Ben Atef

Viet-Anh Youssef
email: viet-anh.tran@gipsa-lab.grenoble-inp.fr

Pierre Tran
email: pierre.badin@gipsa-lab.grenoble-inp.fr

Gérard Badin

Bailly

HMMs and GMMs based methods for acoustic-to-articulatory speech inversion

Afin de récupérer les mouvements des articulateurs tels que les lèvres, la mâchoire ou la langue, à partir du son de parole, nous avons développé et comparé deux méthodes d'inversion basées l'une sur les modèles de Markov cachés (HMMs) et l'autre sur les modèles de mélanges de gaussiennes (GMMs). Les mouvements des articulateurs sont caractérisés par les coordonnées médiosagittales de bobines d'un articulographe électromagnétique (EMA) fixées sur les articulateurs. Dans la première méthode, des HMMs à deux flux, acoustique et articulatoire, sont entrainés à partir de signaux acoustique et articulatoire synchrones. Le HMM acoustique sert à reconnaitre les phones, ainsi que leurs durées. Ces informations sont ensuite utilisées par le HMM articulatoire pour synthétiser les trajectoires articulatoires. Pour la deuxième méthode, un GMM d'association directe entre traits acoustiques et articulatoires est entrainé sur le même corpus suivant le critère de minimum d'erreur quadratique moyenne (MMSE) à partir des trames acoustiques d'empan temporel plus ou moins grand. Pour un corpus de données EMA mono-locuteur enregistré par un locuteur français, l'erreur RMS de reconstruction sur le corpus de test pour la méthode fondée sur les HMMs se situe entre 1.96 et 2.32 mm, tandis qu'elle se situe entre 2.46 et 2.95 mm pour la méthode basée sur les GMMs.

INTRODUCTION

Speech inversion is a long-standing problem, as testified by the famous work by Atal et al. [START_REF] Atal | Inversion of articulatory-toacoustic transformation in the vocal tract by a computer-sorting technique[END_REF] in the seventies. Speech inversion was traditionally based on analysis-by-synthesis, as implemented by [START_REF] Mawass | Synthesis of French fricatives by audio-video to articulatory inversion[END_REF], or by [START_REF] Ouni | Modeling the articulatory space using a hypercube codebook for acoustic-to-articulatory inversion[END_REF] who optimised codebooks to recover vocal tract shapes from formants. But since a decade, more sophisticated learning techniques have appeared, thanks to the advent of the availability of large corpora of articulatory and acoustic data provided by devices such as the ElectroMagnetic Articulograph (EMA) or marker tracking devices based on classical or infrared video.

Our laboratory is thus involved in the development of an inversion system that allows producing augmented speech from the sound signal alone, possibly associated with video images of the speaker's face. Augmented speech consists of audio speech supplemented with signals such as the display of usually hidden articulators such (e.g. tongue or velum) by means of a virtual talking head, or with hand gestures as used in cued speech by hearingimpaired people.

STATE-OF-THE-ART

At least, two classes of statistical models of the speech production mechanisms can be found in the recent literature: Hidden Markov Models (HMMs) (cf. [START_REF] Hiroya | Estimation of articulatory movements from speech acoustics using an HMM-based speech production model[END_REF], [START_REF] Zhang | Acousticarticulatory modeling with the trajectory HMM[END_REF] or [START_REF] Ben Youssef | Acoustic-to-articulatory inversion using speech recognition and trajectory formation based on phoneme hidden Markov models Interspeech[END_REF]), and Gaussian Mixture Models (GMMs) (cf. [START_REF] Toda | Statistical mapping between articulatory movements and acoustic spectrum using a Gaussian mixture model[END_REF]). In addition to the structural differences between HMMs and GMMs, an important difference is that HMMs explicitly use phonetic information and temporal ordering while the GMMs simply cluster the multimodal behaviour of similar speech chunks.

Hiroya & Honda [START_REF] Hiroya | Estimation of articulatory movements from speech acoustics using an HMM-based speech production model[END_REF] developed a method that determines articulatory movements from speech acoustics using a HMM-based speech production model. After proper labelling of the training corpus, each phoneme is modelled by a context-dependent HMM, and a separate linear regression mapping is trained at each HMM state between the observed acoustic and the corresponding articulatory parameters. The articulatory parameters of the statistical model are then determined for a given speech spectrum by maximizing a posteriori estimation. In order to assess the importance of phonetics, they tested their method under two experimental conditions, namely with and without phonemic information. In the former, the phone HMMs were assigned according to the correct phoneme sequence for each test utterance. In the latter, the optimal state sequence was determined among all possible state sequences of the phone HMMs and silence model. They found that the average RMS errors of the estimated articulatory parameters were 1.50 mm from the speech acoustics and the phonemic information in the utterance and 1.73 mm from the speech acoustics only.

Zhang & Renals [START_REF] Zhang | Acousticarticulatory modeling with the trajectory HMM[END_REF] developed a similar approach. Their system jointly optimises multi-stream phone-sized HMMs on synchronous acoustic and articulatory frames. The inversion is carried out in two steps : first a representative HMM state alignment is derived from the acoustic channel ; a smoothed mean trajectory is generated from the HMM state sequence by an articulatory trajectory formation model using the same HMMs. Depending on the availability of the phone labels for the test utterance, the state sequence can be either returned by an HMM decoder, or by forced alignment derived from phone labels, leading to RMS errors of respectively 1.70 mm and 1.58 mm. Toda and coll. [START_REF] Toda | Statistical mapping between articulatory movements and acoustic spectrum using a Gaussian mixture model[END_REF] described a statistical approach for both articulatory-to-acoustic mapping and acoustic-toarticulatory inversion mapping without phonetic information. Such an approach interestingly enables language-independent speech modification and coding. They modelled the joint probability density of articulatory and acoustic frames in context using a Gaussian mixture model (GMM) based on a parallel acoustic-articulatory speech database. They employed two different techniques to establish the GMM mappings. Using a minimum meansquare error (MMSE) criterion with an 11 frames acoustic window and 32 mixture components, they obtained RMS inversion errors of 1.61 mm for one female speaker, and of 1.53 mm for a male speaker. Using a maximum likelihood estimation (MLE) method and 64 mixture components, they improved their results to 1.45 mm for the female speaker, and 1.36 mm for the male speaker. The studies described above do not allow concluding about the optimal inversion method since data, speakers and languages are not comparable. Hiroya & Honda [START_REF] Hiroya | Estimation of articulatory movements from speech acoustics using an HMM-based speech production model[END_REF] and Zhang & Renals [START_REF] Zhang | Acousticarticulatory modeling with the trajectory HMM[END_REF] have shown that using explicit phonetic information to built HMMs gives better results. Toda and coll. [START_REF] Toda | Statistical mapping between articulatory movements and acoustic spectrum using a Gaussian mixture model[END_REF], using GMMs and no phonetic information, get lower RMS errors. However, the corpora as well as training and testing conditions are not completely comparable. Therefore, the aim of the present work is to compare the HMM-based method used in [START_REF] Ben Youssef | Acoustic-to-articulatory inversion using speech recognition and trajectory formation based on phoneme hidden Markov models Interspeech[END_REF] with a GMM-based method similar to that of [START_REF] Toda | Statistical mapping between articulatory movements and acoustic spectrum using a Gaussian mixture model[END_REF] using the minimum mean-square error (MMSE) criterion for the GMM-based mapping method, everything else being comparable.

