Grégoire Lefebvre
email: gregoire.lefebvre@orange-ftgroup.com

Christophe Garcia
email: christophe.garcia@orange-ftgroup.com

A Heterogeneous Descriptor Fusion Process For Visual Concept Identification

Keywords: SOM, bag of keypoints, image classification

In this paper, we propose a novel method for robustly classifying visual concepts. In order to achieve this aim, we propose a scheme that relies on Self Organizing Maps (SOM [6]). Heterogeneous local signatures are first extracted from training images and projected into specialized SOM networks. The extracted signatures activate several neural maps producing activation histograms. These activation histograms are then combined into a global fusion process in order to build our final image representation. This fusion scheme is generic and shows promising results for automatic image classification and objectionable image filtering.

I. INTRODUCTION

In many applications, such as data mining, object recognition, image classification, etc., the data input dimension may be very large, and these features may be provided by different captors or descriptors. Thus, it is a very challenging problem for an analyst to extract the pertinent features or to detect useful structure inside this volume of information. The main idea of this study is to automatically learn visual concepts from learning image series described with several heterogeneous features. Indeed, nowadays, it appears fundamental to take into account a multi-modal strategy to deal with face identification, video content-based retrieval or illicit content filtering. The combination of color, texture, and shape descriptors seems to be very helpful in performing classification rates. Classically, no knowledge about data distribution is a priori available. Consequently, the system should be able to extract the most important information in order to cluster and select these features before fusing the heterogeneous descriptions.

In the state-of-the-art methods, these three operations are realized sequentially and independently. The common techniques join the features in an a priori static fusion process. The feature extraction considers some similarity criterion (mutual information, feature correlation, etc.), and then operates information selection thanks to PCA (Principal Component Analysis) or LDA (Linear Discriminant Analysis) algorithms [START_REF] Zhang | Information fusion in Face Identification[END_REF], and finally agglomerates the multi-modal descriptors with a simple concatenation [START_REF] Spyrou | Fusing MPEG-7 Visual Descriptors for Image Classification[END_REF]. Another issue to join heterogeneous features is called "a posteriori dynamic fusion process", proposing to weight different classifier results with a boosting approach (e.g. Adaboost [START_REF] Freund | Decision-theoretic generalization of on-line learning and an application to boosting[END_REF]). The main drawback of these strategies is the lack of communication between the heterogeneous feature fusion and discriminative information learning. That is why, here, our approach tries to keep crucial features from heterogeneous descriptors by clustering, selecting and fusing them in one learning process.

This paper is organized as follows. In Section II, we present our image categorization scheme based on SOM activation histograms. Then, Sections III and IV expose how to extract relevant image information before fusing them in a final neural model. In Section V, we demonstrate our system's performance with several experimental results and finally conclusions are drawn.

II. PROPOSED SCHEME OVERVIEW

This article presents a new strategy to automatically classify image contents from heterogeneous information. Classically, image classification is realized in a competitive way between several descriptors, and the best configuration results give the best descriptor choice. Here, we propose to use all descriptors to better represent visual concepts. Nevertheless, this huge volume of information should be structured by a selection and fusion strategy, without human intervention. That is why we investigate the use of SOM to select and structure the information. First, for each category, intermediate models are built, one for each descriptor. Then, a final model combines the intermediate representations to give a new image feature vector. The fusion learning process then takes place during the class model constitution, not in the feature extraction or in the final classification, as shown in Figure 1. This proposed architecture is composed of three steps: the first step describes image content with color, texture and shape information; the second step proposes our new image representation; and finally a classifier takes the decision about the image class. Thus, for the first and the last steps, we refer to well known state-ofthe-art results. Describing an image, we extract some points of interest thanks to a salient point detector [START_REF] Bres | Detection of Interest Points for Image Indexation[END_REF], [START_REF] Harris | A Combined Corner and Edge Detector[END_REF], [START_REF] Laurent | In Depth Analysis and Evaluation of Saliency-based Color Image Indexing Methods using Wavelet Salient Features[END_REF], and for each region of interest we compute a local signature focusing on color [START_REF] Swain | Color Indexing[END_REF], texture [START_REF] Manjunath | Color and texture descriptors[END_REF] and shape [START_REF] Laurent | Description of local singularities for image registration[END_REF] information. In the same way, the third step is performed via a classifier: KNN (K-Nearest Neighbor), MLP (Multi-Layer Perceptron [START_REF] Rosenblatt | The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain[END_REF]), RBF (Radial Basis Function [START_REF] Broomhead | Multivariable Functional Interpolation and Adaptive Networks[END_REF]) or SVM (Support Vector Machine [START_REF] Vapnik | The Nature of Statistical Learning Theory[END_REF]).

A. Notation

In the following, let us use the following notations to build our fusion strategy (cf. Figure 1):

-H j (i,d) is the activation histogram of the image i for the category j, obtained with the intermediate model SOM j d from its signatures d; -H j (i) is the activation histogram of the image i for the category j, obtained with the final model SOM j ; -H (i) is the final feature vector of the image i for all categories, used as an input to a classifier.

B. Fusion Strategy

Our main contribution corresponds to the second scheme step where we propose a topological map as an image class model (cf. Figure 1 IV-1). This final single model per image category identifies its visual concept by a neural activation histogram (cf. Figure 12). Indeed, for a test image, the model activation strength designs the belonging class, as shown in our previous studies [START_REF] Lefebvre | Facial biometry by stimulating salient singularity masks. Advanced Video and Signal Based Surveillance[END_REF], [START_REF] Lefebvre | Supervised image classification by SOM activity map comparison[END_REF], [START_REF] Zheng | Fast-learning adaptive-subspace self-organizing map : An application to saliency-based invariant image feature construction[END_REF]. Thus, the final classifier learns the adequacy between a class model and its learning samples in order to deduce which class model is the most representative for a test image. Our final class model construction is built as follows:

• Here, we use a SOM for each image descriptor.

More precisely, the first layer of the second step is composed of 3 SOMs: one for color, one for texture and the third one for shape information. The SOMs are known to automatically emerge descriptors in a competitive and adaptive process. The unsupervised SOM learning process offers three main properties: dimension reduction, topology preservation and data accommodation. Thus, each map synthesizes a particular type of feature for the current category, performing a process of selecting and clustering. Indeed, the learning map operation brings to light inside the 2D lattice the best matching units (BMUs) which better represent the input data in terms of visual similarity. Finally, we focus on BMU neural activity during the learning signature stimulation. This activation is calculated with the quantization error eq c of the BMU c with the signature x d of the image i for the descriptor d (see Algorithm 1 in Section IV).

• The activation histogram H j (i,d) of the image i with its descriptor d of the class j agglomerates the neural activation of the intermediate SOM model. This histogram becomes an intermediate signature, representing the image content for the considered descriptor d. Thus, we use several intermediate image representations (See Figure 1 I-2, II-2 and III-2) which have the same dimension (the SOM size) for different descriptors. These activation histograms H j (i,d) can be compared and learned, corresponding to the adequacy between the color, texture or shape models with its learning examples.

• When an image is proposed to the system, we focus on its three intermediate representations. The three activation histograms are then learned by a final SOM j per category (cf. Figure 1 IV-1). We randomly inject the intermediate activation histograms in this new SOM and the fusion is performed during the SOM learning process to build the final model. This fusion is made possible because the intermediate representations are comparable, using the neural map activations belonging to the same data space.

• The final classification competes on final image representations (cf. Figure 1 IV-2). The final image representation of the image i is an activation histogram H (i) , the result of a concatenation of all final class stimulation H j (i) .

III. FEATURE EXTRACTION AND STRUCTURING

A. Salient Point Detection

The first step of an image categorization scheme is the feature extraction. Extracting local signatures is realized here in two steps: the salient point detection and the region of interest description. The goal of salient point detectors is to find perceptually relevant image locations. Many detectors have been proposed in the literature. In this paper, we investigate three types of interest point (IP) detectors, each one focusing on a particular local property of the image content such as corners [START_REF] Harris | A Combined Corner and Edge Detector[END_REF], contrast [START_REF] Bres | Detection of Interest Points for Image Indexation[END_REF], edges [START_REF] Laurent | In Depth Analysis and Evaluation of Saliency-based Color Image Indexing Methods using Wavelet Salient Features[END_REF] detailed in the following: -The Harris detector [START_REF] Harris | A Combined Corner and Edge Detector[END_REF] aims to locate salient zones on corners by searching for the maxima of a function based on the local autocorrelation matrix of the signal. The authors observed that a corner is a place where the signal varies strongly in two directions. Based on this fact, Harris and Stephens proposed to compute a corner response function at each pixel to indicate the presence of a corner.

(a) (b) (c)
-Motivated by the sensitivity of the human visual system to the multi-resolution and the contrast, the detector presented in [START_REF] Bres | Detection of Interest Points for Image Indexation[END_REF] proposes to locate salient points in high contrast areas. Bres and Jolion define a multi-resolution pyramid of contrast by computing the local and background luminance on different scales. Each point in the pyramid can thus be characterized by a significant local amount of the normalized contrast measure. This normalized contrast measure allows the extraction of an interest point at a different resolution level by searching for the local maxima above a predefined threshold.

