DWT structure even if the same creation eld is applied with an angle of u ¼ 60 . Formation mechanisms of these wall types are sensitively dependent on the initial stages of the OOMMF simulations. Such walls can also be created/ propagated using the Lorentz microscopy. 18,[21][22][23][24][25] Those simulation results were observed using the OOMMF soware where magnetizations in either side of the created DW were dened with different colours, i.e. the magnetization vectors pointing in the le-and right-directions were dened as black and red colours, respectively. 13 Herein, the OOMMF simulation results are based on the Landau-Lifshitz-Gilbert equations for the precession and damping of magnetization under an external magnetic eld. 2,16,[31][32][33] The precession dynamics of the Fig. 1 A domain wall trap (DWT) structure which consists of two horizontal nanowires and three other-90 -tilted ones, it was simulated using the OOMMF software. 16 Each nanowire has an in-plane dimension of 200 Â 1000 nm 2 and a thickness of 20 nm. This trap structure allows to create a single head-to-head DW (H2H-DW), and the created DW can propagate from the first nanowire to the second one using the two field direction method. 14 Results of which are discussed in the text. magnetization vector (M) around an external eld (H e ) can be expressed as, where, dM/dt is the time derivative of the magnetization, g 0 is the gyromagnetic ratio, and H e is an effective eld that relates to the total energy, E, of a ferromagnetic system with a volume (V), described by the following equation, The above relationship describes a continuous precession, however it does not account for a dissipation in energy. Such loss diminishes the precession of M under H e . A dissipation term is thus added into (1), and obtained, where, l is the damping parameter, M S is the saturation magnetization, and a is the damping coefficient (¼ l/gM S ). The During a simulation, the equation is re-evaluated for each spin-spin interaction until the system reaches an equilibrium state, i.e. stable or metastable state. Those states might achieve aer a number of iterations or simulation time. Therefore, a minimum value of the torque, dM/dt, was typically chosen, e.g. 10 À5 A (m s) À1 . The process of nding the equilibrium state is re-evaluated at each step of increasing the applied eld. For the permalloy sample, the OOMMF simulation can ideally include all atoms of the system. Computing power and time are however limited, the process of nding the equilibrium is therefore unachievable. Hence, the principle of OOMMF operation is that the magnetic system is divided into a set of discrete three-dimensional cells. Each cell of the mesh is considered as a spin unit with a magnetic moment, m i . The cell-size is an important parameter which strongly affects the outcome of a simulation, it is usually chosen close to the characteristic exchange length of the permalloy in order to obtain realistic results. [33][34][35] All simulations of this work used a cell-size of 5 nm, this size is comparable to the exchange length, l Py A is dened as the exchange stiffness constant and is temperature dependent. 36 The parameters used for the standard permalloy are, M S ¼ 8.6 Â 10 5 A m À1 and A ¼ 1.3 Â 10 À11 J m À1 . The damping parameter (a) becomes important when the magnetization dynamics is evaluated, a can be used between 0.01 and 0.3 for permalloy. 33,37 However, properties of the trap can be modied aer the deposition and patterning processes, 38-40 a higher a value was therefore used, a ¼ 0.5. Each OOMMF simulation output data le can be separated into three magnetization components, M x,y,z . MAT-LAB soware was used to calculate from OOMMF images directly. The image formation in MATLAB code is calculated using the following equation, 41 The above relation of the three magnetization components in the sample and microscopy parameters will be used to interpret the Lorentz image intensity of the DWT structure. 18,41,42 This was calculated for the linear regime of the TEM transfer function in Fourier space with de-focused value (D, defocus is the aberration where an image is out of focus) in the range of 0 and 160 nm, 0 # D # 160 nm. 41 Nevertheless, experimental results are largely concerned with the non-linear regime of D, e.g. D ¼ 3600 mm, this aims to improve the image contrast of Fresnel images. As assumed that the M z does not contribute to the Lorentz imaging contrast. The M x and M y components are mainly contributed to the Lorentz image intensity prole which is proportional to curl(M) z . 13,41 3 Experimental details

