X-ray photoemission electron microscopy studies of local ...

PHYSICAL REVIEW B 85, 184427 (2012)

X-ray photoemission electron microscopy studies of local magnetization in Py antidot array thin films K. J. Merazzo,1,* C. Castán-Guerrero,2 J. Herrero-Albillos,2,3 F. Kronast,4 F. Bartolomé,2 J. Bartolomé,2 J. Sesé,5 R. P. del Real,1 L. M. Garc´ıa,2 and M. Vázquez1 1

2

Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain Instituto de Ciencia de Materiales de Aragón (ICMA) and Departamento de F´ısica de la Materia Condensada, Consejo Superior de Investigaciones Cient´ıficas—Universidad de Zaragoza, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain 3 Centro Universitario de la Defensa, Ctra. de Huesca s/n, E-50090 Zaragoza, Spain 4 Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Albert-Einstein-Str. 15, 12489 Berlin, Germany 5 Instituto de Nanociencia de Aragón, Universidad de Zaragoza, C/Mariano Esquillor s/n, 50018 Zaragoza, Spain (Received 16 February 2012; published 25 May 2012) Permalloy antidot thin films were grown by sputtering onto anodic alumina templates, replicating their hexagonal order inside micrometric geometric domains. The advanced high-spatial and sensitive x-ray photoemission electron microscopy technique under an applied magnetic field has enabled magnetic domain structure imaging and quantitative hysteresis loop analysis inside nanoscale regions with geometric order and at border regions. The study has been complemented by vibrating sample magnetometry and magneto-optic Kerr effect measurements. The magnetization process is clearly determined by the geometry characteristics of the antidot arrays. Inside geometric ordered domains, the strength of effective in-plane magnetic anisotropy depends on the antidot diameter–to–film thickness ratio, which determines the partial balance between stray fields generated by magnetic charges at the lateral surface of the antidots and those at the upper–bottom film surface. In addition, the border regions between geometric domains act as pinning centers for magnetization reversal and eventually generate a harder magnetic region. DOI: 10.1103/PhysRevB.85.184427

PACS number(s): 75.75.Fk, 75.30.Gw, 75.60.Jk, 75.70.Rf

I. INTRODUCTION

Nanoscale patterned magnetic films are envisaged for technological purposes profiting from the possibility of tuning the local distribution of magnetization in a controlled way. This makes them advantageous in comparison with their continuous thin film counterparts. Their applications range from magnetic recording media1–5 to sensors6 and magnonic devices.7,8 Antidot arrays are thin films containing nanoholes arranged in a given symmetry. Knowledge and control of the magnetization reversal process9 is crucial for the development of these applications. The competition between the intrinsic and the shape anisotropy, together with the local effects originated by the antidots, creates new scenery for engineering the magnetic properties of the thin films by tailoring the geometric parameters. Antidot arrays are currently fabricated by lithography techniques9–12 or using self-assembled, electrochemically grown templates.13–16 The latter technique is relatively simple and low in cost, without requiring any treatment (e.g., heat treatment or reactive ion etching). Such templates are highly reproducible and have attractive properties, such as a long-range porous area, in which the controlled pores’ diameters are a few tens of nanometers, and are hexagonally arranged within geometric domains that are micrometric in size. Besides, the total effective area is on order of square centimeters. Magnetic anisotropy in antidot films, either in or out of plane, can be tuned by suitable selection of geometric parameters, such as diameter, separation of the nanoholes, and film thickness. While there is broad documentation about the 1098-0121/2012/85(18)/184427(9)

magnetic behavior for lithographed17–19 antidots, there is still a lack of detailed studies on antidot arrays prepared following the ordering of precursor anodic templates. Specifically, antidot arrays of permalloy grown onto anodic aluminum templates have shown interesting magnetic properties.14 They lack crystalline and magnetoelastic anisotropies; consequently, their magnetic behavior is essentially determined by macroscopic in-plane anisotropy modified by the presence of local stray fields effects induced by the antidots. They can even show biphase magnetic behavior,20 in spite of being constituted by a single alloy component. The aims of this study were to deepen knowledge of the magnetization reversal processes of Py antidot arrays prepared onto anodic alumina templates and to determine the influence of tuning the geometric parameters, such as antidot diameter and film thickness. To investigate the magnetic behavior of these nanometricthick antidot films, we employed an advanced x-ray photoemission electron microscopy (XPEEM)21 with applied magnetic field capability. XPEEM, coupled with the x-ray magnetic circular dichroism (XMCD) technique,22,23 allows us to observe complex magnetic domain structures.24 In addition, this technique enables experimental determination of the magnetization reversal process with in-plane magnetic sensitivity, not only over a relative large area but also independently over different local geometric domains.25,26 The particular geometry and dimensions of the investigated samples represent real challenges, which have been overcome because of the XPEEM capability.