-The salient point detector in [START_REF] Laurent | In Depth Analysis and Evaluation of Saliency-based Color Image Indexing Methods using Wavelet Salient Features[END_REF] uses a Haar wavelet analysis to find pixels on sharp region boundaries. Working with wavelets is justified by the consideration of the human visual system for which multi-resolution, orientation and frequency analysis are of prime importance. In order to extract the salient points, a wavelet transform is firstly performed on the grayscale image. The obtained wavelet coefficients are represented as introduced by Shapiro [14]. This tree is then scanned for the first time from leaves to the root to compute the saliency value at each node. A second scanning occurs in order to determine the salient path from the root to the locations on the original image, where the raw salient points are located.

B. Local Patch Description

In our study, we are interested in three different types of descriptors to perform a feature fusion. Thus, we present two MPEG-7 descriptors [START_REF] Manjunath | Color and texture descriptors[END_REF] to describe color and texture and a local singularity descriptor proposed in a recent study [START_REF] Laurent | Description of local singularities for image registration[END_REF]:

-The Histogram Color Descriptor (HCD [START_REF] Swain | Color Indexing[END_REF]) is a color histogram in the RGB color space that represents color distribution in the region of interest. Here, we use 32 bins per color channel, resulting in a signature dimension of 32 3 .

-The Homogeneous Texture Descriptor (HTD [START_REF] Manjunath | Color and texture descriptors[END_REF]) is designed to characterize the properties of texture, based on the assumption that the visual properties of the texture are relatively constant over the region. The descriptive features are extracted from a bank of orientation and scale Gabor filters. Its size is 62.

-The Regularity Foveal Descriptor (RFD [START_REF] Laurent | Description of local singularities for image registration[END_REF]) efficiently characterizes an edge by considering its Hölder exponents that evaluate the signal regularity. Then, for each singularity point, the Hölder exponent is estimated with foveal wavelets as presented in [START_REF] Mallat | A Theory for Multiresolution Signal Decomposition: The Wavelet Representation[END_REF]. Gradient orientations θ and Hölder exponents α are then jointly used in 3D histograms. To build such histograms, a 32 × 32 patch around each interest point is split into 16 sub-regions and the number of times each pair (α, θ) appears in each sub-region is quantified. We use three Hölder exponent bins in the range [-1.5, 1.5] and eight orientation bins in [-π 2 , π 2 ]. All 3D histograms are concatenated to form the final signature. The dimension is then: 8 × 3 × 16 = 384.

C. Spatial Information Structuring

In order to structure the local feature vectors into a "bag of features", we propose a system based on Kohonen topological maps. The SOM [START_REF] Kohonen | Self-Organizing Maps[END_REF] is based on the construction of a neuron layer in which neural units are arranged in a lattice L as shown in Figure 3. The neural layer is innervated by some input fibers, called axons, which carry the input signals and excite or inhibit the cells via synaptic connections. The 2D lattice shape changes during the learning process to capture the input information and the topology existing in the input space. These two properties can be considered as competitive learning and topological ordering. At the end of the learning process, the patches are clustered in terms of common visual similarity and each SOM unit synthesizes the most recurrent local signature for each visual concept, composing our "bag of features".

Let us now describe the SOM algorithm by assuming an SOM lattice structure composed of U neural units. Let X = x(t) be the sample set with x(t) ∈ n , t ∈ {1, 2, . . .} being the time index. Supposing M = m k (t) a set of reference vectors (the weights) with m k (t) ∈ n , k ∈ {1, 2, . . . , U }, we define the BMU with (See Figure 3):

c = arg min k ||x(t) -m k (t)||, ∀k = 1, 2, . . . , U. (1)
A kernel-based rule is used to reflect the topological ordering. The updating scheme aims to perform a stronger weight adaptation at the BMU location than in its neighborhood. This kernel-based rule is defined by:

m k (t + 1) = m k (t) + λ(t)φ ck (t)[x(t) -m k (t)], (2)
where λ(t) designates the learning rate i.e. a monotonically decreasing sequence of scalar values with 0 < λ(t) < 1. φ ck (t) represents the neighborhood function. Classically, a Gaussian function is used, leading to:

φ ck = exp - ||r c -r k || 2 2δ(t) 2 . (3)
Here, the Euclidian norm is chosen and r k is the 2D location of the k th neuron in the network. δ(t) specifies the width of the neighborhood during time t.

IV. FINAL MODEL BUILDING

In the proposed method, the new final image representation is performed thanks to two following algorithms. The first one is the creation of three intermediate histograms per image, one for each input descriptor; and the second one builds the final image signature, proposing an image feature vector for the final classification.

For the first algorithm (cf. Algorithm 1), we focus on image information class by class. Firstly, we locate the points of interest for each image. Secondly, local signatures are computed describing color, texture and shape for each region of interest. In the third step, color signatures are used to structure a specialized SOM, representative of the main color information of the current category. Two others SOMs are learned in order to give a texture and a shape model of the current class. The first algorithm presents how intermediate histograms are built from the neural activation of the previously learned SOMs. The SOM neural activation is evaluated by the quantization error eq c (t) between the local signature x d (t) and its BMU m c (t) (cf. Equation 4). This value eq c (t) corresponds to the stimulation of the neuron c at the time t and we build a histogram H j (i,d) (t) resuming all neuronal unit activation of one image i of the class j (cf. Equation 5).

For the second algorithm (cf. Algorithm 2), a similar process creates a final SOM from the three previously computed intermediate histograms H j (i,d) , class by class. Thus, each class information is finally structured by one SOM. Here, the histograms H j (i,d) are used as input vectors for a new SOM learning process. The second algorithm presents how final feature vectors are built for each image. The SOM neural activation is then evaluated by the error quantization eq γ between the local signature H j (i,d) and its BMU m γ (t) (cf. Equation 6). Similar to the first algorithm, the histogram H j (i) [γ] resumes all neuronal unit activations of one image i of the class j (cf. Equation 7). Compute the local signature x d (t) with the descriptor d of the region of interest detected by t.

7:

The SOM j d , corresponding to the descriptor d and the class j, locates the BMU vector mc(t) with the signature x d (t).

8:

We compute the quantization error eqc(t) by:

eqc(t) = ||mc(t) -x d (t)||, (4) 9:
The neural activation histogram H j (i,d) (t) of the map SOM j d is then updated by:

H j (i,d) (t)[c] = H j (i,d) (t -1)[c] + eqc(t), (5)
where c is the BMU index of the map SOM j d . The final map SOM j , corresponding to the class j, locate the BMU vector mγ(t) with the signature H j (i,d) . (N.B. Here, t = d.)

5:

We compute the quantization error eqγ(t) by:

eqγ(t) = ||mγ(t) -H j (i,d) ||, (6) 6:
The neural activation histogram H j (i) (t) of the map SOM j is then updated by:

H j (i) (t)[γ] = H j (i) (t -1)[γ] + eqγ(t), ( 7
)
where γ is the BMU index of the map SOM j .

7:

end for 8:

H j (i) is concatenated with H (j-1) (i)
to form the image feature vector H (i) .

9:

end for 10: end for V. EXPERIMENTS

A. Natural Image Databases

We perform experiments on two different image databases in order to deal with different image classification issues.

• The first experiment tests an objectionable database.

There are respectively 733 adult and 733 benign images in the training set. The test database is composed of 377 adult images and 467 benign images downloaded from the Internet. The benign class creation is a challenging issue. We decide to include: landscapes, flowers, animals, buildings, portraits and planes. We use this database to evaluate our strategy versus other fusion methods.

B. System Configuration

In all experiments, the SOM networks are configured using the following rules to ensure optimal performance in terms of accurate data representation: the learning steps T are 500 times the cell number U ; the learning rate forms a monotone decreasing sequence: λ(t) = T T +99t ; the neighborhood width δ(t) decreases linearly with t from

C. Experimental Results

1) Objectionable Database:

The first experiment examines the assumption of increasing classification rates with descriptor fusion. First of all, we classify the adult image database with each descriptor separately. The color, texture and shape descriptor are computed respectively thanks to the HCD, HTD and RFD descriptor. Here, we study the influence of the salient point detector by locating 2, 000 points with three extractors: Harris, contrast-based and wavelet-based. Moreover, we test the intermediate representation based classification with a SOM of size 20x20. H (I,C) , H (I,T ) , H (I,S) are the activation histograms of the intermediate models of color, texture and shape, built from the HCD, HTD and RFD descriptors respectively. The final classification is performed by an SVM. The results, shown in Table I, demonstrate slightly better performance when we use the wavelet-based detector. Nevertheless, the gain is minor compared to the other detectors, but it can be explained by the salient point location on sharp region boundaries that offers a good criteria for local image signature computation. Moreover, our intermediate image representation allows us to keep the discriminative and redundant information for each initial descriptor thanks to the activation histograms. The SVM classification then gives the following classification rates, respectively 93.36%, 82.11%, and 95.02%. It appears here that color and shape information is fundamental to filter these objectionable images. In the second part of this experiment, we test our fusion architecture using two strategies: 1) Our approach 1 uses one final SOM for all categories to join the three single activation histograms (H (I,C) , H (I,T ) and H (I,S) ); the final image feature vector is then the activation histogram of this SOM; 2) Our approach 2 combines several final SOMs, one for each category; the final image feature vector is then the concatenation of the activation histograms of each SOM.