ARTICULATORY AND ACOUSTIC DATA

The corpus

For this preliminary study, a corpus already recorded was used [Bad08]. It consists of a set of two repetitions of 224 nonsense vowel-consonant-vowel (VCV) sequences (uttered in a slow and controlled way), where C is one of the 16 French consonants and V is one of 14 French oral and nasal vowels; two repetitions of 109 pairs of CVC real French words, differing only by a single cue (the French version of the Diagnostic Rhyme Test); 68 short French sentences, 9 longer phonetically balanced French sentences, and 11 long arbitrary sentences. The corpus was recorded on a single male French subject, which means that no speaker adaptation / normalisation problems will be dealt with in this study.

The phones have initially been labelled for each utterance using a forced alignment procedure based on the audio signal and the corresponding phonetic transcription string based on HMMs. Subsequent manual correction of both phoneme labels and phoneme boundaries were performed using the Praat software [START_REF] Boersma | Praat: doing phonetics by computer (Version 4.3.14)[END_REF]. The centres of allophones were automatically chosen as the average between beginning and end of the phonemes. Altogether the corpus contained 7350 allophones, i.e. about 22 minutes of speech. The 36 phonemes are: [a ɛ e i y u o ø ɔ oe ɑ̃ ɛ̃ oẽ ɔ̃ p t k f s ʃ b d g v z ʒ m n ʁ l w ɥ j ə _ __],

where _ and __ are internal short and utterance initial and final long pauses respectively.

The acoustic and articulatory data

The articulatory data have been recorded by means of an ElectroMagnetic Articulograph (EMA) that allows tracking flesh points of the articulators thanks to small electromagnetic receiver coils. Studies have shown that the number of degrees of freedom of speech articulators (jaw, lips, tongue …) for speech is limited, and that a small but sufficient number of carefully selected measurement locations can allow retrieving them with a good accuracy [START_REF] Badin | Threedimensional linear modeling of tongue: Articulatory data and models[END_REF]Bad08]. In the present study, six coils are used: a jaw coil is attached to the lower incisors (jaw), whereas three coils are attached to the tongue tip (tip), the tongue middle (mid), and the tongue back (bck) at approximately 1.2 cm, 4.2 cm, and 7.3 cm, respectively, from the extremity of the tongue; an upper lip coil (upl) and a lower lip coil (lwl) are attached to the boundaries between the vermilion and the skin in the midsagittal plane. Extra coils attached to the upper incisor and to the nose served as references to compensate for head movements in the midsagittal plane. The audiospeech signal was recorded at a sampling frequency of 22050 Hz, in synchronization with the EMA coordinates, which were recorded at a 500 Hz sampling frequency.

Overview of the data

In order to reduce the noise of the EMA data, the articulatory trajectories were first low pass filtered with a cut-off frequency of 50 Hz. Then we verified that the general articulatory characteristics of each phoneme were in accordance with our expectation by displaying, in the midsagittal plane, the dispersion ellipses of the six coils estimated over the sets of all the instances. The minimum and maximum number of instances per phoneme was 18 (for short pauses) and 348 (for /a/). This illustrates the coherence and the validity of the data. Figure 1, which displays these ellipses for phoneme /t/, illustrates the very low variability of the tongue tip coil for /t/, as could be expected since the tongue is in contact with the hard palate for this articulation. It should however be reminded that the articulations were sampled at the instant midway between the phone boundaries, which does not completely ensure that it corresponds to the actual centre of the phone if the trajectories are not symmetrical.

Context classes for phonemes

Due to coarticulatory effects, it is unlikely that a single context-independent HMM could optimally represent a given allophone. Therefore, context-dependent HMMs were trained. Rather than using a priori phonetic knowledge to define such classes, confusion trees have been built for both vowels and consonants, based on the matrix of City-Block distances of the coils coordinates between each pair of phone. Each allophone was represented by its mean over all the associated instances. Left-to-right, 3-state phoneme HMMs with one Gaussian per state and a diagonal covariance matrix are used. For training and test the HTK3.4 toolkit is used [START_REF] Young | The HTK Book. Revised for HTK Version[END_REF]. The training is performed using the Expectation Maximization (EM) algorithm based on the Maximum Likelihood (ML) criterion.

The acoustic and articulatory features vectors are here considered as two streams in the HTK multi-stream training procedure. Subsequently, the HMMs obtained are split into articulatory HMMs and acoustic HMMs.

A bigram language model considering sequences of phones in context is trained over the complete corpus. Thus, the recognised phoneme sequences respect French phonotactics. No prosodic constraints such as a duration model are added. The acoustic-to-articulatory inversion is achieved in two steps. The first step performs phoneme recognition, based on the acoustic HMMs. The result is a sequence of recognised allophones together with their durations. The recognition results are given in the Table 1. The recognition performances are increased by the use of phonemes in context. The procedure of replacement of the HMMs, which aims to compensate for the too small size of the training sets (cf. [START_REF] Ben Youssef | Acoustic-to-articulatory inversion using speech recognition and trajectory formation based on phoneme hidden Markov models Interspeech[END_REF]), increases the recognition rate from 76.9 to 84.0 %. The second step of the inversion aims at reconstructing the articulatory trajectories from the chain of phoneme labels and boundaries delivered by the recognition procedure. As described in [START_REF] Govokhina | TDA: A new trainable trajectory formation system for facial animation InterSpeech[END_REF], the synthesis is performed as follows, using the software developed by the HTS group [START_REF] Tamura | Text-to-audio-visual speech synthesis based on parameter generation from HMM EUROSPEECH[END_REF][START_REF] Zen | An introduction of trajectory model into HMMbased speech synthesis Fifth ISCA ITRW on Speech Synthesis[END_REF]. A linear sequence of HMM states is built by concatenating the corresponding phone HMMs. The proper state durations are estimated by z-scoring. A sequence of observation parameters is generated using a specific ML-based parameter generation algorithm [START_REF] Zen | An introduction of trajectory model into HMMbased speech synthesis Fifth ISCA ITRW on Speech Synthesis[END_REF]. In order to assess the contribution of the trajectory formation to RMS errors of the complete inversion method, we also synthesised these trajectories directly from the original labels, simulating a perfect acoustic recognition step.

