Zoltán Gálik
email: zoltan.galik@gmail.com

Zoltán

PaedDr. Gálik

Learning through investigative games and internet on-line activities

Keywords: Tele-learning, Internet, On-line activities

Internet is an important phenomenon in our society and already become one of the mostly used media around the world. In human history this is the first media, which is broadly used in so little time. Obviously, it plays an important role also in the life of our children. They use it for communication with each other (chat, email), they use it for finding new information to school, and they search the web or even create their own websites. The investigative games on internet are competitions, through which the pupils can develop large variety of skills in information literacy and problem solving competencies. The aim of the project was to improve student's skills in cooperation and collaboration, also skills of analyzing information and taking the responsibility for their own decision and skills in problem solving in real context.

New competencies of society in general

Many recent research articles are dealing with the growing challenges for teachers. These are the challenges of the new millennium, before all teaching and learning by the information and communication technologies. In 1998 the World Educational Report (see UNESCO [START_REF]Unesco: Teachers and teaching in a changing world[END_REF]) is describing the radical changes, which have to arise in the traditional learning and educating: "New possibilities are emerging which already show a powerful impact on meeting basic learning needs, and it is clear that the educational potential of these new possibilities has barely been tapped. These new possibilities exist largely as a result of two converging forces, both recent by-products of the general development process. First, the quantity of information available in the world -much of it relevant to survival and basic well-being -is exponentially greater than that available only a few years ago, and the rate of its growth is accelerating. A synergistic effect occurs when important information is coupled with a second modern advance -the new capacity to communicate among the people of the world. The opportunity exists to harness this force and use it positively, consciously, and with design, in order to contribute to meeting defined learning needs." (Source: World Conference on Education for All. Meeting Basic Learning Needs, Jomtien, Thailand) There may be difficult debates about what education is. Is it just the transfer of certain knowledge? Is it more linked to the development of human beings? It is obvious, that in the modern society the transmitting of the knowledge from teachers to pupils calls for new methods. The teachers have to keep up with the times, they have to be able to work with ICT and they have to be prepared for the changes in the society. We can compare the education in the modern society to an economic activity. We can describe the knowledge as the raw material and the Education as the activity itself.

Internet: a tool for achieving new goals

Internet is a new phenomenon in our society and already become one of the mostly used media around the world. In human history this is the first media, which is broadly used in so little time. If we consider the birth of internet to be in the middle 70's last century, nearly after 30 years it is widely used all over the world. Obviously, it plays an important role also in the life of our children. They use it for communication with each other (chat, email), they use it for finding new information to school. They search the web or even create their own websites. But, many researchers in the field of didactics (see [START_REF] Kalaš | Digitálne technológie a vízia moderného vzdelávania[END_REF], [START_REF] Curtis | Exploring Collaborative Online Learning[END_REF]) think, that potential of the internet for developing and refining the cognitive process and the mentioned competencies is much higher than we can imagine nowadays.

In an optimal situation the pupils are commonly using internet during the lessons and also at their homework. Searching and processing the findings; sending emails; involving in various online activities; creating web documents. All these should be done on daily basis in our schools. But, before this will happen, we have to think about the way, how to teach internet and how to develop the new competencies on the internet. One of the crucial questions is how to teach students to differentiate between the important and less important information on the internet. On the World Wide Web they can find various data, but not all of them they really need or they will really use. And not all of the information is correct; they have to be aware of it. To differentiate between these things is a really hard task and it is even harder for teacher to find any attractive ways to teach these new competencies. Luckily on the net there are variety of online activities, which could help in achieving these new goals and competencies. Project Sherlock-Holmes is one of them.

Project Sherlock-Holmes

The investigative activities are competitions, through which the pupils can develop variety of skill in information literacy and problem solving competencies. The aim of the project was to improve student's skills in cooperation and collaboration, also skills of analyzing information and taking the responsibility for their own decision and skills in problem solving in real context. We are convinced that these activities have positive influence on learning to work with ICT and developing student's information literacy. The activities also give an attractive format to learning.

History of Sherlock-Holmes investigative games

Some years ago, when the internet was starting to be widely known and used, a new kind of activities was regularly organized by David Cassey from E-ngage Development (not-forprofit company working internationally with schools). The activities were called "Netdetectives". Children had to create groups, register to the activity and on a special day they had to help the police to solve some crimes. They were communicating with the policemen through e-mails. Every 5-10 minutes they received new information about the suspicious persons and then they had to give their comments to police -what to do next, where to go, which person put in prison etc. These whole activities were mostly e-mail based and there wasn't too much searching of new information and learning new things. Based on these activities we decided to create our own activities in Slovak language for students from the whole country. We designed the investigations as a group competition; participating children had to work in teams. The pupils' age was from 12 to 18. The task was usually something like following: on a special day, let's say on 6th December 2006, there was a new activity. We created the activity's website and publish all the necessary information for the pupils in advance. Small groups of students (4-6 in each group) registered for the activity. The 3 [START_REF] Dimitru | Web-based classroom projects (A teacher guide to collaborative projects[END_REF] registered teams on the day of the activity got the first e-mail about the fictional crime somewhere in Slovakia (or somewhere else in the world). This crime was the object of investigation through internet. After the first e-mail they received further information every 5-10 minutes by e-mail. These messages contained various additional information and they had to deal with them. Not all of this information was relevant and important; the participants had to decide which were necessary and which not.

Description of the investigation

The sent messages were not only simple text messages. The e-mails contained new information in various formats, like pictures, sound records, maps, databases etc. Not everything was important to find the criminal; they had to differentiate among all the received messages. This was the point, where they learnt how to decide what is important and what is not. Beside this, many information they had to transform to appropriate shape and form. For example, they received a pictures' negative from a party, where the crime happened. For some teams, it was only an irrelevant negative with no information on it, because they will not be able to read it. But for some other teams, it will be much more. They will create the picture from its negative using graphic editor and finally finding the suspicious person on it how he is leaving the party. From this moment, their investigation will have a completely different dimension and they will be one step ahead all the other teams. Similar situations could happen, when they received a sound record e.g. telephone call between two suspicious persons. There was nothing special on the conversation, but after deep analyzing of the record they could notice some sound in the back-ground (like bells etc.). From this sound a clever detective was able to decide, where the suspicious person was at the moment of the call. This could be crucial for the investigation. There are many examples like these two where the participants need to analyze data not only superficially but deeply and thank to this deep analyzing they could be able to solve the problems. There is also one important dimension which is not very common in schools. This is the group work. During the whole investigation participants had to work in small teams, coping with other views and perspectives from the rest of the team. Team work is mainly prohibited in our schools and the teachers try to develop individual skills. But after leaving the school, pupils will probably work in teams and it is very important to experience the team work also during the school years. If the team will cooperated and collaborated successfully, they had better chance to solve the problem and the crime. Nobody alone could be able to do it. But together they had a chance to divide the problems into smaller parts and solve partial problems first. In the teams they had different roles like team leader, internet surfer, e-mail writer, database analyzer etc.

Types of activities

There were 4 different kinds of activities throughout the whole year:

1. Solving various tasks without the help of organizing team in a time limit of 2 hours. It was basically a competition between the teams -who will be the quickest and most successful. Organizing team was in this case just a technical support -if they encountered any problems with receiving e-mails etc. In this type the common problem was that the detectives tried to solve the task very quickly without a deep analyzing of the task. So it happened that many of them sent unfinished tasks.

2. On the website of the activity they had a huge amount of task and they could decide which tasks they will really solve. This kind of activity didn't last for 2 hours, but it was much longer; about 3 or 4 days. At the beginning they decided which tasks they are going to solve, divided them between themselves and on the next 3-4 days everybody was working on their own task. Before the end of the activity they again met each other, discussed the solutions and sent them to the organizing team.

3. A special program was created for investigation. They had to download it and work with this program only. The program contained various tasks and didn't let them see the next task until they didn't finish the previous one. It was investigation about some crime, but in a completely different way. And obviously they had to learn at first how to use the program. After finishing the last task, they had to send back the program to the organizers, so we could check their solutions.

4. The activity was an online investigation in real time and with a team of police headquarters. This type of activity was the most often used type in the whole project. The task was always different. It could be the following: on the day of the activity, which was announced long enough ago to register to the activity, they received a brief description of a fictive crime. The information was communicated to them by e-mail, but there was also a website containing all the necessary information about the investigation. After the first e-mail they got further information every 5-10 minutes again by e-mail. The messages from the police headquarters were not only simple text messages. The e-mails contained information in various formats, like pictures, sound records, maps, databases etc. Beside this, many information they had to transform to appropriate shape and form. For example, they received a pictures' negative so they had to turn it into real photo, or they had to change in the picture the RGB of the background etc.

