Tailoring magnetic anisotropy gradients by ion bombardment for domain wall positioning in magnetic multilayers with perpendicular anisotropy
© Matczak et al.; licensee Springer. 2014
Received: 9 May 2014
Accepted: 23 June 2014
Published: 13 August 2014
Graded anisotropy magnetic materials possess a coercive field changing laterally with position. A simple fabrication procedure to produce such an anisotropy gradient in a polycrystalline Au/Co layer system without lateral thickness variation and with perpendicular magnetic anisotropy, prototypical for a large variety of thin film systems, is shown. The procedure uses light-ion bombardment without the use of a mask. Magnetization reversal in this polycrystalline layer system takes place by unidirectional movement of a single domain wall only in regions with larger anisotropies and anisotropy gradients. In this anisotropy/anisotropy gradient regime, the domain wall is oriented perpendicular to the coercive field gradient, and it can be positioned along the gradient by an appropriate magnetic field pulse. For smaller anisotropies/anisotropy gradients, the natural anisotropy fluctuations of the polycrystalline layer system induce magnetization reversal dominated by domain nucleation.
75.30.Gw; 75.70.Cn; 75.60.Ch
KeywordsPerpendicular magnetic anisotropy Ion bombardment Domain walls
Magnetic domains in uniform layers with perpendicular magnetic anisotropy (PMA) take various shapes (cylindrical, labyrinth, maze, dendritic) that indicate the lack of preferential direction within the plane of the layer (see, e.g., [1–4]). Furthermore, the propagation velocity of domain walls (DWs), in a uniform field perpendicular to the layer plane, is isotropic. In contrast, in films with a lateral PMA gradient, it has been shown that magnetization reversal in a perpendicular field may occur by unidirectional propagation of a DW parallel to the gradient of the coercive field (HC) towards positions with higher values of HC[3, 5, 6]. This feature has the potential to be used for a controllable motion of the DW by applying a uniform external field , for wall pinning at defined locations [7–9], or for wall injection , with a variety of applications, like, e.g., the transport of magnetic beads by the moving stray field trap of a moving DW [10–14], for fluid mixing by moving particles [11, 12, 14], in sensors registering maximum values of varying magnetic fields , or in mass memories of ‘shift register’ type [16, 17]. If it is possible to fabricate a flat material system with an anisotropy gradient along one coordinate axis with a negligible gradient along the other lateral coordinate, a controlled displacement of a straight DW would become feasible by uniform magnetic field pulses, avoiding complicated external field configurations (fields with special gradients, crossed perpendicular and in-plane fields, see, e.g., ). For a controlled positioning of a straight DW by an external magnetic field, the range of anisotropy of the material system and the gradient along a given direction are the essential characteristics . The requirements on these two parameters are different depending on whether a pinning at a precise position (in the nm range) of the DW is of key importance or whether the displacement of a single straight DW in a given direction over a relatively long distance (in the sub-mm range) is essential. A reproducible DW pinning occurs when the change of PMA takes place on a distance δ much shorter than the width w of the domain wall . The pinning field Hpin is then proportional to the difference of anisotropies Keff,1, Keff,2 at the borders of the graded area: . If, however, the anisotropy gradient extends over a distance much larger than the DW width, the pinning field approaches zero. Nevertheless, a DW in such a system can be displaced for defined distances by pulses of a homogeneous external magnetic field, as was observed for (Co/Au)3 layers  possessing an anisotropy gradient over a distance larger than the DW width. In these latter experiments, however, there have been indications that the magnetization reversal in areas with weak PMA (small HC; Figure three in ) does not take place by propagation of a single DW only, but also by domain nucleation.
In the present contribution, we will first describe a simple method to fabricate the mentioned graded PMA in a polycrystalline Co/Au layer system by a special procedure of kiloelectronvolt light-ion bombardment subsequent to the deposition of the layer system. These prototype polycrystalline graded PMA layer systems are used to investigate how their natural PMA fluctuations influence the magnetization reversal, and under which conditions, the unidirectional propagation of a domain wall is observed. The propagation of DW is investigated for increasing value of magnetic field pulses of 1-s duration.