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©2012 American Physical Society

K. J. MERAZZO et al.


FIG. 1. (Color online) Hexagonal ordering within domains is observed in an antidot array with d = 62 nm and tP y = 10 nm as imaged by (a) SEM and (b) XPEEM. Some (dislocation-like) boundaries between domains and punctual defects are marked by (yellow) lines and circles, respectively. The nearly perfect hexagonal order inside a domain is observed in the inset of (a).

II. EXPERIMENTAL DETAILS ON SAMPLE FABRICATION AND MAGNETIC CHARACTERIZATION

Anodic alumina membrane (AAM) templates were prepared by a two-step anodization process27 in 0.3 M oxalic acid under a constant potential of 40 V, with a first and second anodization of 48 and 3 h, respectively. Template pores are self-assembled into hexagonal arrangement with the lattice parameter D = 105 nm28 and the pore diameter dP = 22 and 35 nm, when the temperature was kept at 0 ◦ C and 4 ◦ C, respectively. A subsequent etching treatment in phosphoric acid, 5% M/M at 35 ◦ C, led to controlled widening of the pores so that the final pore diameters of the templates used for experiments were dP = 22, 35, 48 and 65 nm. These membranes were then polished by low-angle ion milling to reduce the intrinsic AAM surface roughness with a reactive ion beam etch system RIB-Etch 160 electron cyclotron resonance. Permalloy thin films Py(Ni80 Fe20 ) were sputtered on top of the anodic alumina membranes, thus replicating the particular hexagonal ordered pattern of each template. This was performed in a homemade radiofrequency (RF) sputtering system at a working pressure of Pw ≈ 1.2 · 10−3 mbar and RF power of 60 W.29 Two series of antidot films were prepared with thicknesses of tP y = 10 and 20 nm, and a final 2-nm, thin Al capping layer was sputtered over the Py to avoid oxidation. The measurement of the diameters of the AAM and the antidot

arrays was performed by field emission–scanning electron microscopy (FE-SEM, FEI Nova NanoSEM 230 low-voltage high-contrast detector) imaging. As previously reported, the sputtering process leads to a reduction of the effective antidot diameter, because the sputtered material partly enters the upper part of the pores.29 Thus, the final antidot diameter of the investigated films is d = 19, 32, 45, and 62 nm and d = 16, 30, 43, and 60 nm for films with thickness tP y = 10 nm and tP y = 20 nm, respectively. The nearly perfect hexagonal order of the self-assembled pores in the anodic alumina template (lattice parameter D = 105 nm) extends to geometric domains with a micrometric area in the range of 1 to 3 μm2 .26,29 Figure 1(a) shows a FESEM image of a particular antidot film in which such ordered domains are observed. To better distinguish the dislocationlike boundaries between geometric domains, they are marked with lines. The inset shows an enlarged image inside one of the domains, where the hexagonal arrangement is nearly perfect. Figure 1(b) shows a XPEEM image with a field of view of ∼5 μm, where the nanoholes can be observed. The dislocations (lines) and defects (circles) are marked as in Fig. 1(a). The more relevant magnetic characterization was performed by advanced XPEEM. Images of the magnetic domains were obtained using the XPEEM equipment located at the Berlin Electron Storage Ring Society for Synchrotron Radiation (BESSY) II synchrotron facility in Berlin, Germany. Further details can be found in Refs. 30–32. The x-ray energy was tuned to the Ni L3 edge, and the data indicate no oxidation of the samples. To obtain magnetic imaging, two XPEEM intensity images are taken, left and right circularly polarized x rays, from which their difference in intensity divided by their sum results in the XMCD contrast. The intensity in the XMCD image is proportional to the projection of the magnetization to the incident x-ray wave vector, labeled the magnetization sensitivity direction (MSD). To identify its local orientation, magnetization with a parallel or antiparallel direction to the polarization appears in Figs. 4, 5, 8 red (dark gray) or blue (medium gray) in the XMCD image (color online), while magnetization perpendicular to MSD appears white. The normalization of each image with different polarization was made dividing by an image of the same area in a saturating magnetic field. The application of the magnetic field is crucial in this experiment for the observation of magnetic switching in the samples. The magnetic setup allows us to apply a magnetic field of up to 405 Oe without significant distortion or loss in resolution, and it is further described elsewhere.32