Data collection

During the period from May 2006 to December 2006 there were 8 on-line activities. Average number of the participating groups of students was 30; in every group about 5 children. We collected data from the participants by recording their investigation on the video tape and also in every activity the participants had to fill some forms about their previous experiences with ICT and internet. After finishing the whole project we visited the most successful teams and made an interview with the whole group. Because of the shortage of time from the project final activity, we are at the stage of analyzing all the collected data. This period should last until the end of June 2007.

Preliminary results

The responses from the students and teachers are very positive. We have got many e-mails from the participants that they had never experience such kind of activity and team work. The teachers especially appreciate the collaboration between the students which was in a very high level. They worked together like a real team with the team leader and distributed the tasks among themselves. It was interesting to see how they wanted to solve every question and they were eager to know more about ICT and how to use it in order to find the results. Students appreciate the use of ICT. They had to use everyday programs in a way they never used it before. There were many reactions like: "I never knew that I can use this program for such a great thing!" Obviously they learned from each other quite a lot. The whole team got the question at the same time and after a couple of minutes somebody from the team managed to solve it. When he/she got the solution, and then showed the solution also to the others. In this way they learned from each other how to do things by using the ICT.

Detectives and their initial skills

In every activity the detectives had to fill a questionnaire about their initial skills and experiences. Also they had to write little about their team and their position inside the team.

They had to fill their personal information (name, age, team, position in the team etc). The questionnaire also contained some questions about their skills, whether they used internet before, what kind of programs did they used before, what for did they used the internet etc.

Questionnaires from one of the activities

In the following I would like to show some results from the questionnaire in the activity "Disappeared precious jewel". Number of the registered teams was 45 and altogether we evaluated 108 questionnaires. I will show only the questions dealing with the internet and using of various ICT tools. What kind of program children used the most?

The most used programs among the participants were office programs for text editing, creating tables or presentations. Quite popular are programs for playing videos, sounds and sending messages. Less popular are specialized programs for a special kind of activity: sound editing, animation editing or video editing. Use of computers and internet is shown at the following graphs:

How often do you use computer? How often do you use internet?

Example of an investigative game: Disappeared precious jewel

In this activity the crime was situated to Venice. Our police headquarters has visited a young lady (from somewhere abroad). Nobody could understand her single word. The first task of

6(8)
the detectives was to find out from which country is she from. In case of a correct answer the headquarters was able to hire an interpreter, so we could understand her language.

Nearly in every activity they had to solve problems like how to get from place A to place B by different objects (car, bus, train etc.). In this case it was a plane. We wanted to have a task which is not quite easy to be solved, but still could be solved in not very long time. We decided to have the nationality of the young lady being Finnish. The language is not common in Slovakia, so it wasn't an easy task. But after a short search on the internet (the words, what we had from the young lady) they could find out the country. Then they had to find suitable connection through plane from Helsinki to Venice. There are several webpages, which offer flight connection from different places to Venice. We suppose that the children have never done something like ordering tickets for travelling with airplane.

Nearly all of the teams did find out the nationality correctly for the first time. There were 3 teams, which gave wrong answer: Italian, French and Spanish nationality of the young lady.

In this case the headquarters wrote back to the detectives, that we have an interpreter in that language, but the young lady still doesn't seem to understand anything. Try some other languages. After several tries we sent them message that she has on her t-shirt Helsinki. After this everybody was able to find out the language.

Some of the teams did find much more information then we asked for. They didn't find out only the nationality of the lady but also found translation of the sentences what she was saying at the headquarters.

This task we considered to be a well defined problem with only one possible correct answer (see [START_REF] Wallace | a kol: Thinking skills and Problem -Solving[END_REF]). We didn't provide any kind of help in how to solve the task. We could help with additional information, but we did not give any suggestions, that they should use this website or something else. Everybody had their own ways of finding the answer.

After finding the nationality of the young lady, the detectives learn more about her and about the whole story. From this moment the investigation was divided into several aims:

1. the most important thing was to investigate the thievery of the lady's jewel, identification of the the criminal in one of the planes, following his moving on the map of Venice and finally his arresting.

2. To the less important line belonged the story of detective Marc, who at the beginning of the story became personal bodyguard of the young lady. Detectives helped him to find something usefull to do in Venice for them. They helped Marc to find a nice gift for the lady and also to hire a boat in Venice.

In order to find a suitable gift for the lady, they had to find some information about her home country. They had to search for traditions in her country and tried to find something suitable for her in Venice -so she could feel like at home.

Advantages of investigative games

• Cooperation and collaboration -as it was mentioned before, this is the dimension which is not very commonly used in our schools. By all tests, written exams or by answering questions in front of the class, the teacher will never allow students to communicate together or to collaborate during the tests. We try to educate the students as individuals, never to work in team. This is obviously very good in some ways, but we don't have to forget, that after school students will be employed in various companies. They surely will belong to a team or some of them will even be team leaders. Unfortunately our school does not prepare them for this task. This is the point where the investigative activities appear on the scene. During the investigation they have to work together, they have a team leader and they have no choice, they have to collaborate. The team consist of 4-6 members where all of them have their own task. If one of them will not work properly, the overall outcome of the whole team will be worst.

• Analyzing information and responsibility for own decision -working with information is very common in every school on every learning subject. During history lessons they learn about various historical events, they analyze information. During physics or chemistry they are engaged in various experiments and tests. Again, they analyze information. But, in all these cases, every time there is somebody, who can they ask when they are in trouble. There is always a wizard or magician, who knows nearly everything and has the answer to all questions. We usually call this magician simply teacher. During the investigations at online activities, there is no wizard, no magician who can they ask. Obviously there is a teacher, but he does not know the result and has no answers. They can only count on themselves. Only they alone will decide which information is important and which not. They take the whole responsibility for their own decisions.

• Internet, ICT and information literacy -during the whole activity the participants will use the internet as the main communication tool. They have to write e-mails, answer questions, search the web for relevant information. Beside this, they will have to use programs they never used before. For example, for the analyzing the sound records they will have to download a program by which they will be able to read more information then others. Or other example: they will get code breaking program and will have to use this program during investigation. So, we are testing them how can they cope with new situation, on which level is their information literacy and whether they can use ICT programs they never used before. And obviously whether they can use the internet for communication and for finding new information.

• Attractive ways of learning -usually children do not like to learn in traditional way. They like to play; they like to construct their own knowledge of things; they like compete with each other, even better if the competition is between children from the whole country. This is the situation at investigative online activities. The activity is prepared for every school in Slovakia. The pupils know it and they try to have as good results as possible to be the best. At the same time, they learn about new things, they have big motivation to find new information about Slovakia and about other places.

• Problem solving in real context -the result of pupils from Slovakia in PISA 2003 in problem solving (see [START_REF]OECD: Learning for tomorrows world: First result from PISA[END_REF]) was below the European average. In the test they had to proof, that they are able to solve problems from real life, not only mathematical equations. They were tested, whether they could understand the problem by determining relevant conditions. This requires analytical, quantitative, analogical and combinative justifications, which are the core principles of problem solving competencies. This is exactly what happens during investigative activities. They have a real problem, they have to analyze it at first, try to find partial solutions and then proof their assumptions.

Question: Which of these activities have you ever used (at least once) in your life?

	(the number means the amount of the answers out of 108)
	Questions dealing with internet		Questions dealing with something else
	Searching for new information on the net	108	Printing documents on a printer	94
	Sending e-mails	106	Using MP3 player	88
	Registered on various websites	98	Using Pen Drive	85
	Using some kind of chat on the net	95	Using Scanner	73
	Making a phone call through the net 59	Install additional PC components (printer etc.)	69
	Using the program ICQ (or similar)	55	Install a completely new computer	48


H Garad

S Usmani

D Barral

P David

L Cagnon

D Testemale

D Mannix

F Fettar

O Proux

A Rosa

O Mathon

S Pascarelli

Influence of the pore diameter in Cu/Co/Cu antidots: A XANES study

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I. INTRODUCTION

Nano-objects are of great industrial and scientific interest in many fields. Indeed, they present key elements employed in electronic devices using in particular magnetic elements.