The root-mean-square (RMS) error is calculated for the difference between the measured and the estimated articulatory coordinates, excluding the long pauses at the beginning and the end of each utterance. The mean correlation coefficient (Corr) measures the degree of amplitude similarity and the synchrony of the trajectories.

Table 2 shows the RMS errors. The results are consistent with those in Table 1. In addition, Table 2 displays the errors corresponding to cases where the recognition step is bypassed by synthesising the articulatory trajectories directly from the original phoneme sequences; the relatively high level of these errors shows that a significant part of the overall error is due to the trajectory formation model that often oversmooths the predicted movements and does not capture properly coarticulation patterns. Note that all the differences in Table 2 are significant (p < 0.03).

MULTIMODAL GMM MODELS

We apply the GMM-based mapping using the minimum mean-square error (MMSE) criterion, which has been often used for voice conversion. The determination of a target parameter trajectory with appropriate static and dynamic properties is obtained here by combining local estimates of the mean and variance for each frame p(t) and its derivative ∆p(t) with the explicit relationship between static and dynamic features (e.g. ∆p(t) = p(t)p(t-1)) in the MMSE-based mapping.

The 1st to 13th Mel-cepstral coefficients are used as a spectral representation of the speech signal. The shift duration is also 10 ms. The 12-dimensional EMA data is accordingly down sampled to match this 100 Hz sampling rate.

The number of mixture components is varied from 8 to 32. The number of input acoustic frames is fixed to 9 but the size of context window is varied from a phoneme size (~100 ms) to a syllable size (330 ms) (by picking one frame every 1-4 frames). A reduction of the acoustic dimension (9*13 = 117) is performed by Principal Component Analysis (PCA): the number of principal components is set to 24.

It has been reported in the literature that the low pass filtering of training as well as estimated articulatory trajectories improves the mapping performance (e.g., Richmond, 2001). The optimal cut-off frequency of the low pass filter is deemed to be 25Hz.

The RMS error and the correlation coefficient are calculated over the same training and test data used for evaluating the HMM system.

Table 3 shows the RMS error (in mm) and the correlation coefficient for the different experiments using different numbers of mixtures and different sizes of context window. The RMS error decreases when the number of mixtures increases and when the size of context window decreases. The most plausible interpretation is that a phoneme-sized window optimally contains necessary local phonetic cues for inversion. The 32 mixtures appear to constitute the best representation of the 36 phonemes.

The better mapping accuracy is finally achieved when the size of the context window is set to 90 ms and the number of mixture components is set to 32 in this experiment. In that case, the RMS error is 2.46 mm.

COMPARISON AND COMMENTS

Figure 4 displays the measured and reconstructed articulatory trajectories of the Y-coordinates for the two competing systems. It seems that the GMM-based method has difficulty in dealing with the asynchronous behaviour of inter-articulatory coordination.

Our HMM-based system generates an RMS error of 1.96 mm for the same data. Surprisingly, the performance of the HMM-based inversion mapping is significantly more accurate than that of the GMM-based system although results published on voice-conversion experiments seem to suggest the opposite. A possible explanation for this contrastive behaviour lays perhaps in the fact that GMM-based techniques are more appropriate to deal with unimodal mappings where events in source and targets are largely synchronous, whereas HMM-based techniques are able to deal with context-dependent mappings and delays between frames structured by state transitions.

Both systems can however be improved. HMM-based inversion can include more sophisticated treatment of articulatory-to-acoustic asynchrony by introducing delay models that have been quite effective in HMM-based multimodal synthesis [START_REF] Govokhina | Learning optimal audiovisual phasing for a HMM-based control model for facial animation 6 th ISCA Workshop on Speech Synthesis[END_REF]. The GMM-based system could be improved by considering other dimensionality reduction techniques such as Linear Discriminant Analysis (LDA) that are quite effective in HMM-based inversion [START_REF] Tran | Improvement to a NAM captured whisper-to-speech system Interspeech[END_REF]. Both systems can also be improved by incorporating visual information as input and including this additional information more intimately in the optimization process that will consider multimodal coherence between input and output parameters: lips are clearly visible and jaw is indirectly available in facial movements.

Figure 5 displays the statistics of the RMS errors for the HMM-based and GMM-based methods. The difference is highly significant (p<10 -7 ). Figure 5 shows that the HMM-based system produces a global RMS error lower than that produced by the GMM-based one, but produces in some cases errors that are higher than the highest errors obtained with the GMM system.

CONCLUSIONS AND PERSPECTIVES

We have implemented and compared two acoustic-toarticulatory speech inversion techniques, which contrast in the way they capture and exploit a priori multimodal coherence. This work tends to show that the inversion process should be "phonetic-aware". Several reserves can however be made on these first experiments:

First, the HMM system benefits from the phonotactics of the target language. Despite the fact that the language model has not been trained on test data, the phonological structures of test and training utterances are very similar. Note however that French has a rich syllabic inventory and that we can imagine that results obtained with languages such as Japanese, Polish or Spanish with various syllabic complexities may lead to different results.

Secondly, global objective measurements may not entirely mirror phone-specific behaviour that may drastically impact subjective rating of generated articulation. The precision of the recovery is of course a highly important element for the evaluation but other elements such as the precision of the recovery of crucial elements such as vocal tract constrictions are naturally also very important.

Thirdly, we have shown elsewhere [START_REF] Tarabalka | Can you "read tongue movements[END_REF] that viewers have various performance for tongue reading and that performance increases with training. Note also that the realism of motion may compensate for inaccurate detailed shaping: the kinematics of the computed trajectories could be more important for perception that the accuracy of the trajectories themselves.

Finally, the results of this study will allow us to develop a tutoring system for on-line phonetic correction [START_REF] Badin | Towards the use of a virtual talking head and of speech mapping tools for pronunciation training Proceedings of the ESCA Tutorial and Research Workshop on Speech Technology in Language Learning[END_REF], in which recovered articulatory movements will be used to drive a virtual 3D talking head with all possible articulatory degrees-of-freedom [Bad02; Bad08].