FIG. 2. (Color online) MOKE hysteresis loops of antidot films with thicknesses of (a) tP y = 10 nm and (b) tP y = 20 nm. 184427-2

X-RAY PHOTOEMISSION ELECTRON MICROSCOPY . . .


FIG. 3. (Color online) (a) MOKE hysteresis loop and (b) VSM magnetization curves of sample A.

XMCD images were taken in two magnetic configurations: at remanence after applying different magnetic fields and under an applied magnetic field during the measurements. Two sample holders were used. The first one allowed us to measure under a magnetic field up to 120 Oe yet apply up to 360 Oe during very short periods. The second sample holder enabled application of a maximum field of 135 Oe and measurement at remanence after applying a maximum field of 405 Oe. In both cases, the field is applied along the plane of the samples, and its maximum strength corresponds to the ideal case in which the sample is in the center of the sample holder. All images were taken in a field of view of 5 μm. Macroscopic experimental magnetic characterization was performed by vibrating sample magnetometer (VSM) using an ADE magnetic system (model EV7). Four kinds of magnetization curves were measured: (1) the magnetization vs. applied magnetic field (M-H), performed under a maximum in-plane applied magnetic field of 18 kOe; (2) the virgin magnetization curve, obtained after ac demagnetization and measuring the magnetization with increasing applied fields

from 0 to 5000 Oe; (3) the isothermal remanence measurement (IRM) curve, obtained after ac demagnetization and denoting the evolution of remanence after increasing the applied field step by step, which gives information on the irreversible processes; and (4) the reversible curve, calculated by the subtraction of the IRM from the virgin curve, which is linked to reversible mechanisms. The IRM and reversible curves are given in the percentages from which we can quantify the fractional relevance of reversible and irreversible magnetization processes; these percentages are calculated from the total magnetization value of the virgin magnetization curve. The magnetic characterization by VSM, being essentially macroscopic, averages out the geometric effect introduced by domains with different local hexagonal ordering (Fig. 1). Consequently, the averaged magnetization of the Py antidot arrays over AAM templates presents no effective shape anisotropy. Additional surface magnetic characterization was performed with a magneto-optic Kerr effect (MOKE) magnetometer under an in-plane applied field (600 Oe

FIG. 4. (Color online) For sample A, XMCD images of the magnetic domain structure (a)–(c) at remanence and (d)–(f) under the applied field (the outside arrow indicates the applied field magnetic field orientation, together with the corresponding color contrast for the MSD), and (g) a XPEEM image denoting the geometric domains of the samples, with indication of some dislocations and punctual defects. 184427-3



FIG. 5. (Color online) Hysteresis loop of sample A as deduced from XMCD images after applying a field of −405 Oe and then shifting the applied field to different values (blue curve). Also shown is the mirrored XPEEM curve (green curve).

maximum strength) in NanoMOKE equipment (Durham Magneto Optics). The hysteresis loops were obtained by the Kerr effect, where the Kerr signal is normalized to its maximum value. MOKE and XPEEM measurements are comparable in the sense that both represent a measure of the surface magnetization, with a penetration depth of ∼15 and 10 nm, respectively. Nevertheless, although both have a comparable field of view (the effective measured surface is ∼5 μm), the MOKE measures the averaged magnetization of the total hexagonal arrangement inside ordered domains. Meanwhile, the XPEEM has a spatial resolution of ∼20 nm, allowing us to obtain information inside the mentioned local geometric domains. III. EXPERIMENTAL RESULTS AND DISCUSSION