Nanocompounds studied over the last two decade are antidots or nanopores, which constitute two-dimensional nanostructures in geometrically ordered arrays presenting the counterparts to dot nanostructures [1][2][3][4]. The physical properties of antidots are known to be directly linked to both the diameter of nanopores and to their spacing, which represent the key parameters in the design of antidots for industrial applications (see [5] for review).

Magnetic properties of antidots have received widespread attention due to their applications in magnetoresistance [6] and magnetic hardening [7][8][9][10] effects, high density data storage [11,12], and magnetic devices [13][14][15]. They bear several advantages over the conventional dots system, including the absences of a super-paramagnetic lower limit of the bit size, the preservation of magnetic properties, large-area fabrication at low cost, and the absence of damage caused by nanofabrication processes. Several previous studies aimed at establishing the relation between the antidot size and distribution to the nanomagnetic properties; see for example [7][8][9][10] and references therein. This foregoing research has been limited to antidots with relatively large pore size (d) of around 0.1-20 μm and 53 with interpore distances (p, periodic array) of 0.2-50 μm, 54 by implementing physical synthesis methods [7][8][9][10][11]16,17]. 55 However, in order to reach magnetic recording properties that 56 are suitable for industrial applications, small pore sizes below 57 <100 nm together with a sufficiently large p value of ≈100 nm 58 are required [12], leading to a p/d ratio higher than 1.

59

The pioneer work of Masuda et al. [18] has enabled the 60 fabrication of ordered pore sizes below 100 nm using a two-61 step-anodization method. The choice of acid solution presents 62 a key factor in this process as it determines the resulting d 63 and p of the antidot array. The use of sulfuric acid in the 64 anodizing process induces low d and moderate p values of 65 typically 7-46 nm and 60 nm, respectively [19]. Oxalic acid 66 in turn leads to both higher d and p values of 35-66 nm 67 and 105 nm, respectively [20]. Although this method clearly 68 achieves d values below 100 nm, its major limitation is the 69 strong coupling between d and p values, which both increase 70 linearly with the anodizing potential. It is therefore impossible 71 to constantly reduce the pore diameter by keeping the interpore 72 distance constant using this chemical method.

73

For real industrial applications, such as data storage, the 74 pore dimensions have to be reduced to a few nanometers while 75 maintaining a weak coupling between pores. The ratio p/d 76 should be far ideally greater than one [21] for this situation to occur. However, the practical realization of such antidot structures, with a highly ordered arrangement of pores, remains extremely challenging and only a few studies have realized such antidots to date. For example, Chuang et al. [22] reported on multilayered Co/Cu/NiFe porous films with d = 12-17 nm and p = 26-40 nm by using a block copolymer template.

Unfortunately, this technique requires multiple steps, including heat treatment and reactive ion etching that result in a weak p/d ratio close to 2. In comparison, elevated p/d ratios of up to 9 have been recently realized by Rahman et al. [19] on antidots with very small hole diameters of d ≈ 7 nm and with p close to 60 nm. However, these antidots remain structurally problematic as their pore distribution is not perfectly hexagonal, the pore opening shapes are not circular, and the thickness of the alumina membrane is very thin (0.5 μm). Present synthesis methods need to be refined in order to achieve highly ordered and round-shaped antidots with low d values (several nm) and simultaneously high p values (at least 100 nm).

In this paper, we have implemented a method to fabricate pores size in the thick alumina substrate (60 μm) of Cu/Co/Cu antidots ranging between 17 and 78 nm at a constant p value of 105 nm (p/d ratio ranging from 1.4-6.2). This synthesis procedure is based on the two-step-anodization method combined with an additional atomic layer deposition step [21].

The high p/d ratios of antidots achieved with the present approach meet the demands of nanodevice applications. Local structural and chemical information has been obtained from quantitative x-ray absorption spectroscopy in the XANES (x-ray absorption near edge spectroscopy) range. Indeed, among the common structural characterization methods, such as scanning electron microscopy [12,19,20,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37], atomic force microscopy [20,32,[38][39][40], x-ray diffraction [29,30], and Rutherford backscattering spectroscopy [34,36], only a few investigation tools such as XANES, as well as transmission electron microscopy [12,19,31,33,35,38], allow us to distinguish the chemical nature of materials on the surface of antidots from those around the periphery of the nanopores.

In our work, we found that Co atoms are oxidized mainly around the inner pore rims forming therefore CoO nanorings. This result is is in agreement with findings of previous studies on the oxidation of Co and Fe in ultrathin metallic layers [41][42][43]. We also found a linear relationship between the pore diameter and the atomic fraction of oxide rings, allowing us therefore to tune the oxide part during the synthesis. Moreover, we have developed a simple model to spatially localize the Co and CoO components in our antidots using the observations made from our XANES data as well as atomic force microscopy (AFM) observations. Furthermore, our model allows a quantitative determination of atoms around the pores as well as on the antidot surface, which is of great potential interest to the community employing antidots. This morphological and structural information is crucial for the understanding of magnetic properties of antidots [44], as well as other physical properties reported in the literature on these materials, and is therefore of great interest for antidot applications in general.

The present paper is organized as follows: Section II employs experimental synthesis methods, and structural characterization techniques of antidots are described. Section III describes results on the quantitative analysis of the CoO content from x-ray absorption spectroscopy. Section IV is 137 dedicated to the local structure and morphology of antidots 138 from AFM and polarized XAS observations. Finally, in Sec. V, 139 a model is presented to describe the structural and morpholog-140 ical properties of antidots which are directly related to their 141 magnetic properties such as the coercivity. A very simple 142 model is developed to calculate the proportions of atoms 143 deposited on both the top and the periphery of pores.

144

II. EXPERIMENTS

145

A. Antidot preparation 146

In order to prepare antidot arrays, an anodic alumina 147 membrane (AAM) was prepared by the two-step anodization 148 process [18]. After mechanically polishing to a mirror-like 149 aspect and electropolishing at 30 V for 2 minutes in a perchloric 150 acid/methanol mixture (1/4 in volume) at 0 • C, high-purity 151 (99.999%) aluminum foils were anodized in a 0.5 M oxalic acid 152 with a constant potential of 40 V and temperature around 16 • C. 153 The first and second anodizations were performed during 17 h 154 and 7 h, respectively, which led to templates with a thickness 155 of 60 μm, and hole diameter and interpore distance of 40 and 156 105 nm, respectively. Then a pore opening/widening treatment 157 in a phosphoric acid solution at 35 • C was applied during 158 an etching time (t etching ) that was varied between 30 and 90 159 minutes. This procedure permitted us to obtain a pore diameter 160 larger than the native diameter which is close to 40 nm for 30 161 minutes etching time. In order to obtain pores with a diameter 162 smaller than the native one, an alumina deposit was performed 163 using atomic layer deposition (ALD) in exposure mode, with 164 trimethylaluminum and water as precursors [21]. Two native 165 samples were selected where the hole diameter was further 166 reduced by applying two ALD cycles numbers (Nb cycles ) 167 of 75 and 100. Finally, Cu(10 nm)/Co(12 nm)/Cu(10 nm) 168 trilayers were sputtered on all templates to obtain the antidot 169 arrays. Such multilayer compositions exhibit exchange bias 170 effects at low temperature and double magnetic loops, as 171 identified for example in [Cu(10 nm)/Co(8 nm)/Cu(10 nm)] 172 [41]. Additionally, during the deposition of the antidot arrays, 173 a substrate of Si/SiO 2 was used to produce continuous trilayers 174 for comparison. In order to provide one unique batch of 175 samples with similar substrate properties the sputtering process 176 was performed on all 7 substrates at the same time, with a base 177 pressure of approximately 6.0 × 10 -8 mbar, an argon pressure 178 of 3.0 × 10 -3 mbar, a deposition temperature of around 20 • C, 179 and deposition rates of 0.05 and 0.10 nm/s for Co and Cu, 180 respectively.

181

B. Electron microscopy 182

After the multilayer sputtering process, all samples were 183 analyzed using scanning electron microscopy (SEM) to mea-184 sure the pore diameter and the interpore distance. Figure 1 perpendicular antidot arrays [19]. In our study, a saturation of hole diameter seems to occur for the high t etching regime above 70 minutes evidenced by the deviation from the linearity between d and t etching . We therefore conclude that the doubleanodization technique using such fabrication of membranes does not allow obtaining d values greater than ≈80 nm as observed in Refs. [25,26]. Indeed, the reason that may lead to a saturation of d is the space available between two consecutive holes, which is pd where p is close to 100 nm. By increasing d and keeping constant p, this distance is reduced up to 0. Consequently, d reaches a maximum value for a network with a fixed p parameter, around d = p ≈ 100 nm. Here, the maximum d value reaches ≈80 nm lower than the previewed one, indicating that the stabilization of the hexagonal network is stabilized up to 80% of the maximum value.