ACKNOWLEDGMENTS

We sincerely thank Christophe Savariaux for helping us with the EMA recordings. This work has been partially supported by the French ANR ARTIS grant and the French-Japanese PHC SAKURA CASSIS project.

Figure 1 :

 1 Figure 1: Dispersion ellipses of the measured coordinates of the six EMA coils for phoneme /t/. These ellipses are computed from the samples taken at the middle of the 231 instances of /t/ in the corpus.

Figure 2 :Figure 3 :

 23 Figure 2: Dendrogram of 6 classes for vocalic contexts

Figure 5 :

 5 Figure 5: Comparing RMS error of HMM and GMM reconstruction using anova1.

Figure 4 :

 4 Figure 4: Comparing original (thick lines) and synthesized (thin lines) trajectories of ordinates of 6 EMA fleshpoints computed from the acoustic signal. Left: HMM-based inversion and trajectory formation using phone-sized Markov models with right context; right: synthesis by GMM-mapping using a context window of 90 ms and a mixture of 32 Gaussians.

Table 1 :

 1 Recognition rates (Percent Correct, Accuracy) for the experiments with different types of contexts. The star * indicates the series of experiments for which missing HMMs were replaced by the closest model.

	Train -Test	no-ctx	L-ctx	ctx-R	L-ctx-R
	Nb phones	Nb	Nb	Nb		Nb
	Cor, Acc (%)	Cor Acc Cor Acc Cor	Acc	Cor Acc
	1 -1	89,67 70,41 97,63 91,29 98,12 92,95 99,28 97,88 392 1376 387 36
	2/3 -1/3	88.09 67.91 85.56 64.66 87.57 66.19 76.90 68.59 1159 366 358 36
	2/3 -1/3 *		89,09 72.30 91,46 77,18 84,04 75.69 385 379 1312

Table 2 :

 2 RMS errors (mm) and correlation coefficients for the experiments with different types of contexts. The star * indicates the series of experiments for which missing HMMs are replaced by the closest model. The ^ indicate that the synthesis is generated from the original labels.

	-Test		no-ctx	L-ctx	ctx-R L-ctx-R
	1 -1		RMS Corr	2.26 0.72	1.62 0.82	1.62 0.83	1.05 0.90
	2/3 -1/3	RMS Corr	2.32 0.70	2.15 0.71	2.06 0.73	2.31 0.69
	2/3 -1/3 *	RMS Corr		2.07 0.72	1.96 0.75	2.08 0.73
	2/3 -1/3	Train	RMS Corr	2.21 0.75	1.86 0.77	1.87 0.75	1.74 0.82

Table 3 :

 3 RMS errors and correlation coefficient with different numbers of mixtures (# mix) and sizes of context window (ctw)

	ctw	90	170	250	330
	#mix	RMS Corr RMS Corr RMS Corr RMS Corr
	8	2.87 0.56 2.77 0.59 2.84 0.57 2.95 0.55
	16	2.76 0.58 2.61 0.62 2.67 0.60 2.94 0.55
	32	2.46 0.63 2.55 0.63 2.61 0.60 2.87 0.57


Maurizio Helio C N Tolentino
email: helio.tolentino@grenoble.cnrs.fr

De Santis

Jean-Marc Tonnerre

Aline Y Ramos

Veronique Langlais

Stephane Grenier

Aude Bailly

Structure, morphology and magnetism of an ultra-thin [NiO/CoO]/PtCo bilayer with perpendicular exchange bias

Keywords: magnetism, exchange bias, MOKE, synchrotron light

Electronic and magnetic properties of nanoscale materials are closely related to the atomic arrangement at the interface shared by dierent chemical elements. A very precise knowledge of the surface/interface structure is then essential to properly interpret the new properties coming out. Of a particular interest is the relationship between structure, morphology and magnetic properties of exchanged-coupled interfaces in ferromagnetic (FM) and antiferromagnetic (AF) materials. The interaction at the AF/FM interface modies the magnetic switching properties of the FM lm, which turn out to be a usefull property on new magnetic devices technology. We present here an investigation of the buried exchange-coupled interface [NiO/CoO]/[PtCo] grown on a Pt(111) single crystal. The magneto-optical Kerr eect reveals a strong coupling at the interface, by an increasing coercivity, and a spin reorientation of the FM lm when ordering occurs in the AF layer. The combination of grazing incidence X-ray diraction, X-ray reectivity and soft X-ray resonant magnetic scattering yields a comprehensive description of the system.

I. INTRODUCTION

Reduced dimensionality and interface interaction are often at the origin of new properties in ultra-thin lms, playing a crucial role in modern technologies. Twenty years ago, the association of ferromagnetic (FM) and non-ferromagnetic (NF) thin layers in a multilayered material lead to the discover of the giant magnetoresistance (GMR) eect [1]. This property represents an important breakthrough in science and opens the way for building up new sensors and magneto storage devices. GMR based exchange biased magnetic tunnel junctions (MTJ) and spin valves (SV) have useful properties for forming magnetic memory elements in novel device architecture [2]. The exchange bias (EB) eect [3] occurs when an antiferromagnetic (AF) material is placed in contact with a ferromagnetic (FM) one. The interaction at the AF/FM interface yields an increase of the magnetic eld necessary for switching the magnetization and induces an unidirectional anisotropy. The role of the EB eect in devices is to magnetically pin one of the FM layers.

The EB eect was discovered half a century ago by Meiklejohn and Bean when studying magnetic properties of ne Co particles that turned out to be covered by a thin oxide layer [3,4]. About ten years ago, this phenomenon was revived and comprehensive reviews focused on many experimental [5,6] and theoretical [7,8] aspects were published. The basic description of the EB phenomenon was given since the pioneering work. For a temperature T above the AF ordering Néel temperature (T N ) and below the FM layer Curie temperature (T C ), the AF spins are disordered while the FM are or-Figure 1: Schematic illustration of the spin conguration of an AF/FM bilayer: a) above the AF ordering temperature T N , when the AF spins are disordered; b) upon cooling under an applied magnetic eld the AF spins close to the interface couples and align with the FM spins; c) the applied magnetic eld is reversed: the FM spins follows the applied eld while the AF spins are not directely aected; d) scheme of the exchange bias loop shift. dered (Fig. 1-a). A magnetic eld H is applied in order to saturate the FM layer in a direction either parallel or perpendicular to the lm surface. After cooling the AF/FM bilayer under such a magnetic eld below T N , the AF spins at the interface couple with the FM spins (Fig. 1-b), yielding the energetically stable situation for the coupling at the interface. When the magnetic eld H is reversed, the AF spins exert a microscopic torque on the FM spins, tending to keep them in their original direction (Fig. 1c). The eld needed to reverse the magnetization will be larger (|H C1 | > |H C2 |) and the magnetic loop will be shifted by an amount H EB = (H C1 + H C2 )/2, due to this additional interfacial magnetic energy, ∆σ, that has to be overcome (Fig. 1-d).