Figures 2(a) and 2(b) collects the MOKE hysteresis loops for the two sets of antidot array films with the Py thicknesses tP y = 10 and 20 nm, respectively. For the 10-nm-thick films, we observe increasingly noticeable two-phase magnetic behavior with increasing dP , which is deduced from the distinction

of two large irreversible magnetization processes (similar behavior was reported in Ref. 20) For thicker film samples, with tP y = 20 nm, we observe a single-phase behavior—except for the array of antidots with a greater diameter, which exhibit a two-phase behavior that is not so well defined. From a straightforward comparison of the hysteresis loops, we deduce that the geometric parameters of the antidot films fully determine the overall magnetic response. Thus, we proceed in the following to a deeper magnetic characterization by XPEEM for the two samples exhibiting clear biphase and single-phase behaviors: samples A (d = 62 nm, tP y = 10 nm) and B (d = 16 nm, tP y = 20 nm), respectively. Because the distance between antidots is fixed at 105 nm, the geometry of samples A and B can be characterized by an antidot film aspect ratio20 r = (d + dp )/2tP y , which takes the values r = 6.35 and 0.95 for samples A and B, respectively. A. Antidot arrays with a high aspect ratio

The MOKE effect hysteresis loop of sample A (r = 6.35) is observed in Fig. 3(a). As indicated previously, the type of the

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FIG. 6. (Color online) (a) XPEEMimage containing several geometric domains (the red arrows mark the orientation of the applied magnetic field, and the discontinuous lines show a particular the orientation defining the hexagonal order of the lattice). (b) Coercivity Hcx as a function of the angle between such orientation and the field (each value is marked with the corresponding domains on (a)).

two magnetic phases is deduced from the two large, irreversible magnetization processes ∼40 and 350 Oe, separated by a smaller-susceptibility intermediate magnetization process. Such irreversible jumps correspond to the total magnetization change for the soft and the hard phases, respectively, when magnetizing up to 600 Oe. Both reversal processes correspond to the same magnetic alloy, and the different magnetic behaviors should be ascribed to the different local magnetic regions induced by the presence of antidots. Figure 3(b) shows the virgin, IRM, and reversal curves, with their respective percentages. Comparative analysis of VSM and MOKE data allows us to confirm the following. Analysis of the IRM curve confirms that the two mentioned irreversible processes are completed at an applied field of ∼400 Oe, fully observed by MOKE. Nevertheless, reversible processes continue up to a much higher field of a few thousand oersted, reaching the approach to magnetic saturation. We also deduce that reversible processes have a higher contribution to the whole magnetization process.

To obtain the XMCD images, the sample is first magnetized under a field of −405 Oe applied in the negative direction (blue [medium gray] in the red–blue scale) and then taken to the magnetic state of study: (1) at remanence after applying a given positive field, increasing from 0 to +405 Oe, and (2) under a positive magnetic field applied during the measurements, from 0 to +135 Oe. The maximum applied field in the XPEEM experiments allows us to study the irreversible magnetization processes but not the final reversible approach to magnetic saturation. Figure 4 shows XMCD images corresponding to the magnetic domain structure at remanence [Figs. 4(a)–4(c)] and under selected values of the applied field [Figs. 4(d)–4(f)]. The differences in the magnetization between the images at remanence [Figs. 4(a)–4(c)] and those under the applied magnetic field [Figs. 4(d)–4(f)] enable us to identify the degree of irreversibility reached after the application of a given applied field. Figure 4(g) shows a XPEEM image at the L3 Ni edge of the same area, which depicts the topography with indication of geometry defects: dislocations (black lines) and punctual imperfections (black circles). A comparison between magnetic and topological images enables the correlation between magnetic and geometric domains. After applying a negative field overcoming all irreversibilities, the applied field is set to a positive value of 22.5 Oe at which the XMCD image [Fig. 4(d)] is taken. This image indicates that magnetization in a significant fractional volume of the sample has reversed its orientation (as deduced from the major red areas). In addition, a correspondence between magnetically reversed regions and geometric domains is found. The dislocation marked with a black line can be interpreted as a coordination site preventing the magnetic reversal. Thus, as the applied field is removed, at remanence [Fig. 4(a)], the magnetization is mostly blue, (medium gray) denoting that a significant fractional region inside those geometrically ordered domains has changed its magnetization direction, as well as denoting the regions with a softer magnetic character. Also, a given fractional volume has irreversibly reversed the magnetization in comparison with the initial (almost fully blue [medium gray]) negative, nearly saturated state. In this image, several marked defects act as nucleation sites for the reversal magnetization process. A similar comparison can be done for the case of an increased applied field, as shown in Figs. 4(e) and 4(f). An increasing positive applied field increasingly results in regions