FIB patterning the DWT structure
The designed DWT structure was experimentally patterned using a Ga + FIB irradiation method. The FIB used herein was an FEI Â T NOVA NanoLab 200 DualFIB. 13,14,[38][39][40] The FIB patterning can be separated into two main steps: (1) a continuous 20 nm-thick Py lm was evaporated onto an electron transparent Si 3 N 4 TEM membrane using a thermal evaporator with the evaporation rate of 0.03 nm s À1 . 13,14,38 The TEM membrane consists of a 35 nm-thick amorphous Si 3 N 4 supported on a 500 mm-thick silicon frame with a 100 Â 100 nm 2 electron transparent window, obtained from TED PELLA, INC. 43 The evaporated Py lm thickness was controlled and monitored using a quartz crystal microbalance technique where a correlation between mechanical oscillation and resonant frequency was detected. The use of Si 3 N 4 TEM membrane allows the patterned structure which is directly characterized using the Lorentz microscope. 18 (2) The FIB irradiation technique for the DWT structure patterning is fully available in the Kelvin nanocharacterization centre at the University of Glasgow. With this method, the patterned DWT structure was simply isolated from the continuous 20 nm-thick evaporated Py lm, 40,44 as described in Fig. 4.
In the FIB patterning process, each pixel in the irradiated area can receive the same dose, 17 a 0% ion-beam overlap is oen used for patterning, Fig. 4(a). The ion-beam overlap condition can be varied between 0% and 50% to obtain a smoother edge roughness. Prior to FIB irradiations, the milling area was redened using the edge-stream program. This aims to trace out the edge prole of the patterning structure with vector scanning strategy. Such jobs allow the milling area around the patterned DWT structure process with a single/multiple cut. Depending on the size of milling area which will be removed, various input-parameters for the FIB patterning are dened accordingly, i.e. FIB working screen location, dwell time, ionbeam current, pixel overlap/size, sputter rate, milling depth.
The Ga + ion beam current of 9.7 pA was used, this is equivalent to the ion-beam diameter of 10 nm. A longer total dwell time with multiple passes oen uses to obtain smooth edge proles rather than using a single pass with a long dwell time. 39,44,45 Depending on each research direction, patterning conditions can be used differently to obtain expected results.
A number of effects have been investigated on thin ferromagnetic lms using FIB irradiation. 17,39,40,44 However, we simply used the FIB technique with the Ga + ion beam to isolate the designed DWT structure from the continuous Py lm, and to obtain a higher edge-prole quality with the 50% ion-beam overlapping. We used the patterning time for the rst cut was around a minute to avoid beam-dri issues. As an example, a FIB-SEM image of the patterned DWT structure is given in Fig. 4(b). Based on the FIB-SEM image contrast, effects of redeposition can be visualized at the along edges of the patterned structure. Magnetic properties of the trap was characterized with the Fresnel imaging mode of the FEG-LTEM Philips CM20 microscope, 13-15,18,22-25 D ¼ 3600 mm was used for all measurements. To reduce charging effects during the FIB irradiation and TEM imaging acquisition, a very thin conducting gold layer of 5 nm was deposited to the backside of Si 3 N 4 TEM membrane using another sputtering deposition technique with a 99.99% purity-gold target. 22,23

Magnetizing experiment