The phenomenological expression of the exchange eld is H EB = ∆σ/(M F M × t F M ), where M F M and t F M are the magnetic moment density and the thickness of the FM layer, respectively. While this basic description of the exchange bias phenomenon is generally accepted, the microscopic interfacial interactions that yields larger coercivity and exchange bias shift and contributes to the interfacial energy are more controversial. The calculated interfacial magnetic energy density, ∆σ, exceeds the experimental values by orders of magnitude.

Many microscopic models have been proposed for the expression of the total magnetic energy and, in particular, for the interface exchange energy [914]. Among the complex phenomena taking place close to the interface, domain-wall formation in the AF layer, random interface roughness, contribution of compensated AF/FM interfaces, extension of the coupling beyond interfacial layers [15] and noncollinear interface spin conguration are to be considered. Moreover, the role of pinned and unpinned (AF spins that rotate) spins, or switchable interfacial uncompensated AF spins, in the exchange bias has been recently revealed by X-ray photoemission microscopy and X-ray magnetic linear and circular dichroism [16,17]. The study of ideal systems, with atomic scale control and ne characterization of the interface structure and morphology, is essential to disentangle all these parameters.

In AF materials the direction of the atomic moments varies on the length scale of nearest atomic distances. Recently, it has been shown that the magnetic coupling across the AF/FM interface in the FeMn/Co system is mediated by step edges of single-atom height [18]. The authors showed that it is possible to tune the strength of the magnetic coupling among the FM layers across ultra-thin AF one and that the coupling is stronger if steps are distributed in small islands. The reason is that the coupling is mainly mediated by uncompensated spins at monoatomic step edges. This result demonstrates why roughness is so important in some EB systems. A quite dierent situation takes place at the Fe/NiO(001) interface. The concomitant expansion of the interlayer distance and the small buckling of an interfacial FeO layer lead to an increase of the spin magnetic moment of the interfacial Fe atoms, which modies dramatically the exchange interaction [19]. The expanded interlayer distance and buckling seems to be more important to the Fe/NiO(001) AF/FM magnetic coupling than the presence of low density defective sites.

These two examples clearly demonstrate that complex surface interactions are the origin of EB. The electronic and magnetic properties of these nanoscale materials are closely related to the atomic arrangement at the inter-face shared by dierent chemical elements. It is then crucial to gather a very precise knowledge of the surface/interface structure in order to understand such new coming out properties. The availability of synchrotron sources lead to a wealth of well-established tools for structural analysis of surfaces, in particular grazing incidence X-ray diraction, scattering and absorption spectroscopy techniques [START_REF] Nielsen | An Introduction to X-Ray Physics[END_REF]. In addition, element-selective magnetic probes, as x-ray magnetic circular dichroism (XMCD) and x-ray resonant magnetic scattering (XRMS), became available and complement structural and other conventional magnetic probes. Since the AF/FM interface is buried and changes in the structural and magnetic properties are small, combining all these techniques is of paramount importance to tackle the challenging description of such systems.

The major part of exchange bias studies have been performed with the magnetization parallel to the FM/AF interface. Studies on systems with perpendicular (out of plane) magnetic anisotropy (PMA) are rather recent [2123] and only few address the role of spin conguration at the interface [24,25]. We are especially interested in thin ferromagnetic lms with PMA, as is the case in FePt and CoPt surface alloys, coupled to antiferromagnets, like CoO/NiO mixed oxides. PMA is recognized as a way for increasing magnetic storage density. In addition, magneto optical eects are enhancend at polar (sensitive to perpendicular magnetization component) geometry compared to in-plane one [26,27].

We report here on a combined structural and magnetic study of the [NiO/CoO]/[PtCo] perpendicular exchange bias system. Previous experiments on a sputtered Co/Pt multilayer with PMA coupled to a CoO oxide showed that such a system exhibits loop shifts and enhanced coercivities for both parallel and perpendicular applied magnetic elds [22]. The aim of our investigation is to obtain a ne control of the structure and to reach a comprehension of the exchange coupling mechanism at the interface of AF/FM systems that are as close as possible to model ones. Our samples have been prepared by electron beam epitaxy and oxidized in a controlled oxygen partial pressure, as described in the next section. CoO is an AF oxide with T N = 293 K and a large magnetocrystalline anisotropy. NiO presents a much higher ordering temperature, T N = 523 K, and smaller anisotropy. By mixing both oxides we obtained an AF material with a high magnetocrystalline anisotropy and with a Néel temperature intermediate between those of the two oxides [28]. The combination of grazing incidence X-ray diraction, X-ray reectivity and soft X-ray resonant magnetic scattering yields a comprehensive description of the system. An epitaxial [NiO(3ML)/CoO(3ML)]x3/PtCo sample was synthesized by sequential electron beam evaporation over a Pt(111) single crystal in the ultra-high vacuum (UHV) chamber of the French CRG BM32 beamline at ESRF [29]. The layer by layer growth described hereafter was followed step by step by in situ grazing incidence X-ray diraction [30,[START_REF] Robinson | Handbook of Synchrotron Radiation[END_REF]. The structural characteristic of the sample is then perfectly known at each stage of the growth. The very stable oxide layer on top surface enables posterior ex-situ structural, morphological and magnetic studies.

One monolayer (1 ML) of Co was deposited onto a Pt(111) single crystal held at 540 K, previously cleaned under UHV following standard procedures [START_REF] Santis | [END_REF]. These conditions promote the formation of a PtCo surface alloy with about 90% of the Co atoms buried under a Pt layer that terminates the surface. Such a PtCo surface alloy is ferromagnetic (FM) and displays a strong perpendicular magnetic anisotropy (PMA). A coercivity of 1.2 kOe was observed in situ by XMCD at the Co L edges in a similar system [33]. This PtCo(111) surface alloy was then held at 450 K during the procedure of [NiO/CoO] multilayer deposition, performed as follows. 1 ML of Co was deposited and then oxidized by exposure to 50 Langmuir of oxygen. This procedure was repeated three times yielding an epitaxial 3 ML CoO(111) lm with in-plane bulk lattice constant. On top of it, a 3 ML NiO(111) lm was grown following the same procedure. Such NiO/CoO bilayer sequence was repeated three times, leading to the AF lm of about 18 ML, schematically represented in gure 2.