C. XAS

We employed polarized x-ray absorption spectroscopy in order to study in detail the Co-oxide layer forming inside the pores on the ultrathin deposition layers, as developed in Refs. [42,43]. X-ray absorption spectroscopy (XAS) is a powerful technique to provide information on the local chemical and structural environment of selected chemical species. In particular, the x-ray absorption near edge structure (XANES) is sensitive to the symmetry and the three-dimensional arrangement of neighboring atoms surrounding the absorbing atom. Polarization-dependent XANES measurements additionally allow the possibility of distinguishing between bonding characteristics in the plane of the surface and those perpendicular to it (linear dichroism).

XAS measurements at the Co K edge (7.71 keV) were conducted at the French CRG beamline BM30B and the beamline BM23 at the ESRF (Grenoble, France) using a double-crystal monochromator equipped with two Si(220) and two Si(111) crystals, having an energy resolution of approximately 0.4 eV and 1 eV, for BM30B and BM23, respectively. The energy was scanned between 7650 eV and 8550 eV. On BM23, ionization chambers filled with appropriate gas mixtures were used to measure the incoming beam intensity. On BM30B this measurement was ensured using Si photodiodes collecting photons scattered by a Kapton foil. Emitted fluorescence signals were detected using a 30 and a 13 element germanium solid state detector at BM30B and BM23, respectively, placed at 90 • from the incoming beam. Bulk Co, CoO, and Co 3 O 4 references were also used for comparison. For all measurements, the energy calibration of the two beamlines was done with the same method by measuring the XAS spectrum of a Co metallic foil. For the angular measurements, the sample was mounted on a precision goniometer and rotated from normal incidence by 45 • and 80 • (see Fig. 3). These measurement geometries allowed sampling an average of chemical bonds oriented parallel and perpendicular to the surface (α = 45 • rotation) as well as bonds oriented mainly perpendicular to the antidot surface [α = 80 • rotation, Fig. 3(c)] (see red arrows indicating probed bonding direction in Fig. 3). Here, the angle is defined between the electric field vector ( in green in Fig. 3) of the linear polarized incoming x-ray beam and the surface of the aluminum template. After background subtraction of the absorption spectra by linear extrapolation of the pre-edge 3. Schematic view of the measurement geometries employed for polarized XAS. The alumina template is represented in yellow with a pore diameter of 50 nm and interpore distance of 105 nm (scale is shown on the lower left). The Cu/Co/Cu deposition appears in gray (thickness not at the scale). The angle α is defined between the electric field vector ( in green) of the linear polarized incoming x-ray beam and the surface of the aluminum template (blue arrow). In normal incidence geometry α equals 0 • and the bond directions (red arrows) probed are parallel to the surface (a). For the present experiments, α was set to 45 Interestingly, the normalized absorption signal of all spectra coincide at certain energies (i.e., point C and other points). This indicates that these are isosbestic points and that all sample spectra are related linearly to the two reference spectra via differences in concentration and therefore contribution to the total absorption signal, within the uncertainty of the possible Co-Cu bond. The observation on the XANES features suggests that Co metal dominates in the substrate layers, and that the increase of d progressively leads to the oxidation of the Co layer and formation of CoO. As proposed in [41], the oxidation 297 process could be preferentially favored in the vicinity of the 298 antidot, where the overall thickness of the trilayer is reduced 299 due to the crescent shape gradient in thickness of the deposit. 300 This particular crescent shape of the membrane around pores 301 is also reported in Refs. [46,47]. It is therefor likely that the 302 oxidation is preferentially located in the vicinity of the opening 303 of the nanopores, where the covering of the protective Cu layer 304 is reduced. The oxide fraction c(CoO) deduced from WL intensity analysis decreases linearly from 24.2(±1)% to 5.3(±1)% for the substrates with the largest and smallest pore diameters (d = 78.2 nm and 17.0 nm), respectively. A particular point in Fig. 5 is the sample with d = 23.6 nm (corresponding to Nb cycles = 75), which deviates from the linearity. For this antidot Co is slightly more oxidized than the substrate with larger pore diameter d = 42.6 nm. Indeed, the sample d = 42.6 nm has been employed as template for the atomic layer deposition (ALD) of the sample d = 23.6 nm. The deviation from linearity may suggest that oxidation of Co around pores is favored for samples treated additionally with ALD after the double-anodization process. A simple linear relation between c(CoO) and d [Eq. ( 1)] can be deduced (see the straight line in Fig. 5):

c(CoO)(%,±1) = 0.31d, (1)
which highlights the direct relationship between the antidot pore diameter and the degree of Co oxidation. This result is not obvious at first sight. As an explanation, we propose the fact that CoO atoms are preferentially localized around the valley of nanoholes. As a consequence, more the larger the diameter is, the more the CoO content is enhanced. A quantitative model justifying this hypothesis will be introduced in the next part of this study (see Sec. V).

B. Edge energy analysis

In a second step the variation of the edge energy (here referred to as E edge , defined as normalized μ = 0.5) was used as to derive the degree of oxidation in the samples. In general, a shift of the absorption edge to higher energies is either an indicator for an increase of the overall oxidation state of the element [43] or a modification of the interatomic bonding environment. In our samples we observed a continuous shift of the edge energy to higher energies with increasing d (see A in Fig. 4). This progressive shift can be interpreted qualitatively with the increasing degree of Co oxidation, in agreement with observed changes in the WL intensities (B in Fig. 4). In Fig. 6 the position of the edge energy as a function of the pore diameter d is shown, revealing again a simple linear relation. Similarly to the method developed above for the white line, we consider a simple linear variation between E edge and c(CoO), where pure Co [c(CoO) = 0%] corresponds to E edge for the Co bulk structure (7716.91 eV), since no CoO is detected. The extreme case where Co is fully oxidized [c(CoO) = 100%] is represented by E edge of the bulk CoO (here 7718.37 eV). Using the assumption that the oxidation of Co is of the form of bulk CoO, c(CoO) is expressed as c(CoO) = 68.49 × (E edge -7716.91) [here 68.49 is coming from (100 -0)/(7718.37 -7716.91)]. Using this assumption, the content of CoO is found to be 37.7%, for the d = 71.5 nm membrane, which is 50% higher than the value obtained from the analysis of the white line (≈25%;). The replacement of the pure metallic Co standard with the unholed sample spectrum (E edge = 7717.25 eV) resulted in even higher c(CoO) values (≈49% for d = 78.2 nm). Such high degrees of oxidation in the samples seem however unrealistic considering that XANES absorption of the experimental sample spectrum is remodeled using the linear combination of reference spectra. For the LC fitting of sample spectra we followed established procedures [42,43] to extract the oxide content in the Co thin layer as a function of pore size. The normalized XANES sample spectra were fitted in the energy range between 7700 and 7830 eV using one Co metal and one Co-oxide reference spectrum each. The LCF was performed using the program Athena [45], which calculates the relative proportions of end-member spectra in the sample spectra using the following relation [Eq. ( 3)]:

χ (E) = c(Co)χ Co (E) + c(Co oxide)χ Co oxide (E), (3)
where c(Co) and c(CoO) are the Co and CoO contents expressed in percent. Since Co is either metallic or oxidized, the relation c(Co) + c(Co oxide) = 1 is satisfied. We tested different reference spectra, including bulk Co metal, the unholed Co substrate, CoO bulk, CoO thin film (1.5 nm thickness from Ref. [48]), as well as Co 3 O 4 bulk. The two standard compounds that fit best the sample spectrum were evaluated from the χ 2 parameter, which is an indicator for the quality of the fit. Because the measurement uncertainty is difficult to assess for XANES data and the quantification of the independent number of points is not feasible in XANES the absolute value of χ 2 cannot be used to evaluate the quality of the fit. Relative changes in χ 2 can however be used to determine the best fit from a set of fits. Therefore, a relative reduction of χ 2 will indicate whether employed reference compounds are representative for the sample. For the evaluation of the best reference compounds we used the sample spectrum with the highest expected degree of oxidation, i.e., the sample with the greatest pore diameter (78.2 nm). The fitting results of different combinations of reference spectra are presented in Fig. 7, the nature of references being indicated in each graph. χ 2 values and fractions of reference compounds are summarized in Table I.