The magnetic properties of the patterned DWT structure were characterized using the Philips CM20 FEG-LTEM/STEM. The technique has been modied for advanced magnetic imaging purposes. 18,41,45,46 With this technique, the sample is situated between the upper and lower pole-pieces of the objective lens. This means that the specimen is immersed in a magnetic eld strength of z20 000 Oe, this eld aligns parallel to the optical axis of the microscope. Such eld strength is sufficient to destroy the magnetic state of most samples. The objective lens of the microscope is usually switched off. Two additional minilenses are therefore used to replace functions of the objective lens, and those lenses create a eld-free environment for the imaging modes of magnetic samples in both Fresnel and differential phase contrast modes. 18 The electrons extracted from the FEG source of a Lorentz microscope pass through a thin magnetic foil. The emergent electrons are deected by the Lorentz force which produced by the magnetic eld within and surrounding the Py nanostructure, as described in Fig. 3. Therein, if t and B S (B S ¼ m 0 M S ) are alternatively the specimen thickness and the saturation induction of the magnetic material, the deection angle (b L ) can be expressed as, b L ¼ (eB S lt/h), where e ¼ À 1.602 Â 10 À19 C is the electronic charge, h ¼ 6.626 Â 10 À34 J s is the Planck constant and l ¼ 2.51 pm is the electron wavelength in the case of accelerating voltage, V FEG ¼ 200 keV. 18 The Lorentz lens is defocused by values of AE D in the Fresnel imaging mode, either under-focused (+D) or over-focused (ÀD) in respect of the focal plane, resulting magnetic contrast arises in the Lorentz image, as seen in Fig. 3. This hints that if the deected electrons are infocused, no magnetic contrast in the Fresnel image exists. As shown in the inset of Fig. 3, when an electron beam is transmitted through a thin ferromagnetic Py structure which consists of a 180 -domain wall. 18 The transmitted electron beam is deected by the Lorentz force with b L , this force deects the electrons from neighbouring domains in opposite directions, i.e. both sides of a created TDW. The domain wall appears as bright and dark bands against the neutral grey-background, as seen in the bottom-right corner of Fig. 3. Dark fringes appear along the DWT edges which due to the transition between magnetic and non-magnetic materials. 18 A simplied schematic drawing of the in situ Lorentz TEM measurement using a continuous eld, 18 at which a thin Such characteristics will be used to interpret experimental Fresnel images of the Py DWT structure. The imaging contrast arises from the magnetic ripple background appears as a grey band with dark and white boundaries on either side, as seen in the bottom-right corner. Fig. 4 (a) A simplified schematic drawing of the FIB irradiation method which describes the moving path of a 10 nm-diameter ion-beam during a FIB patterning process using the edge-stream program. Those ion-beam spots are indicated by a series of grey-solid-circles. We assumed that the ion-beam spots irradiated on the continuous Py film that have no overlaps (0% ion-beam overlapping). (b) A FIB-SEM image of the Py DWT structure which was patterned by the FIB irradiation with 50% beam overlapping. 17,39,40,44,45 specimen is mounted in the TEM sample rod, as shown in Fig. 5. The rod can be tilted an angle (f) to introduce parallel and perpendicular eld components, H k and H t . The sample is magnetized by applying a DC eld (H) produced by the minilenses/twin lens, and the eld strength can be controlled by adjusting the electric current injected to the objective lens coils. The sample plane is usually oriented to the horizontal plane, the 0 -tilted stage. This means that the objective lens eld is perpendicular to the sample plane, no eld applies to the horizontal plane. When the specimen plane is titled with f, the eld component in the horizontal plane, H k , can be expressed as, H k ¼ H sin(f). The maximum eld value can be achieved at the 90 -tilted stage. The maximum magnetic eld can be produced by the twin lens of the Glasgow LTEM is of 7000 Oe.