Table II shows the gain obtained from our second approach, compared to the previous classifications. Indeed, the classification rate grows to 98.46% with this approach. Moreover, we can see that our fusion strategy performs better (98.46%) with a multi-model scheme than with a single SOM for all categories (92.18%). We can remark that one single SOM is not efficient enough to gather the full information, and that is why a multi-scheme strategy is preferable. Moreover, the second approach permits a competition between the different class models that increases the performances. In this experimental part, we similarly show that several final classifiers are applicable, but here the SVM seems to better deal with our final activation histograms better than a KNN, a MLP or an RBF classification. The performance decreasing of the last three classifiers are due to the curse of dimensionality. Moreover, the SVM classifier with a one-against-all strategy improves the good identification rates. In the third part of this experiment, we evaluate our fusion strategy versus other fusion methods. First, we compare our second approach to two a priori fusion methods before the final SVM classification:

-the a priori 1 method corresponds to the input local descriptor concatenation: HCD, HTD and RFD;

-the a priori 2 method is the concatenation of the intermediate representations: H (I,C) , H (I,T ) and H (I,S) .

Secondly, we test the Adaboost method. This a posteriori method trains a series of classifiers and iteratively focuses on the hard training examples. The algorithm relies on continually changing the weights of its training examples so that those that are frequently misclassified get higher and higher weights. AdaBoost predicts one of the classes based on the sign of a linear combination of the weak classifiers trained at each step. Here, the weak classifiers are obtained with the H (I,C) , H (I,T ) and H (I,S) representation of Table I.

As shown in Table III, our second approach performs better than these a priori and a posteriori methods. These results highlight the importance of fusing different descriptors during the class model learning process.

2) PASCAL 2005 Database: The color, texture and shape descriptors are again computed thanks to the HCD, HTD and RFD descriptors respectively. The wavelet-based salient point detector is used to locate 2, 000 points and each SOM has a size of 20x20. All classification rates are obtained by a SVM.

The second experiment shows that our fusion strategy gives promising results on a visual object classification challenge. Indeed, the final SVM classification achieves 90.56%, overrating each intermediate classification, respectively 77.93%, 83.74% et 85.63%, for color, texture and shape description (cf. Table IV). This gain is performed on the four categories as shown on Table V and Figure 4, where the confusion matrix and the ROC (Receiver Operating Characteristic) curves are displayed for the test 1 database.

For the test 2 dataset, the methods are evaluated by measuring the Area Under the ROC Curve denoted AUC in the following. The comparison of classification results presented during the PASCAL 2005 recognition challenge with our results are presented in table VI. Finally, our method performs very well in comparison with other PASCAL 2005 methods. On this database, our AUC for people is the first one, for bicycles we are in the top two and the AUCs for motorbikes and cars are in fourth place. Thus, the proposed method increases the K-means based method presented by the University of Edinburgh [START_REF] Everingham | The 2005 PASCAL Visual Object Classes Challenge[END_REF], and the SOM-like representation of Helsinki University of Technology [START_REF] Everingham | The 2005 PASCAL Visual Object Classes Challenge[END_REF]. The method called "INRIA-Zhang" has got the best results for this database. This approach represents images as distributions of features extracted from a sparse set of keypoint locations and learns a SVM classifier with a kernel based on an effective measure for comparing distributions. Their vocabulary histograms are built from a direct clustering in opposition to our neural learning process which synthesizes the data in an unsupervised mode. The figures 5 and 6 show respectively samples of good and bad classification with our strategy. It appears that there exists a large variety of color, texture and shape information to define one visual concept, a bicycle for instance. Nevertheless, the intermediate model seems to focus on the more redundant information and the final model combines each description to improve the classification results. The classification error of 9.04% may be explained by a slight confusion between bicycle and motorbike that shares many properties. When two different objects interfere in the same image (cf.

3 rd image of motorbike on Figure 6), the classifier selects the more probable as a class winner. It would be interesting to focus the category learning process on a visual object, and to detect them during the classification process, to deal with such ambiguities.

VI. CONCLUSIONS AND FUTURE STUDIES

In this paper, we have presented a new system to classify visual concepts, jointly using several pieces of descriptor information contained in each region of interest. Based on the main properties of SOM, our scheme gives very promising results to identify the image class. The multi-modal architecture joins the color, texture and shape features to model the two categories in the context of adult image filtering better. We plan to experiment our fusion method on other issues such face recognition.

The advantages of the proposed method are the following: the possible use of whatever image descriptor (color, texture, shape, etc.); several approaches are available: global, local, region-based; the number of descriptors is only limited by the classifier capacity; the final image feature vector is compatible with all classifiers; a feature selection; a heterogeneous feature fusion.

Motorbike People

Figure 1 .

 1 Figure 1. The Proposed System Architecture

Figure 2 .

 2 Figure 2. IP detection with Harris (a), contrast (b) and wavelet (c).

Figure 3 .

 3 Figure 3. Patch projection on SOM lattice.

Algorithm 1

 1 Intermediate Model and Activation Histograms 1: for each category j = {1, . . . , J} do 2:for each image i = {1, . . . , I} do 3:Detect the points of interest of the image i.

4 :

 4 for each point t = {1, . . . , P } do 5:for each descriptor d = {1, . . . , D} do 6:

Algorithm 2

 2 Final Model and Activation Histograms 1: for each category j = {1, . . . , J} do 2:for each image i = {1, . . . , I} do 3:for each histogramm H j (i,d) , d = {1, . . . , D} do 4:

√ 2 2 U

 2 to 0.5.

Figure 5 .Figure 6 .

 56 Figure 5. Good classification: Test 2 PASCAL 2005

•

  The second dataset is the PASCAL 2005 recognition challenge[START_REF] Everingham | The 2005 PASCAL Visual Object Classes Challenge[END_REF]. The training set is composed of 684 images by merging the initial training and validation sets. The test set 1 proposes 689 images for four categories: motorbikes, bicycles, cars and people. This database was constructed with different well-known datasets except test set 2 (1072 images) which was obtained from the Internet. This database is a reference for image classification algorithms and the test set 2 is known to be more difficult, having no relationship with the learning images.

Table VI AUC

 VI VALUES: TEST 2 PASCAL 2005[START_REF] Everingham | The 2005 PASCAL Visual Object Classes Challenge[END_REF]


CNRS and Université de Montpellier, France -http://www.lirmm.fr/rivals/ High-throughput DNA/RNA sequencing is a routine experiment in molecular biology and life sciences in general. For instance, it is increasingly used in the hospital as a key procedure of personalized medicine. Compared to the second generation, third generation sequencing technologies produce longer reads with comparatively lower throughput and higher error rate. Those errors include substitutions, indels, and they hinder or at least complicate downstream analysis like mapping or de novo assembly. However, these long read data are often used in conjunction with short reads of the 2nd generation.

I will present a hybrid strategy for correcting the long reads using the short reads that we introduced last year. Unlike existing error correction tools, ours, called LoRDEC, avoids aligning short reads on long reads, which is computationally intensive. Instead, it takes advantage of a succinct graph LoRDEC is available at http://atgc.lirmm.fr/lordec; joint work with L. Salmela and A. Makrini.

  for keynote presentation at "German Conference in Bioinformatics", Dortmund, Germany Address: Laboratoire d'Informatique de Microélectronique et de Robotique de Montpellier (LIRMM) and Institute of Computational Biology (IBC)

  to represent the short reads, and compares long reads to paths in the graph. Experiments show that LoRDEC outperforms existing methods in running time and memory while achieving a comparable correction performance. It can correct both Pacific Biosciences and MinION reads from Oxford Nanopore.


Anne D Lamirand

Márcio M Soares

Aline Y Ramos

Hélio C N Tolentino

Maurizio De Santis

Julio C Cezar

Abner De Siervo

Spin orientation in an ultrathin CoO/PtFe double-layer with perpendicular exchange coupling

Keywords: x-ray absorption spectrocopy, x-ray linear dichroism, multiplets, antiferromagnetic

We studied by soft x-ray absorption spectroscopy the magnetization axis in an 4nm thin CoO (111) layer exchangecoupled to an ultra thin L1 0 PtFe layer with perpendicular magnetic anisotropy. The angular dependence of the linear magnetic dichroism at 10K and the relative variations of the spectral features provide a full description of the spin orientation in this antiferromagnetic layer. The spins are found in the film plane, pointing along the 110 direction. This results is discussed in relation to the film strain and preferential occupation of t 2g orbitals.The strong orthogonal coupling between Co and Fe spins should be at the origin of the robustness of the exchange bias effect foun in this bilayer system.

Introduction

Antiferromagnetic/ferromagnetic (AFM/FM) bilayers with controllable perpendicular magnetization are of a great interest for potential logic devices with high density, thermal stability and low critical current for current-induced magnetization [START_REF] Chappert | The emergence of spin electronics in data storage[END_REF][START_REF] Mangin | Current-induced magnetization reversal in nanopillars with perpendicular anisotropy[END_REF]. To have an adequate description of AFM/FM couplings, crystallographic order, epitaxial strain, spin orientation and competing anysotropies are essential parameters.