For the oxide component we found that fits with the Co 3 O 4 standard are generally of poor quality compared to the measured data [Fig. 7(a) and Fig. 7(b)] and exhibit χ 2 values (>0.3) much higher than ones obtained by using CoO, suggesting that this is not a component present in the sample. This finding is consistent with our previous analysis from Fig. 4. The replacement of Co 3 O 4 with CoO bulk improves significantly the fit quality and reduces the χ 2 value in the (0.03-0.05) range [Fig. 7(c) and Fig. 7(d)]. The CoO thin layer reference (1.5 nm) spectrum [Fig. 7(e) and Fig. 7(f)] in turn gives very close fitting results compared to the CoO bulk reference, giving only a slightly higher χ 2 value in the (0.05-0.08) range. However, a small deviation of the fit compared to the measured spectrum in the white line region is apparent when the CoO thin layer spectrum is employed, as revealed by arrows in Fig. 7(e) and Fig. 7(f). The CoO thin layer spectrum was obtained from a Pt-Co and CoO-AlO x multilayer substrate reported in Ref. [48]. Additional Co bonding environments such as Pt-Co and Co-Al in the absorption signal of the CoO thin layer spectrum, which are not present in our samples, may explain the lower quality of fits compared to the CoO bulk spectrum. This is the reason why a CoO bulk is favored for the adjustment of XANES data.

For the metallic component, we obtained best fitting results by employing the unholed spectrum as the end member [see Fig. 7(d I]. Insets in each figure show zooms in the normalized μ(E) region between 0.9-1.12 to highlight the quality of each fit. The reduced χ 2 parameter is a measure of the quality of the fit and is displayed above each figure. and exhibits a first XANES peak doublet for polarized XAS measurements close to α = 0 • (Ref. [51]) while a single first XANES peak is observed for high angles of 70 • and 80 • (Ref. [51] and present study). The same observations are obtained for our samples in the case of α = 80 • as developed further in the paper. Clearly, this reason can be excluded. Indeed, these differences might be explained by structural differences such as Co-Cu bonds, or characteristic thin layer bonding environments in general, which lead to a modification of XANES. Since the unholed Cu/Co/Cu multilayer spectrum reproduces best the modulations of different oscillations of sample spectra, it was used as the end member in the LCF analysis.

We found that the degree of oxidation obtained with different end member spectra directly relates to the quality of the fit.

Oxide contents of models with poor fit quality are generally underestimated (models 1 and 2). Oxide contents obtain using the CoO thin layer reference spectrum in turn are elevated (model 5 and 6) and are close to those from edge energy fitting. For the best-fit LCF model (model 4), we obtained oxide content that is in good agreement with the one obtained from the white line fitting, i.e., 22.8(±1)% and 24.2(±1)%, respectively.

Because of the good fit quality, the unholed multilayer and bulk CoO were used as end-members to extract relative contents of metallic and oxidized Co in all other antidot samples. The LCF fitting results are presented in Fig. 8 together with the χ 2 values. As for Fig. 7, the models based on bulk Co and/or CoO thin layers are less relevant for describing the data (curves not shown). A good agreement was obtained for all antidot spectra with χ 2 being below 0.033. An increase of the χ 2 with the oxide content and pore diameter is noted. This result may indicate that our oxide reference compound cannot reproduce with a high degree of accuracy the XANES features.

We therefore conclude that the oxide bonding environment in the ultrathin pores may differ from those of bulk CoO. This 532 may suggest that oxidation in our samples takes place only 533 on the surface of exposed ultrathin Co layers inside the pores. 534 Moreover, as seen in these figures, the higher the pore diameter, 535 the stronger the oxide component. The reason is the progressive 536 oxidation of Co around the pores, causing CoO nanopores. 537 At the same time, χ 2 weakly increases with d. This slight 538 increase is simply understood by the existence of pores which 539 makes slightly more difficult the model by including unholed 540 Cu/Co/Cu and bulk CoO. Finally, the values of oxidized CoO 541 content c(CoO) deduced from the fittings are plotted as a 542 function of pore diameter d in Fig. 8(f). These values of c(CoO) 543 are consistent with those appearing in the bottom right part 544 of Fig. 5, coming from the analysis of the white line. This 545 indicates that the 2 analyses lead to the same result. The linear 546 variation of c(CoO) as well as c(Co), appearing in the straight 547 line in Fig. 8(f), are found as the form [Eq. ( 4) and Eq. ( 5)] From the analysis of the white line as well as the edge energy, only c(CoO) is derived, whereas both c(Co) and c(CoO) are extracted from the LCF method using the absorption signal in the (7700-7830) eV range of energy. This model is valid for d 17 nm since we have used the d = 0 membrane in our model of linear combination of absorption [Eq. ( 3)]. Nevertheless, we remark that for d = 0 in Eq. ( 4) and Eq. ( 5), expected values for Co (≈1) and CoO (≈0) contents are obtained. To reiterate, the main result is the progressive oxidation of antidots from air oxidation when d is raised. As a consequence, the quantity of oxidized Co is tuned by the value of the pore diameter. The same result, seen for the d = 23.4 nm membrane in Fig. 5, is also observed in Fig. 8. By using the atomic layer method, deposition of oxygen at the top of the layer is more favored. As a result, the oxidation of Co is more efficient especially around the pores. This might explain the increase of exchange bias at low temperature for this membrane, as detailed in another paper [44]. In fact, at room temperature, the enhancement of the coercivity is due to the pinning effects.

As developed in another paper [44], exchange bias effects are revealed by lowering the measurement temperature, due to the antiferromagnetic coupling between CoO localized in the valley of nanopores and unoxidized Co on the top of membranes.

An important remark is given about the validity of the linear combination fitting concerning the choice of the references.

The model is tested in that study for the best following references: CoO bulk for CoO and unholed membrane for Co. In fact, the CoO right reference is difficult to be found, due to the fact that for instance the oxidation of the pore material is disordered (vacancies might be formed in the valley of membranes). This aspect leads to the fitted XANES measurements slightly differing from the experimental ones.

Nevertheless, at the end, our model persists in being valid with the employed references, and for other studies, the choice of appropriate references appears to be important.

IV. LOCAL ANTIDOT STRUCTURE AND MORPHOLOGY

The oxidation of antidots when exposed to air has been previously reported [41] from the investigation of magnetic properties and was proposed to be due to the presence of ultrathin deposition layers inside the pores, which preferentially oxidize. In the present paper, the XANES results definitely confirm the presence of oxidized Co in antidots. Indeed, the thickness variation of the deposit trilayer inside the pore exhibits most likely a crescent shape gradient, which has been also proposed in Refs. [46,47]. It is therefore likely that oxidation preferentially occurs in the vicinity of the opening of the nanopores, where the thickness of the protective Cu layer is reduced. Here, we observed the increase of the oxide content with increasing pore size from three different analysis methods of distinct XANES features. Another important result of this study is the discrepancies between the oxide component in the XANES spectra and the chosen CoO bulk reference in the LCF analysis from a quantitative analysis of absorption spectra. Nevertheless, the bulk CoO reference cannot fully reproduce the total absorption signal of the XANES spectra. This indicates that CoO possibly forms on the surface and FIG. 9. Co K-edge XANES normalized profiles for an antidot sputtered on alumina membranes for d = 78.2 nm, for out-of-plane (α = 80 • ) and intermediate (α = 45 • ) polarization geometries. The angle α is the angle between the layer plane and the x-ray polarization vector . Note some differences in data around the white lines and the edge energy (two insets). The curved blue line corresponds to a fit of the α = 80 • measurement (in red) with a linear combination of CoO bulk and unholed Cu/Co/Cu. as nanoclusters on the ultrathin metallic Co layers. Such a 609 scenario is also consistent with the presence of CoO nanorings 610 forming around the pores due to contact with air. The linearity 611 between oxide content and pore diameter further indicates 612 that the hyperfine Co layer inside the pores increases with 613 increasing pore diameter d as the free surface area of the 614 uncovered Co layer increases.