The mixed oxide grow in orientational epitaxy on the Pt(111) substrate (Fig. 3). The rst CoO atomic layer is pseudomorphe on the substrate. After the second oxide layer deposition, the layer relaxes and a bulk-like CoO(111) lattice peak shows up at K = 0.92. An hexagonal unit cell was taken for the Pt(111) crystal [START_REF] Santis | [END_REF][START_REF] Waren | X-Ray Diraction[END_REF]. The peak at K = 1 in the reciprocal space correspond to the interlayer spacing of 0.2266 nm for Pt, yielding an oxide layer in-plane interlayer spacing of 0.245 nm, exactly as in the CoO bulk oxide. The NiO layer grows in coherent epitaxy with the CoO and displays the same in-plane parameter, as observed by its contribution to diraction peak intensity, at exactly the same position in the reciprocal space.

A well dened atomic stacking is observed at each step of the oxide deposition, as well as in the nal sample. On the other hand, CoO diraction rods as well posteriory ex situ measurements show that this nal sample has a quite large rough surface. Kiessig interference fringes [START_REF] Nielsen | An Introduction to X-Ray Physics[END_REF] can hardly be observed in the X-ray reectivity prole (Fig. 4). The tting to the calculated reectivity gives a roughness of about 1 nm at the surface, while the interface is rather at, with roughness of about 0.1 nm. Such a large roughness is not surprinsing due to the polar character of the Pt(111) surface. AFM measurements in a similar oxide surface -a 12 ML CoO lm on the same Pt(111) crystal surface, treated in identical conditionsalso reveal that the surface roughness is roughly 1 nm (Fig. 5).

As a matter of fact, owing to their sligthly dierent in-plane lattice parameters, the superposition of the CoO(111) and Pt(111) lattices gives rise to a Moire structure with a 3.6 nm periodicity. Such Moire modulation, originates from the coincidence of 12 CoO units with 13 Pt atomic distances and might be used as a template

B. Increased coercivity, exchange bias and spin reorientation

Magneto-optic Kerr eect (MOKE) was used to follow the magnetic properties of our sample. MOKE is a wellestablished technique to study magnetism in ultra-thin FM lms [26]. The MOKE sub-monolayer sensitivity has been veried in many situations [27]. Polar and longitudinal MOKE are characterized by a complex rotation of the plane of polarization of the linearly polarized incident light upon reection from the surface of a ferromagnetic material. The rotation is directly related to the magnetization of the material within the probed region of the light.

In order to induce EB, the sample was eld cooled from above the Néel temperature down to room temperature under an applied magnetic eld of 5 kOe. Then, polar MOKE (PMOKE) hysteresis loops were measured at increasing temperatures, up to 383 K (Fig. 6). The coercivity (H C = (H C2 -H C1 )/2) presents a maximum of 1.7 kOe at about 320 K, then decreases monotonically to 1.2 kOe at higher temperatures (Fig. 7). It is worth noting that 1.2 kOe is the same value as for the PtCo surface alloy without any capping oxyde [33]. The FM layer preserves its quality and is altered just by the exchange coupling to the AF ordered layer.

For temperatures below 320 K the hysteresis loops shifts. The temperature below which the shift appears is dened as the blocking temperature, T B = 320 K. At room temperature, the shift is found to be H EB = -0.6 kOe and characterises the perpendicular exchange coupling at the interface between the FM and AF layers. From that, the calculated interfacial exchange energy is ∆σ= 0.16 erg/cm , where we used the FM thickness as t F M = 0.36 nm. This is about 2/3 of the value found by Maat et al. [22] for a multilayer at 10 K. The most striking result in this range is that the hysteresis loops becomes less and less squared, as indicated by the decreasing PMOKE amplitude at remanence and loop elongation (Fig. 6 and7). The decreasing squareness of the loops indicates that the easy magnetization axis of the FM layer is no longer perpendicular. Our interpretation is that, upon eld cooling, the AF spins should align along the spin anisotropy axis that is closest to the applied magnetic eld [36]. This should be particularly applicable for CoO because of its high magnetocrystalline anisotropy constant around the {117} directions. The CoO spins will be oriented along one of the {117} directions, forming an angle of 43.3 • with the surface normal. The orientation of the NiO magnetic moments is assumed to follow the CoO spins because of a strong exchange interaction at the interface [37] and a smaller magnetocrystalline anisotropy constant. Therefore, the change in the hysteresis loops is related to the reorientation of the Co spins in the FM layer due to exchange coupling with the oxide layer. As far as we know, this is the rst experimental observation of the reorientation of the outof-plane interfacial FM spins induced by the ordering of the AF layer. One should note the fact that, in other [Co/Pt]/[CoO] systems, the FM layer is thicker than a single monolayer (e.g. Maat et al [22]).

For temperatures above 320 K the hysteresis loops are squared, with a magnetization at remanence close to magnetization at saturation. In this temperature range there is no exchange shift. The increased coercivity H C is related to the antiferromagnetic order persisting in the mixed oxide layer. The AF ordering temperature T N may be estimated by the inexion point of the coercivity as function of temperature [38] and turns out to be T N = 350 K. This value is smaller by 50 K compared to the average CoO and NiO bulk Néel temperatures due to the reduced thickness eect which lowers the order temperature [36]. As can be also observed, T B is smaller by 30 K than T N , owing to thermal activation of the AF domains. Such kind of dierence has already been pointed out by Maat et al. for the pure CoO coupled to a Co/Pt multilayer.

C. Depth prole spin conguration at the interface

The depth dependence of the out-of-plane magnetization across the interface between the AF and FM layer has been investigated taking advantage of the chemical and spatial sensitivity of soft X-ray Magnetic Reectivity [39]. This polarized synchrotron X-ray technique exploits the magnetization sensitivity of the atomic scattering factor (ASF) at an absorption edge and is known to be sensitive to the three directions of the magnetization with spatial, chemical and orbital selectivity [40]. The soft xray specular reectivity experiments were conducted on the SIM beamline at the Swiss Light Source using the RESOXS endstation [41]. The magnetic saturation of the FM layer was achieved by a 4 kOe permanent magnet brought to the sample perpendicularly to its surface. The measurements were carried out in remanence at T = 340 K, right above T B and below T N , where the FM layer has a strong PMA and where the interfacial magnetic coupling with the AF layer constrains the reversal process, as indicated by the increased H C (Fig. 7). The reected intensity was recorded as a function of the scattering angle at dierent photon energies, and as function of energy at xed scattering settings. The asymmetry ratios, or normalized dichroic dierences, were measured using 98% left and right circularly polarized beam [42]. Absorption spectra were collected simultaneously by recording the drain current as a function of incident photon energy. The spectral shape of the absorption is essentially that of the CoO and NiO oxide, as expected from a total electron yield measurement [43]. In reectivity condition, the penetration depth is large enough to probe the buried Co layer.