The PtFe alloy in the chemically-ordered L1 0 phase has one of the strongest magnetocrystalline anisotropy energy. The L1 0 phase, formed by alternating Fe and Pt atomic planes along the c-axis of the tetragonal structure, leads to an enhanced uniaxial anisotropy along the ordering axis [START_REF] Okamoto | Chemical-order-dependent magnetic anisotropy and exchange stiffness constant of FePt (001) epitaxial films[END_REF] even in the thinnest limit of a few monolayers (ML) [START_REF] Imada | Perpendicular magnetization of L1 0 -ordered FePt films in the thinnest limit[END_REF][START_REF] Soares | Highly anisotropic epitaxial L1 0 FePt on Pt(001)[END_REF]. L1 0 PtFe(001) layer with tetragonal axis perpendicular to the surface provides then an ideal out-of-plane spin network with enhanced perpendicular magnetic anisotropy to study the exchange-coupling properties with thin AFM layers. Among them CoO films are specially relevant for spintronic devices. Bulk CoO has a Néel temperature (T N )

Email address: aline.ramos@grenoble.cnrs.fr (Aline Y. Ramos) 1 present address: ESRF, Grenoble, France of 293 K, close to room temperature (RT), and a magnetic moment of 3.98 µ B [START_REF] Roth | Magnetic structures of MnO, FeO, CoO, and NiO[END_REF][START_REF] Jauch | Crystallographic symmetry and magnetic structure of CoO[END_REF], with a large orbital contribution. In the paramagnetic phase, bulk CoO crystallizes in the rocksalt structure with alternate Co and O (111)-planes (fig. 1). Below T N , AFM ordering goes along with a monoclinic distortion [START_REF] Roth | Magnetic structures of MnO, FeO, CoO, and NiO[END_REF][START_REF] Jauch | Crystallographic symmetry and magnetic structure of CoO[END_REF]. The bulk CoO AFM structure is described as a stacking of uncompensated FM hexagonal planes of Co 2+ 3d 7 ions coupled antiferromagnetically along the trigonal elongation (fig. 1). In thin CoO layers grown on different substrates, polarization dependent soft x-ray absorption spectroscopy shows that the strain induced by epitaxy leads to significant modifications in the magnitude and orientation of the magnetic moments [START_REF] Csiszar | Controlling orbital moment and spin orientation in CoO layers by strain[END_REF], confirming the important sensitivity to magnetostriction. These results motivate our combined investigation of structural distortion and spin orientation in an ultrathin CoO/PtFe double-layer with perpendicular exchange coupling.

Experiments

The films have been grown by molecular beam epitaxy and studied in situ by grazing incidence x-ray diffraction (GI-XRD) at the French CRG BM32 beamline at the European Synchrotron Radiation Facility (ESRF, France). The Pt-terminated L1 0 PtFe(001) thin 001) substrate [START_REF] Soares | Chemically ordered MnPt ultrathin films on Pt(001) substrate: Growth, atomic structure, and magnetic properties[END_REF] hold at 600 K is in coherent epitaxy on Pt(001). A CoO layer with 4nm thickness was grown by reactive molecular beam epitaxy on the ultrathin PtFe(001) layer hold at 523 K [START_REF] Lamirand | Growth and strain of CoO layers on Pt(001) and FePt(001) surfaces[END_REF]. GI-XRD shows that the growth by reactive molecular beam epitaxy of the cobalt oxide on a Pt-terminated PtFe/Pt(001) surface gives rise to an hexagonal (111)-like surface. The strain imposed by the substrate on the CoO layer leads to a slight monoclinic distortion at room temperature. The monoclinic distortion can be described as a tetragonal distortion with with an additional slight trigonal distortion along the rocksalt [111] direction. The [001] axis of the tetragonal distortion is not perpendicular to the surface, but tilted by θ 0 =54.74 • in relation to the normal surface. The growth proceeds in fourfold equivalent wellcrystallized domains, so that the [001] axis is fourfold degenerated. The detailled growth procedure and x-ray diffraction study will be described elsewhere [START_REF] Lamirand | Growth and strain of CoO layers on Pt(001) and FePt(001) surfaces[END_REF]. The double layer shows perpendicular magnetic anisotropy and an exchange bias shift of 800 Oe at 10 K [START_REF] Lamirand | Steadfast perpendicular exchange coupling in an ultrathin CoO/PtFe double-layer: strain and spin orientation[END_REF].

The orientation of the spin moments in the CoO layer at low temperature (T ≈ 10 K) was investigated ex situ by soft x-ray absorption spectroscopy (XAS) using linear dichroism at Co L 2,3 edges, at the PGM beamline of the Laboratorio Nacional de Luz Sincrotron (LNLS, Brazil). The spectral resolution was E/∆E=6000 and the degree of linear polarization close to 100%. The sample was cooled down with an applied magnetic field of 5 kOe perpendicular to the surface plane. The magnetic field was then set to zero and the spectra were collected using the total electron yield. The sample was allowed to rotate about a vertical axis, with the polar angle (θ) defined as the angle between the surface normal and the x-ray propagation (fig. 2-a, inset). In this experimental geometry the variation of the escape length of the electrons as a function of θ should be corrected in order to recover the real x-ray absorption signal. This has been systematically corrected using the standard procedure for electron yield saturation effects [START_REF] Regan | Chemical effects at metal/oxide interfaces studied by x-ray-absorption spectroscopy[END_REF]. To check this correction, for each θ, the x-ray absorption spectrum collected with vertical polarization was used as reference. At each angle, the x-ray linear dichroism (XLD) is obtained by two ways : (1) from the difference between the absorption with horizontal and vertical x-ray polarizations and (2) with horizontal x-ray polarization, from the difference between the absorption at θ and at θ =0 • . The two methods give the same signals, within the accuracy of the measurements.

Results

Figure 2-a shows the Co L 3 edge XAS spectra at 10 K for four θ values from θ=0 • (polarization vector in the surface) to θ=70 • (polarization vector towards the surface normal). The spectra, normalized far from L 2,3 edges, show a clear linear dichroism. Four main features (labelled A to D) are observed in the XAS and XLD signals. They correspond to transitions towards orbitals of Magnetic and non-magnetic effects mixed by the local crystal field symmetry contribute to the polarization contrast. However, we have observed that the angular dependence dramatically decreases when the temperature increases and almost vanishes above 300 K, when the magnetic contribution to the anisotropy has vanished [START_REF] Lamirand | Steadfast perpendicular exchange coupling in an ultrathin CoO/PtFe double-layer: strain and spin orientation[END_REF]. The XLD signal at 10 K, then, measures essentially the magnetic dichroism, i.e. the charge anisotropy associated to the magnetic moment anisotropy through the spin-orbit coupling [START_REF] Van Der Laan | Influence of crystal field on anisotropic x-ray magnetic linear dichroism at the Co 2+ L 2,3 edges[END_REF][START_REF] Wu | Direct measurement of rotatable and frozen CoO spins in exchange bias system of CoO/Fe/Ag(001)[END_REF][START_REF] Csiszar | Controlling orbital moment and spin orientation in CoO layers by strain[END_REF]. Relatively to the magnetic axis, this anisotropy due to local exchange fields and spin-orbit coupling writes:

I XMLD ∝ | m. E | 2 ,
with E the electric field polarization and m along the magnetic axis. A cos 2 θ dependence is then expected for the magnetism-sensitive transitions. The feature C shows the largest dichroism and fits well with a cos 2 θ function, with a minimum at theta=90 • . From multiplet calculations it has been demonstrated that the situation when the polarization vector is perpendicular to the magnetic axis, m ⊥ E, corresponds to C minimum and B maximum [START_REF] Van Der Laan | Influence of crystal field on anisotropic x-ray magnetic linear dichroism at the Co 2+ L 2,3 edges[END_REF][START_REF] Wu | Direct measurement of rotatable and frozen CoO spins in exchange bias system of CoO/Fe/Ag(001)[END_REF]. This is obtained for θ=90 • , within an accuracy of a few degrees. We can then conclude that the Co spins are essentially parallel to the surface plane. As the FePt spin axis is perpendicular to the layer, the coupling between Co and Fe spins at the interface is orthogonal (fig. 3).

Additional information on the orientation of the spins within the plane can be drawn from the relative variation of the different features. For the same relative orientations of E and m, multiplet calculations show quite different XAS and XLD features when the spin axis m are along <110> or along <100> direction [START_REF] Van Der Laan | Influence of crystal field on anisotropic x-ray magnetic linear dichroism at the Co 2+ L 2,3 edges[END_REF]. In the first case A and C features have the same variation with θ, in the second their variations are opposite. The experimental data show that A and C vary in the same way (figure 2-b, inset). We deduce that the Co spins are pointing along the <110> direction.

Discussion

The relationship between the orientation of the magnetic moments and the sign of the crystal field effect has been demonstrated by Csiszar and coworkers [START_REF] Csiszar | Controlling orbital moment and spin orientation in CoO layers by strain[END_REF]. In the case of CoO(001) on Ag(100), the strain induces a small tetragonal distortion with c/a >1. In the CoO 6 octahedron the elongation of the distances along the c axis goes along with a splitting of the t 2g orbitals. The partial filling of the Co 2+ t 2g orbitals in this geometry is recalled in figure 4-a. The low lying t 2g d xz and d yz orbitals are filled and the t 2g hole will occupy the higher d xy orbital. We should note that in our film the tetragonal distortion is weak (c/a <1.008) and that its influence on the orbital occupancy may be called into question. The integrated intensity of the XAS spectra may provide a direct experimental verification of the orbital occupation [START_REF] Csiszar | Controlling orbital moment and spin orientation in CoO layers by strain[END_REF]. We have calculated the integral I θ over the entire L 2,3 spectral region (775eV to 801eV) for the different angles θ and plotted in figure 4-b the ratio (I θ -I 0 )/I 0 . The increase of this ratio gives clear evidence of the increase of accessible t 2g holes as θ increases. In a simple experimental geometry of CoO(001) on Ag(001), where the film plane would also be the d xy orbital plane, we could straightforward conclude about the preferential orbital occupancy. In the case of CoO(111) on PtFe/Pt(001), however, the normal of the planes containing d xy orbitals are tilted by an angle of θ 0 =54.74 • in relation the surface normal (see fig. 3) and the growth proceeds in fourfold equivalent domains. Instead of a simple cos 2 (θ) angular dependence, the intensity I xy (θ) of the transition towards d xy orbitals should be geometrically derived and averaged over the four domains. We found that I xy ∝ cos 2 (θ-θ 0 ) + cos 2 (θ+ θ 0 ). This function shows a maximum for θ=90 • and minimum at θ=0 • . The experi- 3). This is in full agreement with the conclusions drawn from the study of the multiplet features.