Move the sample to a position where the ion beam just misses the sample. The position of the ion beam center xcb in a coordinate system with x = 0 defining the left edge of the sample is then at xcb = −1 mm. Move then the computer-controlled sample stage along the − x-direction at constant velocity and reverse the movement, when the ion beam center is at xcb = +1 mm, i.e., at a position when the 2 × 2 mm2 ion beam bombards the whole x range from x = 0 to 2 mm. Move again the sample backward with a constant velocity to the starting position. With this first track, a constant fluence gradient dF/dx along the x-direction within the first 2 mm of the sample is achieved. After this first track, move the sample stage relative to the ion beam center from its starting position (xcb = −1 mm) to xcb = +3 mm where the movement again is reversed. The reversal point is chosen such that it is displaced relative to the reversal point of the first track by one width of the ion beam. The stage movement of the second track adds a constant fluence of 2 × Ftrack to the already existing gradient within the first 2 mm in the x-direction and causes the same gradient in the x-direction within the next 2 mm as the one fabricated in the first 2 mm by the first track. By subsequent tracks, increasing each time the travel of the stage by one width of the ion beam, the cumulative fluence applied to the sample results in a constant gradient in the x-direction within the bombarded stripe. The experiments were carried out with a home-built He+ ion source set to 10-kV acceleration voltage with low divergence . A 2 × 2 mm2 square aperture cuts out a portion of the beam displaying an approximate square ion flux cross-section, with a plateau-like flux j(x, y) = dN(x, y)/(dt · dA) (N = number of He ions, t = time, A = area through which the He ions flowed) in the middle of the square and decreasing flux at the four edges of the square (Figure 1b). Two stripes (stripe 1 and stripe 2) were bombarded with two different plateau fluxes j applying the sample movement scheme described above. Fluence profiles F(x,y) = ∫j(x, y)dt were calculated for a 12-mm-long stripe which agreed, within experimental error, with that expected from the ideal rectangular profile. For both stripes, the relative fluence profiles F(x)/Fmax are the same (Figure 1a). The areas of the two stripes were magnetically characterized at room temperature by polar magneto-optical Kerr effect (P-MOKE). Local hysteresis loops (diameter of laser spot on the sample surface - 0.5 mm) were measured with a magnetic field sweep rate of 1.4 (kA/m)/s. The measurements were performed as a function of the x-coordinate with the laser beam center in the center of the bombarded stripe. For comparison, loops of unbombarded areas were also measured. After the six tracks, the cumulated maximum fluence Fmax for stripe 1 was 1.06 × 1015 He+/cm2 and for the second stripe 5.03 × 1014 He+/cm2. The stage velocity was chosen for an average fluence gradient of dF/dx = 8.8 × 1013 (He+/cm2)/mm for stripe 1 and 4.4 × 1013 (He+/cm2)/mm for stripe 2 and maximum fluences based on previous investigations [19, 21]. Due to the flux decrease of the ion beam at the edges of the rectangle, also a fluence gradient along the y-direction is observed. This gradient changes with the x-coordinate between dF/dy (x = 0 mm) = 7.5 × 1014 (He+/cm2)/mm to dF/dy (x = 8 mm) = 2.5 × 1014 (He+/cm2)/mm. At small x-coordinates, gradients along the y-direction are roughly 1 order of magnitude larger as the ones along the x-direction.
Results and discussion
The measurement of hysteresis loops along the gradient in the y-direction (at the stripe border) has not been carried out as the observation area would encompass regions of significantly different HC.
The nonlinearity of HC(x) and HC(F) results probably from a distinct difference in the character of magnetization reversal in areas of small and large fluences (high and small HC values) (see the discussion of Figure 3). It should be noted that the Keff dependence on the fluence is not linear .
This process is shown in more details in Figure 3 whose panel (a) displays wall propagation in the x-direction and panel (b) in the y-direction, and panel (c) shows the mean DW position as a function of field pulse amplitude. The x-coordinate of area B (indicated in Figure 4) was chosen such that the DW propagation in both x- and y-directions could be measured within the same field range. This implies that the applied He+ ion fluence range is similar for both discussed areas. The interpretation of the magnetization reversal mechanisms deduced from the magnetic structure images of the two areas A (small coercive field gradient = small gradient in average anisotropy) and B (high coercive field gradient = high gradient in average anisotropy) after the application of consecutive external field pulses with increasing magnitude Hext will be discussed for graded anisotropy areas A and B separately. For the low anisotropy gradient area A, magnetization reversal starts for small Hext in the area with the lowest HC, where Hext ≈ HC. This area corresponds to the area bombarded by the high ion fluence. There, many small domains nucleate as seen in Figure 3a (uppermost panel). Their density decreases as HC increases along the x-coordinate of the stripe.
For this low external field, no straight DW is present. In contrast, a gradual transition from one to the other magnetization state by a gradual increase of the density of nucleated domains and their coalescence over an x-coordinate range Δx is observed. In the areas of significantly reduced PMA (low HC, high F), domain nucleation is the dominant magnetization reversal mechanism. The formation of a multidomain state is more likely the closer the fluence causes a perpendicular anisotropy decrease close to the magnetization reorientation transition . Domain nucleation is a signature of inherent lateral fluctuations of the effective anisotropy [2, 28, 29] in a material with small average anisotropy such that the energetic cost of DW formation is small.