FIG. 7. (Color online) (a) MOKE hysteresis loop of sample B. (b) VSM magnetization curves. 184427-5



with reversed “positive” magnetization (red). A comparison between images under an applied field and at remanence indicates that after removing the applied field, magnetization at remanence reverses in local regions (from red in the bottom to blue in the upper areas, Figs. 4(b) and 4(c)). For a 90-Oe applied field, the magnetization in Fig. 4(f) has not reached full magnetic saturation, and its difference with Fig. 4(c) denotes significant reversible rotations. Topological imperfections (marked in black in Fig. 4(g)) can be identified along the XMCD images, where the magnetization exhibits a significant perpendicular component to the x rays, indicated by white in Figs. 4(a)–4(f). From the comparison between these images, the defects can be understood as local pinning centers for magnetization reversal, thus determining the irreversible processes.33,34 These regions separating the geometric domains, with significant perpendicular magnetization, can be ascribed to the magnetically harder phase. In turn, inside the geometric ordered domains, magnetization reverses at a smaller field, so they can be ascribed to the magnetically softer phase mentioned previously. A quantitative analysis of each XMCD image can be performed to estimate the net magnetization under a given applied field by ascribing locally the corresponding magnetic moment. Integrating this value over an area (the whole field of view of 5 μm) enables the evaluation of corresponding hysteresis loops. Figure 5 shows the hysteresis loop of sample A obtained after quantitative analysis of individual XMCD images taken under an increasing applied magnetic field (blue curve). The symmetric curve (green curve) is the mirrored XPEEM curve for explanatory purposes. From the first XMCD image (corresponding to −135 Oe after applying a field of −405 Oe) to the second one (at nearly zero magnetization), the net magnetization changes drastically in color from blue to mix of blue, red, and white,

denoting the existence of regions with negative, positive, and perpendicular magnetization, respectively. The following images correspond to an increasing applied field: we observe a significant irreversible magnetization process ∼20 Oe, and then magnetization grows with more reduced susceptibility up to the maximum field at +135 Oe. The reversing magnetization at local regions mimics the geometric domains until magnetic saturation. A rough comparison between hysteresis loops obtained by XPEEM in Fig. 5 and those for VSM and MOKE measurements in Fig. 3 indicates that the XPEEM maximum applied field only enables the study of the irreversible magnetization process of the softer phase. Irreversible processes of the harder phase are attained by MOKE, and high-field reversible processes are only achieved by VSM. To analyze in further detail the magnetization reversal, we studied the local magnetization process of several geometric domains. The red arrows in Fig. 6 left show the orientation of the applied field, and the dashed lines indicate the nearest orientation of the hexagonal ordering inside each geometric domain that may be considered as a local shape anisotropy easy axis (e.a.). The distribution in orientation of such an axis results in a distributed local magnetic anisotropy e.a. From local hysteresis loops, we can obtain the local coercivity Hc of each domain, which is plotted in Fig. 6(b). The highest Hc corresponds to a parallel alignment of the magnetic field with the shape anisotropy local axis, and the lowest Hc corresponds to an effective in-plane hard axis at an angle of 30◦ . In Fig. 6(a), we can visualize how the local magnetic hardness depends directly on the lattice orientation. Finally, we compared Hc = 19.8 Oe in the XMCD hysteresis loop in Fig. 5 and the averaged value Hc = 19.4 Oe from Fig. 6 (Hc = (Hc1 + · · · + Hc7 )/7), demonstrating that the loop represents average magnetic behavior.

FIG. 8. (Color online) (a) Sample B with left circularly polarized x rays. (b)–(k) XMCD images taken at remanence after nearly saturating under +360 Oe and then applying the magnetic field Happl of (b) 0 Oe, (c) −2.04 Oe, (d) −10.04 Oe, (e) −13.76 Oe, (f) −22.16 Oe, (g) −27.04 Oe, (h) −47.88 Oe, (1) −56.72 Oe, (j) −64.6 Oe, and (k) −360 Oe. 184427-6



B. Antidot arrays with small-aspect ratio–XPEEM measurements and analysis

images. Region 3 is inside the geometric domain, while region 4 contains a dislocation-like defect border between two geometric domains. A comparison between these loops indicates that region 3 is magnetically softer, with Hc = 10 Oe. Region 4 is significantly harder, with Hc = 55 Oe, and contains two steps in its magnetization process, which can be ascribed to a magnetically softer region inside the geometric domain (with a large irreversible magnetization process at an applied field of H = 11 Oe) and to the magnetically harder border region between domains (with a large magnetization jump at 55 Oe). This two-phase magnetic behavior is averaged out when considering a sufficiently large area enclosing several domains and corresponding borders.