Co spins are parallel to the surface plane, so that the coupling between Co and Fe spins at the interface is at 90 degrees. This 90 degrees coupling has been reported for the (in-plane anisotropy) CoO/Fe interface on Ag(001) [START_REF] Wu | Direct measurement of rotatable and frozen CoO spins in exchange bias system of CoO/Fe/Ag(001)[END_REF], where the AFM interface is formed by compensated Co spins. Such orthogonal coupling is, indeed, the most stable configuration when the exchange field of a FM layer interacts with a completly compensated AFM layer. Both the good crystallinity of the interface and the robust orthogonal coupling should be at the origin of the robust exchange bias found in this bilayer system [START_REF] Lamirand | Steadfast perpendicular exchange coupling in an ultrathin CoO/PtFe double-layer: strain and spin orientation[END_REF].

This work received financial support from International programs for scientific cooperation (PICS 05918). We acknowledge LNLS for beamtime at the PGM beamline and the beamline staff for the efficient technical support.

Figure 1 :

 1 Figure 1: bulk CoO structure showing the Co(111) FM sheets coupled antiferromagnetically along the [111] direction. The hached surface corresponds to the hexagon lying on the FePt layer in the CoO/PtFe bilayer. An CoO6 octahedron is shown

Figure 2 :

 2 Figure 2: (a) Co L 3 edge XAS as function of θ. Iinset: experimental geometry; ( b) XLD as function of θ. Inset : angular variation of the intensity of the main XMLD features

Figure 3 :

 3 Figure 3: Sketches of the spin orientation in the CoO/PtFe bilayer (a) top view; (b) perspective. The [001] axis of tetragonal elongation is indicated in the CoO6 octahedron.

Figure 4 :

 4 Figure 4: (a) Shematic figure of the 3d orbital occupancy for Co 2+ in octahedral environment. For the axial elongation of the point charge octahedron along z, the degeneracy of the t 2g orbitals is lifted and the lowest level unpaired electron lies in the dxy orbital; (b) experimental angular variation of the integrated intensity of the XAS spectra (dots). The dotted line corresponds to the calculated I xy (θ) function.


Anne D Lamirand

Márcio M Soares

Maurizio De Santis

Aline Y Ramos

Stéphane Grenier

Hélio C N Tolentino

Strain driven monoclinic distortion of ultrathin CoO films in the exchange-coupled CoO/FePt/Pt(001) system

The structure and strain of ultrathin CoO films grown on a Pt(001) substrate and on a ferromagnetic FePt pseudomorphic layer on Pt(001) have been determined with insitu and real time surface x-ray diffraction. The films grow epitaxially on both surfaces with an in-plane hexagonal pattern that yields a pseudo-cubic CoO(111) surface. A refined x-ray diffraction analysis reveals a slight monoclinic distortion at RT induced by the anisotropic stress at the interface. The tetragonal contribution to the distortion results in a ratio c a > 1, opposite to that found in the low temperature bulk CoO phase. This distortion leads to a stable Co 2+ spin configuration within the plane of the film.

INTRODUCTION

Critical phenomena at the nanoscale size follow a different behaviour than in bulk. A reduction of critical temperature with thickness is expected in magnetic films when their size is comparable to the characteristic correlation length associated to the interatomic magnetic interaction. This intrinsic effect is often hindered by unwanted changes in the structure and in the chemical composition, as well as by interface effects. The importance of interface parameters tends to increase with the constant search for reduction of dimensions in technological systems. The complete structure of these systems is a key to properly disentangle finite size, bulk and surface structural effects.

Due to its technological applications the exchange bias (EB) effect, which takes place at ferromagnetic-antiferromagnetic (FM-AFM) interfaces, has been widely investigated in the last decades. Below a critical blocking temperature (T B ), the coupling between the two layers induces a shift of the hysteresis loop of the FM layer due to an intrinsic exchange bias field (H EB ) 1,2 . Despite its scientific relevance and its widespread use in magnetoelectronic applications, several aspects of this effect have not been completely elucidated, especially the assessment of the magnetic structure at the interface and throughout the volume of the AFM layer 3,4 . This latter is strongly influenced by the interface structural parameters 5 as reduced coordination of surface atoms, atomic modifications induced by strain or chemical diffusion at interfaces. For example, an apparent discrepancy between the amplitude of the reduction of the Néel temperature (T N ) with the thickness in nano-periodic CoO/SiO 2 6 and CoO/MgO multilayers 7 was explained several years later by the presence of an amorphous CoO layer at the interface with SiO 2 . 8 Bulk CoO is AFM with T N of 293 K and a large magnetic anisotropy. In the paramagnetic phase, it crystallizes in rock-salt structure with a CoO =4.261 Å. Co and O planes alternate along the [111] directions, with an in-plane atomic arrangement given by an hexagonal mesh and an interatomic distance of 3.013 Å. The AFM transition goes along with a cubic-tomonoclinic crystallographic distortion. At 10 K, the monoclinic constants are a=5.18190 (6) Å, b=3.01761(3) Å, c=3.01860(3) Å and β=125.5792 (9), with β the angle between a and c. 9 In the pseudo-cubic face-centered setting, this corresponds to an angle of 89.962 • between the two edges of different lengths. Its magnetic structure is collinear with high spin Co 2+ ions forming a stacking of FM planes coupled antiferromagnetically along the pseudo-cubic [111] axis. The moments are oriented in the monoclinic ac plane, pointing close to the [001] axis 9,10 . This magnetic structure, usually denoted as AFM II 10 , is stabilized by superexchange mediated by the oxygen atoms 11 .

In films with nanometric thicknesses, the CoO structure is extremely influenced by the substrate, through the epitaxial strain and interface chemistry, as well as by the growth conditions. [12][13][14][15][16] The structural differences are likely to strongly influence the magnetic properties of the films, as nicely demonstrated by a spin reorientation related to the nature -compressive or expansive-of the strain mbar. The Pt(001) single-crystal substrate was prepared by cycles of 800 eV Ar + sputtering and annealing at about 1200 K. After preparation no impurities were detected by Auger electron spectroscopy and SXRD showed large terraces of the typical quasi-hexagonal reconstruction 19,20 . With respect to the Pt(001) plane, this surface layer contains about 25% atoms in excess that mix with the adlayer when the reconstruction is lifted. Fe, Co and Pt were deposited by molecular beam epitaxy (MBE), using pure rods inserted in watercooled electron beam evaporators. The deposition rate, calibrated with a quartz crystal microbalance, was typically 1 ML per 10 minutes for Fe and Co, and 1 ML per 45 minutes for Pt. CoO films were grown with the Pt substrate held at 520 K by reactive deposition of Co, keeping a molecular oxygen pressure in the chamber of P O 2 ∼ 5 × 10 -7 mbar during evaporation.

The diffracted intensity as function of momentum transfer (Q = 4πsinθ λ ) from a truncated crystal (or an ultrathin epitaxial film) shows sharp scattering line-shape parallel to the surface and continuous line-shape in the out-of-plane direction. These out-of-plane intensity distributions at determined (HK) indexes of the surface mesh are known as (HK) diffraction rods. When originating from the substrate they are called crystal truncation rod (CTR) 21 .

The surface unit-cell is defined by the three vectors a P t,i of a tetragonal body centered mesh related to the fcc substrate by a P t,1 = a P t 2 [110], a P t,2 = a P t 2 [110], and a P t,3 = a P t [001] with a P t = 3.924 Å. An (HK) CTR is the intensity distribution along the reciprocal space variable L, linking the bulk Bragg peaks with the same (HK) indexes. When a film grows in registry with the substrate, film and substrate contributions interfere on the same rod. The film structure has to be resolved by a fine analysis of these CTRs intensities 22 . It requires quantitative data, which are obtained by an integration of the scattered intensity at (HKL) nodes along the CTR, by rocking the sample around the surface normal. Then the structure factors are extracted applying standard correction factors 23 and averaged over symmetry equivalent reflections. The data reduction and structural analysis are performed using the ANA-ROD package that uses a χ 2 minimization for fitting occupation profiles and interplane distances 22,23 .

Two samples were studied in detail by SXRD. Their growth procedure, including the deposition rates, the oxidation conditions and the substrate temperature, was optimized to result in epitaxial layers with large coherent length domains. The first sample is a nominally 3.5-nm-thick CoO layer grown on a clean Pt(001) substrate held at 520 K by reactive Co deposition. The second one is a CoO/FePt/Pt(001) double-layer film, where the CoO layer is coupled to a FM L1 0 ordered FePt layer in registry with the Pt(001) substrate. The FePt layer was grown by evaporation of nominally 3 ML of Fe on a clean Pt(001) substrate held at 600 K, followed by 1 ML Pt deposition. This strategy of FePt growth stems from the fact that at room temperature an atomic site exchange process takes place between Fe adatoms and Pt atoms of the substrate 24 . At higher temperatures, the process is reinforced and the Fe adatoms interdiffuse into the Pt substrate to form an epitaxial surface alloy 25 .