615

A. Polarized XAS observations 616

Polarized XAS is a powerful tool to characterize in detail 617 anisotropic bonding environments [52], in our case the surface 618 oxidation of Co inside the nanopores and the inclination of this 619 oxidized layer inside the pores. As outlined in Fig. 3, we have 620 performed polarized XAS measurements in 45 • and 80 • ge-621 ometries. Due to the presence of pores which exhibit multilayer 622 surfaces on their walls that are most likely inclined [46,47], we 623 need to distinguish additionally two environments: the Co on 624 the top of the surface (namely Co top ) and Co inside the pores 625 (namely Co pore ). For α = 45 • , an average of perpendicular and 626 parallel bonds to the substrate surface is sampled, while bonds 627 perpendicular to the substrate surface are sampled for α = 90 • . 628 Indeed, the contribution of the surface atoms on the total XAS 629 signal is as important as the measurement is performed under 630 grazing incidence. Figure 9 compares the XANES signals 631 obtained in 45 • and 80 • geometries (black and red spectra, 632 respectively) for the sample with the greatest pore diameter 633 (d = 78.2 nm), since this sample exhibits the highest degree 634 of oxidation and therefore might show the greatest differences 635 in XANES between the two geometries.

636

It seems that there is no preferential orientation of our Co 637 antidots due to weak differences between the two absorption 638 signals recorded for the 2 angles [53]. Nevertheless, we observe 639 several distinct modifications of the absorption signal between 640 the two geometries, including a shift of the edge energy to 641 006000-9 lower energies, a decrease of the white line intensity, as well 642 as a decrease of the amplitude of the first EXAFS oscillation 643 when changing from the 45 • to the 80 • geometry (see the oxidation of Co on top of the substrate can be neglected because the Cu deposited layer remains thick at this location and therefore prevents any oxidation. Moreover, the linear increase of the oxide content with pore diameter suggests the oxidation of pore surfaces and the formation of nanorings. At the K edge the photoelectron probes the Co p orbitals parallel to the polarization direction of the beam. In the 80 • geometry mainly intralayer bonds are probed that are dominated by Co-Co bonds as derived oxide contents are smaller. In contrast, in 45 • in which a higher degree of oxidation has been obtain, Co p orbitals perpendicular to the thin layer surface are probed, which therefore have to be composed of mainly Co-O bonds. The later observation confirms that oxidation takes place only on the inner pore surfaces at the exposed ultrathin Co layer (Co pore oxidized in part with oxygen). Moreover, even if the sample is probably polycrystalline (no preferential direction due to the sputtering process), the observations also indicate an inclination of this layer relative to the substrate surface which is in agreement with the crescent shape proposed in earlier works.

The determined relations between CoO contents and pore diameter d extracted from the three different analysis methods and for spectra collected in the two different geometries are summarized in Table II. We have obtained very good least-squares fits to the XANES spectra by using a linear combination of reference spectra, similarly to Ref. [43]. We believe that the linear combination analysis provides a very good estimation of metallic and oxidized Co contents. Our confidence in this model comes the large range of energy and the appropriate reference compounds used in the linear combination method. Moreover, structural investigations performed by polarized XANES studies confirm that Co oxidation preferentially forms at the surface of the inner pore walls.

B. Antidot morphology

Atomic force microscopy (AFM) is another tool used to gain a more detailed local picture of nanometric surface features of antidots. An AFM topography map for a moderate pore diameter is presented in Fig. 11(a). The pore diameter is close to the measured one by SEM (d ≈ 60 nm). Consistent also with SEM observations, a regular hexagonal arrangement of nanopores (p ≈ 105 nm) on the membrane surfaces is evident in the AFM map. In fact, as pointed out by [38], due to the limited detecting ability of the atomic force microscope technique into the nanopores, only the top part of the membrane, as well as the partial view of nanopores, can be imaged by this method. Indeed, the deposition in the antidot arrays is mainly on the 11(a)]. The antidot surface appears to be modulated with a periodic length of the nanohills of ≈50 nm, which is similar to AFM observations reported in [54]. The height of nanohills relative to the substrate surface reaches between 15 nm as deduced from this scale, which is in agreement with previous observations [38,54].

It is well known that the topography of anodic alumina membranes is composed of both nanopores as well as surrounding nanohills (see for example Refs. [5,38,39,[54][55][56]). This particular deposition is often observed together with the appearance of the crescent shape of the multilayer deposit inside the nanopores, as previously assumed in our antidots [41] and detailed in [12]. The reason might be explained by the double-anodization technique which induces alumina nanohills on the top of membranes. Artifacts caused by the tip shape could induce particular topology of the antidots, as revealed by the AFM view of Fig. 11(b). Consequently, conclusions about the morphology around the pores have to prudently be discussed. Nevertheless, additional investigations performed by SEM when the sample is tilted confirm the crescent shape of the antidots (views not shown). In addition, the curvature of the nanoholes is well described by transmission electron microscope measurements for similar antidots studied in the literature [31,35].

V. A MORPHOLOGICAL MODEL

750

A. Model 751

Unfortunately, it appears to be difficult to evaluate both the 752 nature and the quantity of materials along the walls of antidots. 753 As a consequence, an open question is the comparison of the 754 two deposited quantities: one on the top of the antidot (on 755 the undulated antidots) and the second one on the walls of 756 membranes [inclined as sketched in Fig. 11(b)]. The detailed 757 knowledge on the extent and chemical nature of the CoO layer 758 inside the pores is crucial for understanding the nanomagnetic 759 properties of antidots [44]. Specifically, the direction of mag-760 netic moments is directly related to antidot morphology and 761 chemical composition. Thus, to refine our current picture on 762 the oxidation of ultrathin sputtered transition-metal layers (i.e., 763 Co or Fe) inside nanopores in general, we developed a method 764 to calculate the quantity of material deposited on the substrate 765 surfaces and inner antidot pore wall. Finally we used the model 766 to determine the fraction of deposited material on top of the 767 antidot surface, which is of general interest for antidots. It is also interesting to evaluate the relative proportions of Co atoms deposited inside the nanopores versus those on the top of membranes, namely c walls and c top , respectively. In the present study, the walls of the nanopores are composed of both metallic Co and CoO and participate in the c walls value, whereas only metallic Co is deposited on the top of antidots and contributes to c top . Starting from the calculations developed above, c walls and c top can be easily expressed by the following equations:

c top = S top Co S Total = 1 -(π/4)(d/p) 2 S Total , ( 10
)
c walls = S walls Co,CoO S Total = πdL/p 2 S Total , ( 11
)
where S T otal = 1π (d/2p) 2 + πdL/(p) 2 . These equations can be applied to calculate proportions of deposited material inside the pores and on top for any antidot with pore diameter since then d and period p are known. For instance, in the case of our antidots, c walls varies from 16% to 61% when d is enhanced from 17 nm to 68 nm. This result indicates the important influence of atoms deposited on the walls of antidots for the highest d value.

Our model could be easily used in the literature for estimating atomic fractions around nanoholes and on the top of membranes. An important remark has to be discussed about the fact that atoms might be deposited by deposition methods using a more favored direction (for instance perpendicular to the layers), such as the e-beam technique. In that case, the deposition of material inside the pores is suspected to be minimal. Nevertheless, our model persists in being applied, resulting in atomic proportions more weak in the valley of nanopores compared to ones found in that present study (using the sputtering technique less directional).

B. Comparison model/experiments

In the following we compare the p/d ratios to the maximum and minimum values of c walls and c top obtained from our models to experimental findings of this study and those reported in the literature (Table III). For the calculation, a penetration depth of L = 40 nm was assumed. We observe, as expected, that the maximum (minimum) of c walls and minimum (maximum) of c top are directly related to the lowest (highest) p/d ratio.

In order to understand the effect of these quantities on the antidot properties we listed additionally the maximum and minimum ambient temperature coercivities (H max C and H min C ) of holed antidots and unholed templates (in parentheses) in Table III. Literature values compared here are from antidot substrates that have similar multilayer thickness compared to the samples investigated in this study (indicated in bold in Table III). H min C and H max C for this study are taken for the sample with the lowest and highest pore diameter, respectively. The direction of the applied magnetic field is systematically orientated following the easy axis, except for Ref. [19]. In this last reference, the large value is explained by the loss of the perpendicular magnetic anisotropy for the high-d regime. present study [25,26]. The latter may induce exchange bias effects and a potential increase in coercivity.

Variations of antidot coercivities observed in

Nevertheless, a general observation is the significant increase of H C with the presence of pores in the substrate. and Kronmüller [58]. This type of behavior is currently observed for published studies [34,36] in the literature. This is simply understood by the fact that the pinning effects become more efficient when the magnetic atoms are mainly deposited around the nanoholes. Consequently, the more d increases, the smaller the value of pd becomes, causing an enhancement of the coercivity according to the previous law.

A strong magnetic field is necessary to overcome the pinning coupling.