Sample B (r = 0.95) exhibits a different magnetic response, which the hysteresis loop [Fig. 7(a)] presents as a single irreversible magnetization process with coercivity of ∼27 Oe, roughly corresponding to the magnetically soft phase in the loop of sample A. Figure 7(b) shows the VSM reversal curves, with indication of the percentage of reversible and irreversible processes. The IRM curve has an important increase at low fields up to ∼60 Oe, where irreversible processes saturate. At higher fields, magnetization increases reversibly until approaching magnetic saturation. As deduced from the highfield region, reversible and irreversible processes contribute nearly equally to the whole magnetization process. For the XMCD images, the sample was nearly saturated under the maximum field of +360 Oe. Then, each image was taken in the remanence state after increasing the field in the opposite direction step by step until −360 Oe. Unlike for sample A, the maximum applied field for sample B was strong to reach the final rotational reversible processes. The XMCD images are presented in Figs. 8(b)–8(k), showing the irreversible process. In Fig. 8(a), we show absorption XPEEM image with left circularly polarized x rays, where several geometric domains are marked with circles to follow the reversal magnetization process. Some dislocation-like defects are also marked with discontinuous yellow lines separating geometric domains. The (edge-to-edge) distance between antidots is significantly larger for sample B (D − d ≈ 90 nm) in comparison with sample A (D − d ≈ 43 nm). From an overall comparison among images in Fig. 8, the local evolution of irreversibilities can be followed (with initial near saturation in the positive direction, marked in red). There are two main processes. First, from Fig. 8(a) to (e) (Happl = − 22 Oe, a value close to coercivity, as deduced from the MOKE loop), the predominant color is red, denoting that up to that field processes are mostly reversible; furthermore, topological regions with different contrast are already clearly observed in Fig. 8(d), which indicates that domain walls can be locally pinned at the border between geometric domains. Second, for Fig. 8(j) and (k) (Happl = 57 Oe), the dominant color is already blue, indicating that most irreversible processes have already taken place. Figures 9(a) and 9(b) show the hysteresis loops at remanence (after applying the indicated applied fields) obtained in local regions 3 and 4, marked in Fig. 8(a) through XMCD

IV. FURTHER ANALYSIS AND FINAL CONCLUSIONS

In the XMCD images (see Figs. 5 and 8), the magnetization with the out-of-plane component, or with perpendicular orientation to the positive or negative magnetization in the plane of the sample, is indicated by white. In both samples, we deduce that magnetization lies mainly in plane but at the boundaries of the geometric domains where magnetization has a different component, again represented by white. This contribution seems to be particularly important in sample A, which shows a kind of magnetically harder second-phase magnetization process that is not achievable by XPEEM. Consequently, further interpretation of the magnetization distribution should be done with complementary magnetic measurements, such as with the out-of-plane hysteresis loops measured by VSM. The role played by the magnetostatic energy is determined by the presence of antidots, that is, the role of magnetic charges accumulated around the nanoholes.20 Locally distributed magnetic charges can generate significant local stray fields that result in an effective macroscopic anisotropy much larger than the one in continuous thin films. A competition among local stray fields should be considered by charges accumulated at (1) the lateral surface of antidots, where magnetostatic energy density is minimized in the out-of-plane magnetization direction, and (2) the upper and bottom surfaces of the film, which promote an in-plane magnetization orientation.35 Figure 10 shows the loops in in-plane HI P and outof-plane HOOP configurations for both samples, with clear differences. The loops for sample A are relatively similar, whose comparison and analysis allow us evaluate an effective

FIG. 9. (Color online) Local hysteresis loops inside geometric domains (a) 3 and (b) 4 of Fig. 8(a). 184427-7



FIG. 10. (Color online) In-plane (HI P ) and out-of-plane (HOOP ) loops by VSM of (a) sample A and (b) sample B.