The additional Pt monolayer ensures a Pt rich interface with CoO, intended to limit Fe oxidation and produce a similar interface chemistry as for a clean Pt substrate. The resulting FePt(001) layer is pseudomorphic with the substrate. No traces of L1 2 type ordered alloys or L1 0 domains with the c-axis lying in-plane were found. Then, a CoO layer was grown at 520 K starting by deposition of 2 ML of metallic Co followed by oxidation during 10 min and additional reactive Co deposition up to a 4-nm-thick CoO layer. For the analysis of these non-pseudomorph CoO layers, the intensity of the additional rods appearing between those of the substrate was measured simply by scanning the momentum transfer perpendicular to the surface (L-scans). The structure factors were extracted using the so called stationary geometry corrections, after a background substraction 23 . The structure of the CoO layer turns out to be essentially the same on both Pt(001) substrate and Pt-terminated FePt(001) FM layer.

To provide a fully structural description of the exchanged-coupled system, a total of 128 non-equivalent reflections belonging to the (10), (11), and ( 20) CTRs (as indexed in the surface unit-cell) were used for the determination of the atomic structure of the FePt layer.

The FePt layer rods measured before and after CoO growth show minor changes ascribed to some oxidation of Fe at the interface. In order to estimate the extent of this oxidation, x-ray absorption spectroscopy (XAS) at the Fe L 2,3 edges was performed ex situ at the soft x-ray beamline of the ESRF. All spectra were collected with a spectral resolution of E/∆E ∼ 6000 and using total electron yield, corrected for electron yield saturation effects and normalized far from L 2,3 edges.

III. RESULTS AND DISCUSSION

A. Structure of FePt layer and interfaces

Reference scans were collected for the clean substrate prior to metal deposition. They show, besides the CTRs, additional rods coming from the typical Pt(001) quasi-hexagonal reconstruction 19,20 . After Fe deposition, the reconstruction is lifted and scans of the mo- Occupation rates (occ F e and occ P t ) and interplane distance d n,n-1 to the preceeding layer are described for each layers. The last column (occ F e / occ P t ) reports an estimation of the occupancies obtained thanks to wide angular scans performed at the superstructure peaks maximum.

mentum transfer parallel to the surface (Q // ) do not show any extra peak or shoulder close to the CTR. These measurements, repeated at different values of the momentum transfer perpendicular to the surface (Q z ), ensure that the layer is in registry with the substrate, without any in-plane relaxation. The CTR structure factors reflect then the interference between the scattering from the FePt film and the Pt substrate. Broad peaks have shown up between the substrate Bragg peaks at Q z ∼ 3.68 Å-1 for (1 0) and at Q z ∼ 1.84 Å-1 for

(1 1) and (2 0) CTRs (pointed by arrows in Fig. 1), indicating a doubling of the electronic density period along the growing direction. These order peaks correspond to the L1 0 phase with c-axis perpendicular to the surface 20,25 Some outcomes should be emphasized. In the fully ordered L1 0 phase, pure Pt and Fe

planes alternate along the c-axis. The occupancies obtained for the FePt alloy from n =3 to 6 (Table I) correspond to alternate Fe rich and Pt rich layers. The degree of order can be quantified by the parameter S, defined in a binary alloy as S = r a -w a , where r a and w a are the ratio of a-sites occupied by the right and by the wrong kind on atoms, respectively [START_REF] Warren | X-ray diffraction[END_REF] . S = 0 (S = 1) for a complete disordered (perfectly ordered) alloy. Applying this definition to the layers from 3 to 6, we have S = 0.5(1) on average. Actually, this value is largely underestimated because the intensity coming from small ordered domains is scattered over a large reciprocal space region and is not fully integrated during the standard rocking scans over the CTRs. A more accurate order parameter is obtained by performing wider angular scans (inset Fig. 1) about the order peaks (indicated by arrows in Fig. 1). The corresponding reevaluated structure factors are reported in Fig. 1. Within the same model, the Pt and on Pt(001) 25 .

The interface with the CoO is a mixture of different phases and its complete structure can be hardly obtained by SXRD. It is then simply modeled with partially occupied layers of only Pt. It should be pointed out that in these layers a Pt fraction could be replaced by a larger Fe fraction, which has a lower atomic scattering factor, without a relevant increase of the χ 2 . Therefore, the reported Pt occupancies at the interface represent an upper limit. It should be kept in mind that, if some amount of Fe is present at that interface, it has to be Pt covered, otherwise it would form a relaxed oxide that does not contribute to CTRs. To wrap up, the FePt interface with the CoO layer is satisfactorily described by a mixture of Ptcovered metallic Fe and Pt islands embedded in a relaxed Co (Fe) oxide layer. Coexistence of CoO and Pt islands has already been reported in the literature 16 .

The total Fe content summed over the metallic alloy film (n=1 to 6) is 2.6 ML, smaller than the nominal 3 ML value, highlighting a partial Fe oxidation. The extent of this oxidation is estimated by comparing the XAS spectrum of the CoO/FePt/Pt(001) sample with those of a metallic FePt and a double-layer CoO(4nm)/Fe 3 O 4 (2nm)/Ag(001), previously prepared and used as references. Figure 2 shows a linear combination (full line) of the two reference spectra with a weight 0.35 for the Fe oxide (dash) and 0.65 for the metallic Fe (dot). It gives a very good agreement over the entire spectrum, including the multiplet structure at the L 2 edge. Taking 2.6 ML (65%) as the metallic contribution, we found out that approximately 1.4 ML (35%) of Fe are an oxide environment.

Fe oxidation close to the interface is expected owing to its high oxidation potential [START_REF] Regan | [END_REF] .

Reactive CoO deposition on pure Fe results in the oxidation of at least 2 ML of Fe at 340 K 28 . Our Pt-terminated FePt(001) layer shows a smaller oxide contribution even if the deposition temperature (520 K) was higher than that. Such small oxide contribution is likely related to Fe atoms dispersed within the CoO layer or from Fe-O bonds at the interface. It demonstrates the good resistance to corrosion of the FePt alloy film. As a matter of fact, the Fe XMCD spectrum of this sample is characteristic of metallic L1 0 FePt and has no noticeable contribution from the Fe oxide content 29 . Diffusion of Co atoms into the metallic FePt alloy prior to the oxidation is discarded, since no metallic component was observable in the XAS measurements around the Co L 2,3 edges 29 .

B. Structure of the CoO layer

After CoO growth, scans of the momentum transfer parallel to the surface (Q // ) have been performed along different directions in the reciprocal space. They show that the CoO diffraction pattern exhibits a sixfold in plane symmetry, like a (111)-oriented film with twinned domains. Comparing two scans performed along a P t,1 and in the direction rotated by 60 • in-plane, respectively, a small but significant shift of the rod position is clearly detected (Fig. 3), indicating that the hexagonal mesh is non regular. From the rod FWHM we estimate a characteristic domain size of about 8 nm parallel to the surface. By successive rotation of the sample by 90 • around the surface normal, four growth variants are observed.

They are due to the fourfold symmetry of the substrate. An in-plane schematic view of one of these variants is given in Fig. 4. For the sake of clarity only the two variants related by mirror symmetry are discussed in this paper, but reflections of all variants have been collected, treated and averaged to improve data's quality. The rods position and shape and the related strains are qualitatively the same for the CoO film grown on the clean substrate and on the Pt-terminated FePt/Pt(001) surface, highlighting the same structural behavior. The CoO parameters will be given in the following for the last sample, which is more interesting for its magnetic behaviour and for which a larger data set is available.

The in-plane lattice constants of the non-regular CoO hexagonal mesh h 2 (parallel to a P t,2 ) and h 1 (at 120 a P t,2 ) of about +8%, and between the CoO row spacing 1 2 (2 × h 1 ) 2 -h 2 2 = 2.610 Å and a P t,1 of -6%. The anisotropic stress induced by these misfit values is the responsible for the non-regular hexagonal mesh. Red arrows in Fig. 4 indicate the sense of displacement of the atoms of Co related to the regular hexagon. As we will see later, the oxygen atoms are also displaced, in such a way that the hexagonal stacking is slightly inclined related to the normal.

The analysis of the structure of the CoO film is founded on the in-plane position of several rods and their intensity distribution versus the momentum transfer perpendicular to the surface Q z (Fig. 5). It takes into account the four growth variants due to the substrate symmetry and requires a clear identification of the diffraction features associated to each of them. If we use a rectangular surface mesh, defined by the vector a parallel to a P t,1 and b parallel to a P t,2 (Fig. 4), the four variants correspond to the rotation of this unit cell by the fourfold symmetry axis normal to the substrate. For each variant the positions of the CoO diffraction rods form a non-regular hexagonal mesh on the surface plane. These positions are represented in Fig. 6 for two variants related to each other by a rotation of 180 • . These variants can be seen as mirror variants and their relation can also be expressed as an inversion of the coordinate along a. In the reciprocal space (hk), rods of one variant merge with the (hk) rods of its mirror variant. The second set of mirror variants is deduced by 90 • rotation of this set. Their rods are clearly separated from those of the first set and are not represented.