Angle dependent reected intensity (Fig. 8-a) were collected at 776.9 and 778.5 eV close to the Co L 3 edge. At both energies, a separation of the curves with right and left polarized ligth is observed. The asymmetry ratios at both energies are close to zero at small angles and exhibit a larger amplitude at high angles (Fig. 8-b), in agreement with the geometrical dependence of the atomic scattering factor arising from an out-of-plane magnetization component. This angle dependence is mainly due to the Co magnetization in the Pt-Co layer and in the oxide layer.

The structural parameters of the lm were derived from the the renement of the average reectivity. The total thicknesses is about 5.45 nm of oxide and 0.36 nm of PtCo. This is in good agreement with the expected thickness from the sequential deposition of 18 ML of oxide and 1ML of Co. The roughnesses are 0.02 and 0.9 nm for the interface CoO/PtCo and for the top NiO/CoO interfaces, respectively, is in agreement the X-ray reectivity and AFM results, too. The magnetic prole comes from the analysis of the asymmetry ratio at both energies. The interference at about 32 • indicates a magnetic thickness smaller than the total oxide thickness. A model assuming that Co atoms in the oxide may be magnetically ordered up to the rst CoO/NiO interface works well. The renement of the magnetic structure was performed by dividing the rst CoO layer in three slices and by adjusting their thicknesses as well as the magnetic moments carried by the Co atoms. The results indicate the out-of-plane magnetization is distributed beyond the 0.36 nm Pt-Co layer and extends over 1 nm in the oxide layer. The coupling to the FM Co spins is parallel in a 0.3 nm thick slice, roughly the rst CoO monolayer.Then, it is antiparallel in a 0.7 nm thick one, with similar amplitude. The last slice that completes the CoO layer is found to be 0.2 nm thick and has no net magnetization. Considering models with no magnetization in the oxide layer, completely parallel or antiparallel magnetic slices and more extended magnetization with reduced magnetic amplitude do not t the interference eect observed experimentally. This result can be understood as follows: the Co atoms in the rst CoO slice, right on top of the Pt-Co layer, have a mixed electronic character in between metallic and oxidized state. Their net induced magnetization are likely to be dominated by the proximity of the Pt-Co layer and are ferromagnetically coupled to it. For the next CoO slice, the Co atoms are fully oxidized and the net magnetization is antiferromagnetically coupled to the rst one. The net magnetization found equal to zero in the third slice means that beyond the second oxide layer the AF material break into domains that are not biased by the eld cooling processes.

III. SUMMARY

Our results show that valuable insights into the surface structure and magnetism in the CoO/PtCo system emerge from combination of in situ, ex situ, and in-depth sensitive structural and magnetic characterizations. In situ grazing incidence X-ray diraction (GIXRD) results demonstrate that the AF oxide grows epitaxially on top of the PtCo(111) surface alloy. The top surface of the mixed oxide is rough while the interface CoO/PtCo is quite at over the whole crystal. The perpendicular magnetic anisotropy, well above the Néel temperature, is the same as for the uncapped PtCo layer, showing that the quality of the layer is preserved after oxide deposition. Upon eld cooling, slightly above T B , the ultra thin Co ferromagnetic layer exhibits a strong perpendicular anisotropy and magnetic ordering is induced over a few oxide atomic layers. The out-of-plane magnetic prole shows that oxidized Co atoms closest to the interface are ferromagnetically coupled to the PtCo ferromagnetic layer. The second oxide layer then couples to this interfacial one antiferromagnetically. Below the blocking temperature T B , MOKE indicates a spin reorientation in the FM layer that would follow the blocked Co spins of the AF layers. Such reorientation in that FM surface layer indicates that the interfacial spins in a thicker FM layer is strongly modied by the ordering of the top AF layer.

IV. AKNOWLEDGEMENTS

We would to acknowledge the French CRG BM32 beamline at ESRF and the SIM beamline at SLS, specially U. Staub for his help and discussions. Yves Souche (Institut Néel, CNRS, France) is also acknowledge for helping during MOKE measurements.

Figure 2 :

 2 Figure 2: Schematic sequence of the AF/FM bilayer [NiO(3ML)/CoO(3ML)]x3/PtCo sample. Insert: close view of the spin conguration at the interface CoO/PtCo, assuming that both layers are ordered and non-interacting

Figure 3 :

 3 Figure 3: Surface X-ray diraction pattern during the growth of the NiO/CoO mixed oxide over the PtCo(111) surface alloy

Figure 4 :

 4 Photon energy : Cu K

Figure 5 :

 5 Figure 5: AFM of a 12 ML CoO layer grown by electron beam evaporation on top of a Pt(111) single crystal. A roughness close to 1 nm can be observed

Figure 6 :Figure 7 :

 67 Figure 6: PMOKE hysteresis loops measured at dierent temperatures, after eld cooling from 400 K under 5 kOe.

Figure 8 :

 8 Figure 8: XRMS at the Co L3 edge. Upper curves correspond to the two polarizations at E=778.5. The curves display the asymmetry ratio at two dierent energies about the edge.

Brazilian Journal of Physics, vol.38, no. ?, ???, 2008


F Fettar

H Garad

L Ortega

A Y Ramos

B Zawilski

P Plaindoux

S Auffret

; B Rodmacq

B Dieny

Investigation of metallic/oxide interfaces in Pt/Co/AlO x trilayers by hard x-ray reflectivity

Keywords: X-ray measurements, X-ray chemical analysis, Perpendicular magnetic anisotropy, Metal-insulator structures, Magnetic layered films, Oxidation, Reflectometry, Simulation, X-ray chemical analysis

X-ray reflectivity (XRR) is used to determine the oxidation front at the nanometer scale in sputtered perpendicular semi tunnel junctions, as the form Pt/Co/AlOx, by varying the oxidation time tOx of the capping layer. From XRR simulations, we show that the nature of the stack is gradually defined according to the value of tOx. For low tOx values (<40 s), a simple Pt/Co/Al/AlOx multilayer is appearing whereas a Pt/Co/CoO/AlOx architecture takes place for higher tOx. The oxygen-induced magnetic properties obtained by extraordinary Hall effects measurements are explained by the structural results. The increase of Co-O bondings with tOx is at the origin of the appearing of the perpendicular magnetic anisotropy (PMA).