Results and discussion
A bright eld TEM (BF-TEM) image of the DWT structure patterned by the FIB irradiation method is given in Fig. 6(a), at which the width of nanowires was measured around (200 AE 5) nm. This value is comparable to the simulated one. As also seen from the BF-TEM image, some grains denoted as darker and brighter particles appear along the DWT edges. This indicates that the patterned DWT structure was affected by the irradiation processes of the FIB fabrication. Such imperfect behaviour of the edges induces DW propagation through the DWT structure under the two eld-direction method. 13,14 De pinning eld strength (H depin ) at each corner of the DWT structure is particularly emphasized. The constant procedure used herein is, the unchanged eld of 7000 Oe was applied about the angle of u ¼ 60 with respect to the easy-axes of the two horizontal nanowires, as described in Fig. 1 and 2, at which either TDW or VDW can be created in the simulated structure, whilst a VDW was experimentally nucleated at the C 1 area, as seen in Fig. 6(b). The chirality of created VDW sensitively depends on the eld strength/angle applied to the structure and structural properties of the C 1 corner, such effects were partially investigated by other authors. 15,22 We discussed a part of our observations with both simulation and experimental results using a sequence of two eld directions (H x and H y ). 14 Using the combination of those eld components, a created VDW was successfully propagated from the rst to second nanowire. The de-pinning eld required to propagate a DW through the DWT corners is more reproducible in the simulation results with the 0 -tilted eld, while it is less in the patterned structure. To understand characteristics of DW movements under the two-eld direction method with a variation in propagation eld directions (AEq) at each DWT corner, as illustrated in the inset of Fig. 6(b). This hints that not only the two-eld directions apply parallel to the horizontal nanowires and the vertical ones, however the eld direction at each sequence also varies, i.e. in a range of AE50 . Such experimental procedures can indirectly explore the role of each DWT corner at which the four corners of the patterned structure are considered as four pinning points. De-pinning elds of those corners (H depin ) as a function of eld angles/directions (q) in the forward process are plotted for the C 1 , C 2 and C 3 corners, as given in Fig. 7(a-c). Such relationship was also simulated using the OOMMF soware for the C 1 corner of the designed DWT structure, as shown in Fig. 7(d), for a comparison. Fig. 7(a-c) show the experimental results of de-pinning eld values (H depin ) as a function of eld angles (AEq) where the depining elds at a certain corner relate to the energies which need to push a created/propagated DW out of the C 1/3 corners. As seen in the relations between H depin and AEq (H depin -q) that are entirely asymmetric on both sides of the 0 -eld angle. This asymmetric behaviour might belong to the dependence of depinning elds on a combination effect of the energy landscape at each corner and the local spin conguration inside the created DW in respect of the eld direction and/or the VDW chirality. 21,22 However, the external elds required to de-pin the   Fig. 1 and 2. The created VDW was pinned in the first corner (C 1 ) of the structure, similar as a particle or an entity confined to a potential well which is created by the C 1 corner geometry. To propagate the pinned VDW through the structure, this VDW should be de-pinned out of the corner by a propagation field, the so-called depinning field, H depin , as discussed in the text. created/propagated TDWs in the simulated structure at the C 1 corner in the negative eld directions (Àq) are slightly lower than that obtained in the positive ones (+q). As discussed, the AEq dened as the eld directions oriented to the le-and rightsides of the horizontal and vertical nanowires, as already indicated in Fig. 6(b). The discrepancies of those de-pinning eld values on both sides of the parallel eld direction (the 0 -tilted eld) might originate from the spin conguration of the created/propagated DW and the precise location of the DW at each corner.
The trend of experimental H depin -q data points, Fig. 7(a), is consistent with the simulated ones, Fig. 7(d). A small difference in those curves at the negative angle (Àq) might come from the initial stages of those DWs. The wall created at the C 1 corner of the patterned structure is a CW-VDW, Fig. 6(b), whilst it is a TDW in the simulated one. Besides, the domain wall energy landscapes at the C 1 corner are different between the simulated and patterned structures where effects of the edge roughness are incomparable. The de-pinning elds of those created walls at the C 1 corner with q ¼ 0 are also different, as compared the simulated values to the experimental ones. These variations might also come from thermal effects that were excluded from the simulation, while the experiment was realized at room temperature. Moreover, other parameters could be included in a simulation, i.e. pixelation, re-deposition, structural surface, residual eld in the Lorentz TEM, quality of the deposited Py lm.