For the CoO(111) film with cubic rock-salt phase, the rods labeled here (20) and ( 11) are equivalent, the surface normal being a three-fold symmetry axis. These rods merge with the ( 20) and ( 11) ones of the mirror variant (also equivalent among them in the rock-salt structure). In our data a small but clear shift is observed between the out-of-plane peak positions of the ( 20) and ( 11) rods (Fig. 5-c). Similar shift is observed between ( 20) and the (11) peak positions (Fig. 5-d). This shift can only be taken into account if the c vector of the CoO unit cell is not perpendicular to the surface, but has an in-plane component: atoms of the fourth Co atomic layer of the oxide film are not exactly above Co atoms of the first one, characterizing a monoclinic distortion. A second experimental observation confirms this statement. The (02), (31), and ( 31) rods are equivalent in a cubic CoO(111) structure, but not in the monoclinic film. In our experiments Bragg peaks observed along the (31) and ( 31) rods are wider compared to those along the (02). The (02) rod is located in the inversion-symmetry plane. Only a single component (021) Bragg peak has been measured. The wider peak, observed for the same Q z range along the (31) rod, corresponds to the superposition of the (310) peak and the ( 312) one of the mirror domain.

The monoclinic unit cell can be described using bases vector a = (a, 0, 0) (parallel to a P t,1 ), b = (0, b, 0) (parallel to a P t,2 ), and c = (-c 1 , c 2 , c 3 ). As b is in the mirror plane, if c 2 = 0 there should be 8 variants instead of the 4 experimentally observed. We have then c = (-c 1 , 0, c 3 ). If we chose c as the shortest vector joining Co atoms in the Pt (010) plane, the crystal structure is made up of a basis of four atoms : Co(0, 0, 0),

Experimental data Fit 1,0 1, 5 2,0 2,5 3,0 3,5 (20) and (20) rods (202) a (200) (201) (110)
(111) (111) |F| (arb. unit) Q z (Å -1 ) (11) and (11) rods b 3,3 3,4 3,5 3,6 (202) (111) cubic Q z (Å -1 ) d 1,5 1,6 1,7 1,8 1,9 (200) (111)
Co( 1 2 , 1 2 , 0),O( 1 2 , 0, 1 2 ),O(0, 1 2 , 1 2 ) and the reciprocal space vectors are a * = 2π a .(1, 0, c 1 c 3 ), b * = 2π b .(0, 1, 0), c * = 2π c 3 .
(0, 0, 1). The Bragg peak positions for the monoclinic system are given by Q

(hkl) = 2π.( h a , k b , 1 c 3 (l + h c 1 a )
). We can express c 1 a as c 1 a = 1 3 + δ. For the rock-salt cubic structure δ=0. Thus (200) and(111) reflections have the same Q z . For a monoclinic lattice these two reflections are shifted by ∆Q = Q z (2, 0, 0) -Q z (1, 1, 1) = 2π c 3 (3 * δ). From Fig. 5-c ∆Q < 0 then δ < 0 and c 1 < a 3 . Once the monoclinic distortion is qualitatively described, the structural parameters of the CoO films should be obtained. The first step is the calculations of precise in-plane parameters a and b from a collection of Q // -scans. The position of the Bragg peaks (Q x ,Q y ) were evaluated by fitting the in-plane line-shape of 12 rods belonging to different variants.

Equivalent positions were averaged to get the four inequivalent couples reported in Table II. Errors bars were obtained from the dispersion of the data in symmetry equivalent rods.

rod Q x ( Å-1 ) Q y ( Å-1 ) Q // ( Å-
// = Q 2 x + Q 2 y .
The small ∆Q // between (11) and (20) and between (02) and ( 31) rod positions reveals the in-plane distortion of the film.

The intensity distribution as function of Q z was measured for the same 12 rods, which were treated and symmetry averaged giving the (20), (11), (31) and (02) non-equivalent rods, two of them reported in Fig. 5. A model of the CoO film with monoclinic structure was fitted to reproduce these structure factor amplitudes. In this model the interlayer spacing was taken uniform over the full thickness. The measured signal decreases quickly along the rods when moving farther away from the CoO Bragg peaks, which is an indication of large surface roughness expected for such polar surface. This latter was simulated by introducing an occupancy value Occ(n) for each atomic layer n of the oxide film that has been modelized by an error function erfc(z). This model is based on the assumption that the distribution of the terrace's width is described by a Gaussian with maximum at z 0 and with a variance σ. In this second step of the structural analysis, the interlayer spacing parameter c 3 and occupancies were obtained through a fit of the (02) rod, which is insensitive to the distortion parameter δ. After that step, occupancies are fixed and the fit of the ensemble of rods is performed to determine c 1 and optimize c 3 . As (hk) and (hk) rods of two mirrors variants are merged, the model structure is calculated for these two variants with identical weight.

The best fit lattice parameters are reported in Table III, as well as the values of δ,

C. Implications on magnetic structure

The RT monoclinic distortion imposed by epitaxy for the CoO films is of the same order of magnitude of that observed in low temperature bulk CoO phase. The structure of these two phases can be compared within the distorted cubic cell, taking as lattice basis a = b -c, b = b + c, and c = a + c (Fig. 7). The lattice parameters for both structures are reported in Table IV, along with the cell volume and the Co-O coordination distances.

In the regular cubic structure, Co atoms are embedded in the octahedral crystal field of its first neighbors O atoms. The Co 2+ ions are in the high spin 3d 7 configuration, which leaves a hole in a t 2g orbital. At local scale, the tetragonal distortion, characterised by c a =1, leads to a splitting of the t 2g orbitals by the orthorhombic crystal field 30 magnetic moments of CoO films on the strain induced by the substrate by comparing two cases: on Ag(001), the strain induces an extensive ( c a > 1) tetragonal deformation of the CoO layer, leading to a Co 2+ spins with (x , y ) symmetry in the film plane. As opposite, a CoO layer sandwiched between MnO(100) layers presents a slightly compressive ( c a < 1) deformation and has its moment directed out-of-plane, along the c -axis.

The remarkable difference between low temperature CoO bulk and our films is the opposite c a ratio, reflecting opposite tetragonal distortions. In the low temperature bulk structure, the apical Co-O interatomic distance d 1

Co-O is shorter than the d 2 Co-O distance and, based only on the orbital occupation and spin-orbit coupling energy, the spin should point along the c -axis. Nevertheless, the spin orientation is sligthly inclined by about 11 o to 20 o from the c axis 9,10 . In order to minimize dipole-dipole interaction 32 , the Co 2+ spins, which are ferromagnetically coupled, tend to be within the (111) plane of the distorted cubic cell. The competition between spin-orbit coupling and dipolar energy leads to the slight inclination.

In our films, the apical oxygen distance d 1

Co-O is larger than the d 2 Co-O distance in the (a , b ) plane and the t 2g hole has z symmetry. As a consequence, the spin should be within the (a , b ) plane, as in the case of CoO/Ag(001). To completely define the spin orientation, we have to consider now the dipole-dipole interaction. The break in cubic symmetry is identified in the film by the decrease in β in the monoclinic cell. Such symmetry breaking sets the (111) plane apart, amongst the other {111} planes. One can then deduce that this is the plane where Co 2+ spins are coupled ferromagnetically. To minimize the dipolar interaction 32 , the spins should be within this plane. As opposite to the bulk case, both interactions are not competing and may be simultaneously satisfied if the spins align along the monoclinic b-axis, i.e. parallel to the a P t,2 (Fig. 4 and7). Such a conclusion, based solely on structural distortion and symmetry arguments, is in agreement with the experimental finding by x-ray absorption spectroscopy 29 .

One may note that the RT unit cell volume of the film (77.0 Å3 ) (Table IV) ranges between the bulk RT rock-salt (77.36 Å3 ) and the low temperature monoclinic (76.77 Å3 ) ones. The difference is small but may be of importance for the strength of the exchange interaction.

The volume decrease leads to an increase in orbital superposition and a subsequent increase in the superexchange interaction. This might be correlated to the exceptionally high ordering temperature of the film (T N =293 K) and to the robust perpendicular exchange bias shift, kept up to the T N , as seen in our previous report 29 .

We have reported the growth and structure of ultrathin CoO layers on Pt(001) and FePt/Pt(001) surfaces. The cobalt oxide grows very similarly on both surfaces with (111) rock-salt-like orientation. Its structure corresponds to a distorted hexagonal stacking with alternate planes of Co and O and displays a rough surface. Even then, the structure develops and keeps a monoclinic distortion in the ultrathin regime. The anisotropic epitaxial mismatch with the substrates leads to a stress that deforms the Co hexagon along one of the main Pt axes; the second hexagonal layer formed by oxygen reinforces this distortion.

Such anisotropy is at the origin of the monoclinic distortion when the CoO film develops.

The magnetic performance of our sample highlights the high-quality epitaxial growth control and the importance of the strain in the stabilization of the magnetic properties.

The presence of the monoclinic phase and its characteristics illustrate that epitaxy can be exploited to tune both the onset of the magnetic transition and the magnetic moment orientation in ultrathin films.

FIG. 1 .

 1 FIG. 1. (color online) X-ray scattering through the Pt rods [(10), (11) and (20) CTRs] after FePt and CoO growth. The scattered marks (experiment) are associated to error bars calculated from data dispersion of symmetry equivalent rods. Calculated structure factor amplitudes are represented by solid lines. The broad peaks associated to the doubling of the electronic density in FePt are pointed by arrows. Black circles represent experimental structure factor amplitudes extracted from much wider angular scans (inset) for the integration of the CTR intensity.

  Fig.1 along with data.