We note also that, for the largest d value, the magnetic atomic species located around pores are dominant (50%) in the structure, leading to strong coercivity. Moreover, the ratio p/d seems also to be a key factor to relate the magnetic properties to the antidot structure. In our model the p/d ratio is directly related to c walls in our model [see Eq. ( 11)]. Indeed, c walls progressively increase with this ratio. We therefore propose that the quantities of atoms deposited on the walls of membranes strongly contribute to the enhancement of the coercivity. The local structural characteristics of these membranes have 935 been investigated using polarized x-ray absorption near edge 936 spectroscopy (XANES) as well as SEM and AFM microscopy 937 techniques. All membranes exhibit a regular hexagonal net-938 work of pores, and only substrates treated with the ALD 939 process show slight deviations from a circular pore shape. 940 Polarized XANES allowed us to determine the proportions 941 of metallic Co and CoO in different parts of the membranes. 942 We tested three different analytical methods for this evaluation, 943 including variation of the white line intensity as well as the edge 944 energy, and finally the linear combination fitting procedure. 945 We found that the latter gave the most robust results. We 946 further found that metallic Co is the dominating species on 947 the membrane surface as well as inside the pores. We show 948 the formation of CoO (maximum of 25% of CoO) inside the 949 pore walls, which appears most likely as nanorings. The CoO 950 content increases linearly with the pore diameter. This is related 951 to the crescent shape of the multilayer inside the pores and the 952 reduction of thickness of the uppermost Cu layer that leads to 953 the oxidation of the centered ultrathin Co layer when exposed 954 to the air. We have developed a simple geometrical model to 955 evaluate the proportions and layer length of Co and CoO on the 956 pore rims and inside the pore walls. Moreover, we also provide 957 a simple formula that allows us to determine the proportion of 958 material deposited on top of the surface as well as inside the 959 walls for any antidot from the period p, the pore diameter 960 d, and the penetration length L [see Eq. (10) and Eq. ( 11)]. 961 The physical properties of nanopores studied in the literature 962 might be in part explained by the atomic proportions thanks 963 to our model. In the case of our antidots, the crescent shape 964 006000-13

FIG. 1 .

 1 FIG. 1. SEM images of Cu(10 nm)/Co(12 nm)/Cu(10 nm) sputtered on alumina membranes with different pore diameters, where the etching time t etching is indicated. For the lowest t etching [36 minutes, 3 panel (b)], an atomic layer deposition process was added to the double-anodization process, with 100 as the number of ALD cycles, leading to a reduction of the pore diameter (a).

  FIG.3. Schematic view of the measurement geometries employed for polarized XAS. The alumina template is represented in yellow with a pore diameter of 50 nm and interpore distance of 105 nm (scale is shown on the lower left). The Cu/Co/Cu deposition appears in gray (thickness not at the scale). The angle α is defined between the electric field vector ( in green) of the linear polarized incoming x-ray beam and the surface of the aluminum template (blue arrow). In normal incidence geometry α equals 0 • and the bond directions (red arrows) probed are parallel to the surface (a). For the present experiments, α was set to 45 • and 80 • to probe an average of bond directions perpendicular and parallel to the surface [panel (b), α = 45 • ] and only those bonds oriented almost perpendicular to the template surface [panel (c), α = 80 • ].

Figure 4

 4 FIG.3. Schematic view of the measurement geometries employed for polarized XAS. The alumina template is represented in yellow with a pore diameter of 50 nm and interpore distance of 105 nm (scale is shown on the lower left). The Cu/Co/Cu deposition appears in gray (thickness not at the scale). The angle α is defined between the electric field vector ( in green) of the linear polarized incoming x-ray beam and the surface of the aluminum template (blue arrow). In normal incidence geometry α equals 0 • and the bond directions (red arrows) probed are parallel to the surface (a). For the present experiments, α was set to 45 • and 80 • to probe an average of bond directions perpendicular and parallel to the surface [panel (b), α = 45 • ] and only those bonds oriented almost perpendicular to the template surface [panel (c), α = 80 • ]. region, the spectra were normalized in the high energy range [extended x-ray absorption fine structure (EXAFS), not shown here] using the program Athena [45]. In the following, first measurements conducted at 45 • are discussed and in the second part compared with those obtained at 80 • .

305FIG. 4 .FIG. 5 .

 45 FIG.4. Normalized Co K-edge XANES spectra of antidots with different pore size d, as well as the bulk CoO and Co metal reference spectra collected at α = 45 • . Letters from A to D delineate spectral regions of interest that are zoomed in the inlets on the right side. Black arrows in the inlets delineate the evolution of XANES spectra with increasing pore diameter d (from orange to blue). Note the similarities between the unholed sample (pink) and the Co metal reference (red) as well as the divergence of sample spectra towards the CoO reference spectra (gray) with increasing pore size.

323A.

  White line analysis 324The progressive increase of the white line intensity (WL) 325 of sample spectra (see B in Fig. 4) was used to determine the 326 fraction of CoO [c(CoO)] as a function of the pore diameter 327 d (Fig. 5) following the procedure of Ref. [42]. The left 328 side of Fig. 5 plots the extracted absolute WL intensities of 329 normalized sample spectra versus the pore diameter, revealing 330 a linear relationship. In order to estimate the oxide content, 331 we used the maximal WL intensities of the pure Co metal 332 spectra (normalized μ = 0.98 at 7727.6 eV) and the CoO 333 bulk spectra (normalized μ = 1.5 at 7727.0 eV) as references 334 for oxide contents of 0 and 100%, respectively (see second 335 inset in Fig. 4). Next, a linear variation between WL and 336 c(CoO) was assumed with WL = 0.53 × 10 -2 × c(CoO) + 337 0.98. Resulting c(CoO) for the different substrates are plotted 338 on the right vertical axis in Fig. 5, which can therefore be directly related to the pore diameter d.

  FIG. 6. Position of the Co K-edge energy E edge as a function of pore diameter d (left y axis) deduced from Fig. 4 for normalized sample spectra of Cu/Co/Cu antidots. The right y axis presents the extracted concentration of oxide content c(CoO) versus pore diameter d assuming a progressive oxidation of metallic Co in the nanopores. d = 0 corresponds to the unholed multilayer, the angle α (between and layer plane) being equal to 45 • .

  FIG. 7. LCF model fits to the normalized Co K-edge XANES spectra of the antidot with d = 78.2 nm (obtained at α = 45 • ). The 6 different LCF models (red lines) are based on a linear combination of two reference spectra (one for metallic Co end member and one for the Co oxide end member, as indicated in the legend on the right) to fit the sample spectrum (black lines) [(a)-(f), models 1-6; see also TableI]. Insets in each figure show zooms in the normalized μ(E) region between 0.9-1.12 to highlight the quality of each fit. The reduced χ 2 parameter is a measure of the quality of the fit and is displayed above each figure.

Fig. 7 (

 7 Fig. 7(c)]. The bulk and the unholed spectrum exhibit several 486

FIG. 8 .

 8 FIG. 8. (a)-(e) Data and simulated Co K-edge EXAFS profiles for Cu(10 nm)/Co(12 nm)/Cu(10 nm) sputtered on alumina membranes for different pore diameters d in the (17.0-71.5) nm range. Zooms in the (0.9-1.12) y-axis range are also shown to highlight the good quality of fits. The model is based on a sum of 2 components of absorption, unholed Cu/Co/Cu and bulk CoO components of absorption. (f) Co and CoO contents deduced from these fits are plotted as a function of d. In dotted line are represented the CoO and Co contents calculated from a model developed further [see Eq. (8)]. Here, α = 45 • and χ 2 are also given in (a)-(e).

  548 c(CoO)(%,±0.5) = 0.28d + 0.49, (4) c(Co)(%,±0.5) = -0.28d + 99.50.(5)A comparable law is obtained from the study of the white 549 line for CoO: c(CoO)(%,±1) = 0.31 × d, which makes our 550 analysis of XANES by two different methods more robust.

FIG. 10 .

 10 FIG.10. CoO content deduced from 3 different procedures (edge energy, while line, and linear combination) as a function of pore diameter d for antidots sputtered on alumina membranes, for an out-of-plane (α = 80 • ) polarization geometry. d = 0 corresponds to the unholed multilayer.