In Figure 3a, the lowermost four panels, a gradual formation of a single nearly straight DW with only a few additionally nucleated domains is obvious for magnetic field pulses of higher Hext, i.e., in areas bombarded with lower fluences and therefore having higher average HC. In a material with laterally fluctuating but in average higher Keff, the energetic cost of DW formation (∝l√KeffA, A is the exchange stiffness) is higher such that the total lengths l of the domain walls in the system will be minimized, leading preferentially to a single straight wall. Therefore, the results shown in Figure 3a indicate that suitably high values of HC in the whole graded anisotropy material system are a necessary condition for the magnetization reversal by the propagation of a single DW. The distinct difference in magnetization reversal for areas bombarded with high and low fluences (i.e., characterized by weak and strong anisotropy) is probably responsible for the nonlinear dependences presented in Figure 2.
In Figure 3b, the magnetization reversal in an area with high anisotropy gradient is imaged. For low Hext (Hext < 21.9 kA/m), the magnetization reversal also takes place by small domain nucleation. However, the coalescence of the domains and formation of a single DW is observed at smaller Hext as in area A. Therefore, in contrast to the low anisotropy gradient area A, the reversal process occurs virtually in the whole presented Hext range by the propagation of a single, nearly straight DW. The realization of the propagation of a single, straight DW in the direction perpendicular to the HC gradient is thus easier in systems with larger gradients. In the high gradient material, the influence of intrinsic fluctuations of anisotropy is hardly visible. It should be remarked that the distance travelled by the DW is in the tenths of millimeter range as required for magnetic particle manipulation . The fact that displacements of DW (ΔxDW, ΔyDW), in the range of small fluences, are proportional to the amplitude of the magnetic field pulse is a significant advantage of a system with HC gradient (see Figure 3c). This circumstance and a significant (about tenfold) difference of the displacement range of the DW in areas with different HC gradients (areas A and B) indicate that DW propagation in our system progresses differently than in areas that were not bombarded. The results shown in Figure 3 indicate, in our opinion, that the coercive field gradient limits thermally activated DW propagation, wherein the effect is stronger the higher dHC/dx(y). This is of practical importance because it can be used for precise positioning of a DW with pulses of uniform magnetic field. To quantitatively describe DW motion and to specify its regime of propagation in layered systems with an anisotropy gradient, additional measurements are required. However, based on Figure 3c and remembering that pulse duration equals 1 s, we estimated the domain wall velocity vA > 0.6 mm/s within area A and vB > 0.05 mm/s within area B in the fields 24 < Hext < 32 kA/m. Thus, we can assume that DW propagation most probably occur in the ‘depinning’ regime, i.e., the one intermediate between creep and viscous flow regimes .
The images of the domain structure shown in Figures 3 and 4 exhibit only two contrasts (gray levels) indicating that the magnetization reversal in both Co layers takes place simultaneously by the propagation of two parallelly moving DWs in the two ferromagnetic layers which has been achieved by the present choice of the Au layer thickness. This effect, in contrast to the independent magnetization reversal of the individual layers observed in , is important for ‘magnetic bead transport’ as much higher stray fields over DWs can be fabricated.
In summary, a dedicated scheme for magnetic multilayer bombardment with light ions was introduced enabling to realize a defined fluence gradient for bombardment of samples along a given coordinate without necessitating a wedged ion stopper layer. This bombardment scheme was applied to Au/Co/Au/Co/Au multilayers, where it allowed to create in both Co layers an approximately constant gradient in perpendicular anisotropy along a preset direction. This scheme allowed a systematic investigation of the conditions to generate in both ferromagnetic layers straight domain walls which can be simultaneously moved and reproducibly positioned by external field pulses of defined amplitude. Quasi-one-dimensional walls can be generated in areas of relatively high HC and dHC/dx. For small HC and dHC/dx, magnetization reversal is dominated by domain nucleation caused by lateral anisotropy fluctuations in the layer system. If dHC/dx is larger than these inherent lateral HC variations, the domain wall becomes straight. These findings are the basis for generating and controllably moving straight domain walls in laterally graded anisotropy layer systems for magnetic bead transport.
perpendicular magnetic anisotropy
polar magneto-optical Kerr effect.
This work was partially supported by the Polish Ministry of Science and Higher Education under the Grant IP No. 2011 028371 and by the SYMPHONY project operated within the Foundation for Polish Science Team Programme co-financed by the EU European Regional Development Fund, OPIE 2007-2013, and National Science Centre Poland under HARMONIA funding scheme for international research projects: decision No. DEC-2013/08/M/ST3/00960. PK is also supported by the Foundation for Polish Science.
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