When the created DW moves to the C 2 corner, it is then propagated to the C 3 under the second eld direction (H y ), the de-pinning elds as a function of eld angles (q) are given in Fig. 7(b). The H depin -q curve shows a new trend which differs to that obtained from Fig. 7(a). This hints that the de-pinning eld strongly relates to the local spin conguration at an individual area and the DW chirality changed on reaching the C 3 corner. 14 The propagated DW at the C 3 continuously moves to the C 4 corner with the rst eld direction (H x ), Fig. 7(c). A difference in those cases, Fig. 7(a and b), is that the propagated DW at the C 3 area was unstable when the rst eld direction applied with q > +10 , a couple of data points are therefore excluded from Fig. 7(c).
Based on the discussed results, using a sequence of the two eld directions (H x + H y ) with different eld angles (AEq), a created DW successfully propagates from one end of the rst nanowire to another end of the second one. Each data point of Fig. 7(a-c), was calculated from ve different measurements with the same condition, i.e. u, q, the creation eld strength of 7000 Oe. The potential energy landscapes/proles of those corners/curvatures were indirectly explored with various characteristics, i.e. H C1 depin ¼ 11.8 Oe, H C2 depin ¼ 21 Oe, H C3 depin ¼ 24 Oe. These experiment values belong to the created CW-VDWs propagated with the 0 -eld, whilst the simulation value of H C1 depin ¼ 250 Oe belongs to the created TWD. Moreover, the VDW chirality was also changed during the propagation process. 14,22,27 Such changes relate to magneto-static effects, this leads to DW distortion, results in reducing the total energy of the Py system. This is similar to each created/propagated DW which can be conned to potential wells where a combination effect of shape anisotropies and magneto-static energies at those patterned DWT corners. The characteristics of each DWT corner, for examples, edge roughness, potential energy landscapes, domain wall spin congurations, were indirectly explored using the two-eld direction method with a variation of AEq in the forward process. In principle, the DW propagated to the C 4 corner which could be driven back to the C 1 via the reversal process of the two eld direction method. However, the DW propagation in the reversal process is less reproducible than that obtained in the forward one. Such discrepancies might result from the propagated DW positions in the forward and reversal processes are somehow different. Moreover, the geometrical parameter of the trap is changed in respect of the eld directions in the forward and reversal processes.

Conclusions
The DWT structure consists of ve Py nanowires which was patterned using the FIB irradiation technique. Propagation behaviour of a DW created in the DWT structure was characterized with the Lorentz microscopy and its associated techniques. Moreover, with the switching of 90 -two-eld directions, DW propagation in the designed DWT structure was systematically studied by means of the OOMMF simulation. Propagation characteristics of the created TDW in the simulated structure are reproducible with both forward and reversal processes using the 0 -tilted propagation elds. Characteristics of DW movements at each corner of the patterned structure were particularly characterized with different eld angles/ orientations (AEq), as compared to the horizontal plane. A combination of those eld directions was mainly investigated, we assigned that a few dominant parameters affected the DW propagation, i.e. edge roughness, potential energy landscapes, domain wall spin congurations, geometrical parameters in respect of eld directions. Based on the experimental observations, we also found that the de-pinning elds required at each corner are different in the patterned DWT structure. Such differences mainly come from the local spin conguration in respect of the applied eld direction at a particular location of the structure. This leads us conclude that DW pinning and transformation of wall chirality are sensitively correlated to edge roughness and/or structural geometries at a certain area. This hints that effects of shape characteristics and local spin congurations at the curved sections particularly play a crucial role. Our results contributed to a road map of nding a nanostructure which is suitable for the eld driven DW motion between two straight nanowires linked by another one using a sequence of 90 -two-eld directions, this is also of interest for concepts of high-tech applications.

Conflicts of interest
There are no conicts of interest to declare.