FIG. 11

 11 FIG. 11. (a) Top-view AFM map of sample d = 63.8 nm (corresponding to t etching = 60 minutes) of a surface area of 1000 × 1000 nm 2 having a depth resolution of 160 nm. The vertical dimension is expressed as color scale with white being the uppermost and black being the lowest portions of the sample. Note the hexagonal arrangement of holes and the secondary hexagonal pattern of the nanohills (white dots). (b) Schematic cross section in the (x,z) plane through a nanohole and adjacent nanohill structures. Abbreviations are as follows: top, Co layer on substrate surface; L, total length of Co layer in the inner hole walls; L pores Co , length of the unoxidized Co layer along the hole walls; L pores CoO , length of the oxidized Co layer in deeper portions of the nanoholes. Here, L = L pores Co + L pores CoO . Note the nanohill doublet seen on the side of the hole that has a periodicity of 500 nm. top and the inner wall of the templates, since the diameter is in the nanometric range and the height in the micrometer regime. Consequently, no deposited material can reach the bottom of the pores. Interestingly, a secondary hexagonal network around each nanopore can be distinguished on the substrate surfaces, which is composed of 6 white point first neighbors surrounding the pore [white dots in Fig. 11(a); see also color scale on the right]. Figure 11(b) shows a schematic cross section through a nanopore in the (x,z) plane together with the surrounding substrate surface [see the straight line in Fig. 11(a)]. The antidot surface appears to be modulated with a

768

  In our model, we assumed a flat sample surface area S o of 769 1 cm 2 , for the top part of antidots, for simplicity of calculations. 770 The density of pores [namely density(pores)] can then be 771 expressed as density(pores) = 1/(p 2 ) due to the symmetric 772 hexagonal arrangement of pores as observed from AFM and 773 SEM investigations. The surface area of metallic Co sputtered 774 only on the substrate surface [see this surface on the top of 775 antidots in Fig.11(b)] can be calculated from S top Co = S o -776 density(pores) × π (d 2 )/4, with π (d 2 )/4 the surface area of 777 one pore. Substituting S o and density(pores) for our model 778 we derive S top Co = 1π (d/2p) 2 as the surface area of the 779 membrane without pores (with p the period, 105 nm in our 780 case). The total penetration length (L) of the deposited Co layer 781 along the inner pore wall is obtained from L = L of the unoxidized Co layer that 783 is covered with a sufficiently thick Cu layer, and L pores CoO being the length of the oxidized Co layer exposed to air. in Fig. 11(b). The total surface of and L pores Co of approximately 50%, due to the conservation of 828 volume. For instance, an increase of L pores CoO and L pores Co by 50%, 829 i.e., ≈17.7 nm and ≈21 nm, respectively will lead to a total 830 length L of ≈40 nm.

  831

  Second, H max C also increases with the proportion of material deposited inside the pores (c walls ). Starting from these two observations, the clear increase of the coercivity is caused by the opening of nanostructures, where the pinning of the domain walls induces a strong coupling. This leads to an increase of the coercivity H C . In fact, the variation of H C with the geometrical parameters, namely p and d, is assumed to be of the form H C = 1/(pd), initially predicted by Hilzinger

  More details will be discussed in another paper devoted to magnetic properties of the Cu/Co/Co antidots, specially by varying both the temperature and the magnetic field (amplitude/orientation), and for a series of different pore diameters, in the light of our structural investigations. As known in the literature, and for the first time, the exchange bias effect was discovered 60 years ago by Meiklejohn and Bean [59], for CoO associated with Co, whereas the antiferromagnetic coupling is not expected when CoO is replaced by Co 3 O 4 . For a more comprehensive understanding of exchange bias effects, Ref. [60] reviews the phenomenology of such effects, for antiferromagnetic/ferromagnetic structures, with in particular intensive investigations using CoO as an antiferromagnetic 925 material. 926 VI. CONCLUSION 927 We have synthesized Cu(10 nm)/Co(12 nm)/Cu(10 nm) 928 sputtered on antidots with a range of different pore diameters 929 d (20-80 nm). Conventional pore diameters [d = (40-80) nm] 930 were obtained with the double-anodization technique while 931 weaker d values (20-40 nm) could be achieved with an 932 additional atomic layer deposition treatment of antidots. Re-933 sulting antidots exhibit a period of the array p of 105 nm. 934

TABLE I .

 I Six different models used for adjusting the XANES profile for the 78.2 nm antidot by taking into account a linear combination of Co and oxide components. Columns: Number of model, nature of pure and oxidized Co, χ 2 , pure and oxidized Co content in percent. The values in parentheses indicate the errors.

	13310M	PRMATERIALS	June 5, 2018	14:0
	H. GARAD et al.				PHYSICAL REVIEW MATERIALS 00, 006000 (2018)
	Considered model	Pure and oxidized Co	χ 2	Co content (%)	Oxide content (%)
	1		C o a n d C o 3 O 4 bulks	0.408	82.4 (1.1)	17.6 (1.1)
	2		Co unholed and Co 3 O 4 bulk	0.317	84.8 (1.0)	15.2 (1.0)
	3		Co and CoO bulks	0.049	74.6 (0.4)	25.4 (0.4)
	4		Co unholed and CoO bulk	0.029	77.2 (0.3)	22.8 (0.3)
	5		Co unholed and CoO thin layer	0.050	65.4 (0.6)	34.6 (0.6)
	6		Co bulk and CoO thin layer	0.080	62.1 (00.7)	37.9 (0.7)
				006000-7

TABLE II .

 II

TABLE III .

 III Table III may however also be related to differences in stacks and in particular in the ferromagnetic or in some cases antiferromagnetic layer Comparison of structural characteristic and magnetic properties of antidots reported in the literature and determined in the present study. Listed information of antidots includes type of acid used during synthesis, the multilayer system (thickness in nm), period p and pore diameter d (in nm), d/p ratio, as well as calculated proportions of material deposited on the substrate surface (c top , ±2) and walls (c walls , ±2) in percent from our model [see Eq. (10) and Eq. (11)]. Reported magnetic properties correspond to the minimum and maximum coercivity H min

	13310M	PRMATERIALS	June 5, 2018	14:0
	INFLUENCE OF THE PORE DIAMETER IN Cu/Co/Cu …		PHYSICAL REVIEW MATERIALS 00, 006000 (2018)
	C	and H max C , as well as the coercivity for the unholed stack in parentheses, and associated references.
	Type of acid		Systems	p (nm) d (nm)	p/d	c walls (%)	c top (%)	H min C /H max C	at RT	References
	sulfuric	[Co(0.5)/Pt(2)] 20	60	9-48 6.67/1.25 24.2/77.1 75.8/22.9	540/1350(140)	[19]
	sulfuric	IrMn(8)/CoFe(10)	60	10-48 6.00/1.25 26.3/77.1 73.7/22.9	217/501(27)	[25]
	oxalic		Co(20-210)	100	35-90 2.86/1.11 32.7/75.7 67.3/24.3	≈50/503(7)	[27]
	oxalic	CoCrPt(10-20)	105	40-80 2.63/1.31 33.9/62.7 66.1/37.3	420/430(150)	[37]
	oxalic		NiFe(18-138)	105	35-66 3.00/1.59 30.4/52.2 69.6/47.8	70/240(few Oe)	[20]
	oxalic	[NiFe(20-100)/FeMn(15)] 10	120	30-80 4.00/1.50 21.6/51.7 78.4/48.3	23/30(11)	[26]
	oxalic		NiFe(10-20)	105	22-65 4.77/1.62 20.6/51.3 79.4/48.7 (few Oe)/40(not given)	[28]
	oxalic		Co(12)	105	17-78 6.18/1.35 16.5/60.9 83.5/39.1	27/880(5)
							006000-12

  PHYSICAL REVIEW MATERIALS 00, 006000 (2018) of the multilayer inside the pores and the presence of CoO 965 nanorings induce particular magnetic reversal and exchange 966 bias effects at low temperature, as developed in a forthcoming

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		H. GARAD et al.

967

paper.

insets in Fig.9). These differences may indicate a higher

ACKNOWLEDGMENTS

This work was supported by the French Ministry of Foreign Affairs. The authors are thankful to O. Fruchart for the AFM measurements.

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665

The differences between the XANES and degree of oxida-666 tion obtained in the two geometries can be related to different 667 bond directions probed inside the pores (Co pore ). Indeed, the Co sputtered on the inner pore walls can be calculated from

As CoO is expected to form only at the deeper portions of the

In the following we further assume that the thickness of well as the pore periodicity p [Eq. ( 8) and Eq. ( 9)]:

In the above expressions we obtain c(CoO) = 0 and