macroscopic HI P magnetic anisotropy36 of 104 erg/cm3 . This is around one order of magnitude higher than the anisotropy constant of a continuous thin film of Py.37 The relatively soft behavior in the HOOP configuration in sample A seems closely related to the magnetostatic energy, partly compensated by the charges at the lateral surface of nanoholes and those at the upper–bottom surfaces mentioned previously. In sample B, the effective HI P anisotropy constant is on the order of 106 erg/cm3 , two orders of magnitude higher than in sample A. Here, because of the reduced aspect ratio, the upper–bottom charges have a stronger effect to determine a strong HI P anisotropy. The HOOP loop in Fig. 10(b) corresponds to a hard magnetization direction. The magnetization process, as followed by the XPEEM images under an increasing in-plane applied field, is clearly determined by the topological ordering of the antidot arrays. Because of the lack of other anisotropy terms, we conclude that two geometric facts determine the magnetization process in Py antidot arrays hexagonally ordered at the microscopic scale: (1) Magnetostatic stray field energy. For high-aspect ratio films (i.e., sample A), the partial balance between stray fields generated by charges at the lateral surface of antidots and those at the upper–bottom surface promotes a modest in-plane effective magnetic anisotropy. In turn, for small-aspect ratio films (i.e., sample B), a strong in-plane shape anisotropy is obtained. For both kinds of samples, a relatively soft in-plane magnetization behavior is achieved, particularly for sample B. (2) Pinning mechanism at the border of geometrically ordered domains. Comparative analysis of XPEEM images (see Figs. 5 and 8) confirms that a softer magnetization process takes place inside geometric domains, as is further confirmed by local quantitative analysis of local coercivity of sample B (i.e., Fig. 6). In turn, a harder process originates at the borders of such geometric domains. The harder magnetic phase is

*

[email protected] R. P. Cowburn, A. O. Adeyeye, and J. A. Bland, Appl. Phys. Lett. 70, 2309 (1997). 2 M. B. A. Jalil, J. Appl. Phys. 93, 7053 (2003). 3 J. G. Zhu, and Y. Tang, IEEE Trans. Magn. 43, 687 (2007). 4 G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, A. O. Adeyeye, and M. Kostylev, J. Phys. D Appl. Phys. 43, 264003 (2010). 1

observed clearly in sample A but not so clearly in sample B because of the stronger magnetostatic effect mentioned previously (in Fig. 2(b), the biphase behavior starts to appear for the sample with larger antidot diameter). As a final conclusion, it is confirmed that the magnetic response strongly depends on the geometry of the AAM template and consequently of the antidot thin film: antidot diameter and film thickness. At the long scale, the magnetization process in antidot thin films with hexagonally ordered geometric domains of several square micrometers is moderately soft. At a short scale, inside geometric domains, there is a correlation among antidot diameter, edge-to-edge antidot distance, and film thickness to determine the local stray fields that results in effective in-plane local magnetic anisotropy and soft behavior. In turn, local border regions between such domains where topological defects concentrate are magnetically harder, because they act as pinning centers for the magnetization reversal. Finally, the high-spatial resolution and sensitivity of the XPEEM technique under an applied magnetic field enables the magnetic characterization at a very local scale, including magnetic domain structure imaging and quantitative hysteresis loop analysis. Nevertheless, complementary MOKE and VSM magnetic measurements are necessary to reach a full understanding of the magnetization process. ACKNOWLEDGMENTS

This project has the financial support under the proposal no. 2011_1_101192 from BESSY II. The work has been supported by the Spanish Ministry of Science and Innovation under projects MAT2010-20798-C05-01, MAT11/23791 and MAT2009-13977-C03. K. J. Merazzo acknowledges the PhD grant from University of Costa Rica and CSIC.

˚ M. I. Montero, K. Liu, O. M. Stoll, A. Hoffmann, J. J. Akerman, J. I. Mart´ın, J. L. Vicent, S. M. Baker, T. P. Russell, C. Leighton, J. Nogués, and I. K. Schuller, J. Phys. D Appl. Phys. 35, 2398 (2002). 6 J. M. Gonzalez, O. A. Chubykalo-Fesenko, F. Garcia-Sanchez, J. M. T. Bruna, J. Bartolome, and L. M. G. Vinuesa, IEEE Trans. Magn. 41, 3106 (2005). 5

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