Fe occupancies for layers 3 to 6

 6 were adjusted to match the corrected structure factors, all other structural parameters being unchanged. This results in the final Fe and Pt occupancies reported in the last column of TableI. One ends up with an order parameter of S ∼ 0.7(1).The lattice constant c alloy = 2d alloy =3.61(1) Å is compressed by 2.8% with respect to bulk FePt one. This compensates the (001) plane atomic density reduction, which results from the substrate induced in-plane strain. The tetragonal distortion of this pseudomorphic layer (c/a) alloy = 0.920(3) is enhanced compared to the bulk value (c/a) bulk = 0.962. A similar value was previously measured on a 2.0-nm-thick FePt film grown by alternate deposition ( a r b . u n i t s )E n e r g y ( e V ) F e 3 O 4 r e f .

FIG. 2 .

 2 FIG. 2. (color online) Comparison of CoO/FePt/Pt(001) sample L 2,3 -edges XAS (a) with a linear combination (b) of two reference spectra: metallic FePt (c) and Fe 3 O 4 /CoO (d).

FIG. 3 .

 3 FIG. 3. (color online) Intensity distribution as function of the momentum transfer modulus parallel (Q // ) to the surface at Q z =0.873 Å-1 . The plain (blue) line corresponds to a scan along a P t,1 and crosses both Pt and CoO rods. The dashed (black) line corresponds to a scan along a direction rotated by 60 • with respect to a P t,1 . The shift between the CoO rod positions, pointed by the plain (blue) and dashed (black) lines, reveals the distortion of the in-plane hexagonal pattern.

FIG. 4 .

 4 FIG. 4. (color online) Top view of the CoO structure on Pt(001) (or FePt(001)). The non-regular hexagon is described by a rectangular surface mesh formed by the in-plane vectors a and b .

1 )FIG. 5 .

 15 FIG. 5. (color online) X-ray scattering through the CoO rods: ( 11) plus (11) (a) and ( plus (20) (b); enlarged view of (200) plus ( 111) (c) and of ( 202) plus (111) Bragg peaks. Scattered marks correspond to experimental data and plain lines are obtained by the structural refinement procedure. Vertical lines indicate the two peaks in monoclinic (plain blue) and in cubic (dashed red) cells. Peak positions for the cubic cell are calculated using CoO bulk data from 9 .

a

  and b lattice constants were derived from the Q(hkl) formula through a weighted average of these values. Their values are a = 5.220(2) Å and b = 3.005(1) Å in agreement with h 1 and h 2 values found previously.

3 TABLE

 3 III. Best-fitted parameters of the CoO film structures. The first line concerns the basic structural parameters. In the second line, the monoclinic distortion is highlighted with δ and β. z 0 and σ are linked to the roughness of the films. X 2 marks the quality of the fit. β = 180 • -arctan( c 3 c 1 ) and c. The corresponding curves are plotted in Fig.5. In the cubic system β = 180 • -arctan( √ 2)=125.264 • . The smaller value of β = 125.05(7) • expresses the deviation from cubic unit-cell. The average film thickness is found at 4.3(9) nm, while σ is about 1.8 nm. This should be considered only as a rough estimation, the error bar on such values being quite large. However, this estimation is in fair agreement with the thickness and roughness of the CoO layer obtained from complementary measurements (not presented here) by x-ray reflectivity (z 0 = 3.5(6) nm and σ = 0.8(3) nm) and atomic force microscopy (surface roughness rms = 1.0(2)nm).

  . The elongation in the CoO 6 octahedron determines then the symmetry (x , y ) or z of the empty t 2g orbital. The strong spin-orbit coupling completes the scenario and imposes the Co 2+ spin-orientation. Experiments 17 supported by theoretical calculations 31 have demonstrated such a behavior. Csiszar and coworkers 17 established the dependence of the magnitude and orientation of the

FIG. 7 .

 7 FIG. 7. (color online) Illustration of CoO monoclinic ( a , b, and c) and distorted cubic ( a , b , and c ) lattice basis. a and c axes of tetragonal elongation are indicated in the CoO 6 octahedron (red lines).

  17 . Unexpectedly, the growth of CoO on Pt(001) has never been reported in the literature. Moreover, epitaxial CoO film on Pt(001) opens the way towards a CoO/FePt AFM/FM bilayer on Pt, since Pt-terminated FePt(001) and Pt(001) present rather the same chemical surface.

	II. EXPERIMENTAL
	Surface x-ray diffraction experiments at grazing incidence (SXRD) were performed at the
	French CRG-IF BM32 beamline 18 at the European Synchrotron Radiation Facility (ESRF)
	using a photon energy of 22 keV (λ=0.56354 Å). The ultrahigh vacuum (UHV) chamber,
	fully equipped for sample preparation, was working at a base pressure of P ∼ 2 × 10 -10

In this paper we report epitaxial growth of CoO films on a Pt(001) substrate and on a FM FePt(001) pseudomorphic alloy on Pt(001). We have succeeded at the growth of strained ultrathin (111)-oriented CoO films on both Pt(001) and Pt-terminated FePt(001) surfaces and have precisely determined the strain and the structure of CoO layers with insitu and real time surface x-ray diffraction. We find that on both surfaces the CoO structure presents a slight monoclinic distortion stable at room temperature (RT) evocative of the low temperature and magnetically driven distortion of the bulk. At local scale, such a distortion notably translates into a tetragonal distortion of the octahedra formed by the first oxygen neighbors around Co atoms. The implications of that distortion on magnetism and spin orientation of Co 2+ ions are discussed.

  layer (n) region d n,n-1 occ P t /occ F e occ P t /occ F e

	1			1.97 (1)	1/0
	2	interface with Pt 1.99 (1) 0.7(1)/0.3
	3	FePt	Fe plane	1.804(5) 0.10(5)/0.9	0.1/0.9
	4	alloy	Pt plane	1.804(5) 0.7(1)/0.3	0.8/0.2
	5	film	Fe plane	1.804(5) 0.2(1)/0.8	0.1/0.9
	6		Pt plane	1.804(5) 0.7(1)/0.3	0.8/0.2
	7			1.93(2)	0.5(1)/ -
	8	interface with CoO 1.80(4)	0.4(1)/ -
	9			1.97(2) 0.15(5)/ -

TABLE I. Fitting results of a 4 ML FePt alloy and its interfaces after cobalt oxide deposition.

  . The lattice mismatch favours this orientated growth because the bulk FePt L1 0 lattice parameters, a bulk =3.860 Å and c bulk =3.713 Å are smaller than a P t by 1.6% and 5.4%, respectively. parameters are occupancy rates (occ F e and occ P t ) and interplane distance d n,n-1 to the previous layer, with occ F e + occ P t = 1 for each layer (except at the CoO interface). An average Debye-Waller factor is considered for the whole alloy layer. The Pt interface is defined by two atomic layers. Layer 1 contains Pt only, while Fe is allowed to diffuse to the layer 2. d 1,0 and d 2,1 distances are free and independent. Layers 3 to 6 correspond to the FePt alloy film, with a single interlayer distance d alloy . Fe and Pt occupation rates are fitted on each layer. For the CoO interface region (n > 6), distances are free and independent. Fe and Pt occupation rates are adjusted with the only constraint of occ F e + occ P t < 1. The best fit Debye-Waller factor, B alloy = 0.96, turns out to be larger than the Fe and Pt bulk ones (0.39 and 0.31, respectively) indicating that the structural disorder dominates and justifying the use of a single parameter. The best fit parameters are summarized in TableIand the best fit curves are plotted in

As stated here above, the FePt film grows in registry with the substrate. The layer adopts the in-plane lattice parameter of Pt. The film structure parameters are optimized through a best fit of the calculated structure factors to the measured ones

22

. The model consists of a partially ordered FePt(001) film between two interface regions: one with the Pt substrate and the other with the CoO overlayer. For each layer n, atoms occupy bulk-like sites and the fit

  • ) are evaluated from the rod positions. Their values are h 2 =3.005(1) Å and h 1 =3.012(1) Å. While this second value is close to the bulk one for RT CoO rock-salt structure ( a CoO √ 2 =3.013 Å) the first one is clearly below, revealing an in-plane contraction of the CoO structure. The CoO epitaxy is characterized by a misfit between the unit-mesh length h 2 and the substrate surface row spacing a P t,2 (

	h 2 -a P t,2

TABLE II .

 II In-plane CoO peaks positions Q x , Q y and Q

				1 )
	(11) 1.207 (2) 2.092(1) 2.415(2)
	(20) 2.4069(7)	0	2.407(1)
	(02)	0	4.180(1) 4.180(1)
	(31) 3.614(3) 2.087(1) 4.173(2)

TABLE IV .

 IV CoO film (this work) CoO bulk values at 10 K (from Jauch et al.9 ) Comparison of CoO monoclinic phases in a distorted unit cell.

	a = b ( Å)	4.245	4.2682
	c ( Å)	4.273	4.2145
	α (deg)	90.00	90.038
	β (deg)	90.00	89.962
	γ (deg)	89.866	90.018
	c /a	1.007	0.987
	V ( Å3 )	77.00	76.77
	d 1 Co-O ( Å)	2.137	2.1073
	d 2 Co-O ( Å)	2.122	2.1341

ACKNOWLEDGMENTS

Beamtime is acknowledged at the French CRG BM32/ESRF beamline. Special thanks to O. Geaymond for his invaluable technical support at the beamline. We also would like to thank E. Mossang for the assistance in the complementary experiments by x-ray reflectivity. * maurizio.de-santis@neel.cnrs.fr † aline.ramos@neel.cnrs.fr