I. INTRODUCTION

Multilayered magnetic systems containing magnetic (MM) and nonmagnetic materials (NM) constitute a wonderful challenge from a fundamental and industrial point of view, since these artificial media exhibit fascinating properties. For example, magnetic tunnel junctions, consisting of thin insulating barriers layers (~ 1-2 nm) sandwiched between ferromagnetic layers, have been intensively studied over the last 14 years [START_REF] Moodera | Large Magnetoresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions[END_REF]. In measured Tunnel MagnetoResistance (TMR) effects, the exact chemical composition along the different interfaces (between MM and NM layers) plays a very significant role since it determines the degree of polarizations (related to TMR) of the tunnelling electrons. Furthermore, the presence of selected layers for magnetic electrodes could induce a perpendicular magnetic anisotropy which is more interesting than in-plane magnetic anisotropy (high density hard disk media and magneto-optical recording). In this field, Pt/Co seems to be a model system due to the good control of the form of the magnetic loop from deposition parameters (different thicknesses, natures of buffer and protective layers), as published in the literature. As a consequence, the Pt/Co/AlO x system with a perpendicular magnetic anisotropy [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF], which is the studied structure in the present paper, has specific interests (MRAM, less sensitivity to border defects).

In order to investigate the oxidation dynamic of subnanometer Al and underlayed layers, the oxidation time of Al, namely t Ox , is an interesting deposition parameter to explore. Because by modifying it, different oxidation regimes appear: The [under -optimized -over] state is obtained when t Ox is progressively increased. Thus, the physical characteristics, such as TMR or the magnetic anisotropy (in plane vs. out of plane) are strongly dependent on the quantity of O 2 in different layers. For instance, in the reference [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF], the oxygen-induced perpendicular magnetic anisotropy induced by varying the plasma oxidation time (t Ox ) was studied in Pt/Co/AlO x . A set of characterizations (x-ray photoelectron spectroscopy,

x-ray absorption spectroscopy, and Extraordinary Hall Effect) showed that the maximum of outof-plane magnetic anisotropy seems to be related to the appearance of a significant density of Co-O bonds at the Cointerface. The aim of the present study is to confirm this hypothesis, by using hard x-ray reflectivity technique.

These physical properties (TMR and/or anisotropy) of such magnetic compounds have been clearly related to structural characteristics (the presence of O 2 in different metallic layers), as in [START_REF] Lacour | Magnetic properties of postoxidized Pt/Co/Al layers with perpendicular anisotropy[END_REF]- [START_REF] Yoon | Effect of localized antiferromagnetic phases at interfaces between AlOx insulating barriers and Co50Fe50 electrodes in magnetic tunnel junctions[END_REF]. But, the studied systems in these precedent references are complex, with a lot of elements (Mn, Ni, Fe, Co, Al, O, Ta). In addition, several oxidized metals (FeO x , CoO x , AlO x ) are appearing and insufficient structural techniques are devoted to the series with different t Ox . Consequently, it leads to a difficult understanding of experimental results in these references [START_REF] Lacour | Magnetic properties of postoxidized Pt/Co/Al layers with perpendicular anisotropy[END_REF]- [START_REF] Yoon | Effect of localized antiferromagnetic phases at interfaces between AlOx insulating barriers and Co50Fe50 electrodes in magnetic tunnel junctions[END_REF].

X-ray reflectivity is a relevant, non destructive and large area sensitive technique for detailing with a high precision the architecture of magnetic nanostructures [START_REF] Asgharizadeh | Ruthenium nano-oxide layer in CoFe-Ru-CoFe trilayer system: An x-ray reflectivity study[END_REF]. It leads to a better understanding of physical properties. However, systematic XRR studies on magnetic nanostructures when the deposition time is varied in a series of samples are surprisingly scarce in the literature [START_REF]Leptos version 3.03[END_REF]. In this work, we intensively have used hard X-Ray Reflectivity (XRR) in the aim to explore the thickness, the roughness and the density of different layers by supposing a change of the stack architecture related to t Ox . Magnetic properties, as found in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF] and in this present paper, are clearly explained with respect to their chemical composition thanks to XRR results. In particular, the role of oxygen for sufficient dose is to increase the magnetic coupling between the ferromagnetic Co layer and the antiferromagnetic CoO entities.

II. EXPERIMENTS

In a first step, Pt/Co/Al trilayers were successively deposited onto thermally oxidized Si by conventional dcmagnetron sputtering. The nominal thicknesses were 3, 0.6 and 1.6 nm for Pt, Co and Al respectively. Secondly, samples were then transferred under vacuum in a separate treatment chamber and oxidized using an oxygen rf plasma during an oxidation time t Ox in the range [15-60] seconds. More information on the samples is detailed in reference [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF]. The reflectometry was carried out with a Bruker D8 Discover diffractometer using a line focus from a Cu target x-ray tube. Göbel multilayer optics was used to select Cu K<α> wavelength ( =1.5418 Å) and to make the beam quasiparallel (divergence ≤ 0.028°). The beam size at sample position was 50 µm in the incidence plane. The sample size was 3 mm wide by 12 mm long and the same pieces were used for magnetic measurements. Data were collected using a scintillation detector in the [0-16°] 2Ө angular range, with an increment of 0.04° and an acquisition time of 40 sec/step. The interpretation of XRR measurements is carried out by fitting the experimental scans with theoretical curves using Bruker LEPTOS® software [START_REF] Quade | Investigation of oxidation process on plasma treated thin Al-films by GIXR and GIXRD[END_REF]. The magnetic properties were carried out by extraordinary Hall Effect (EHE) measurements for different temperatures T (4-293K) and magnetic fields H (0-5 Teslas) perpendicular or parallel to the sample plane.

III. RESULTS

A. Magnetic characterization

Perpendicular magnetic normalized measurements, performed by EHE at different temperatures T (4.2-293K) for t Ox =40 s, are shown in Fig. 1. Only the half part of the hysteresis is represented for H comprised between 0 and 1.5 T, and the return to 0 T (see the arrows in Fig. 1 indicating the magnetization reversal at 4.2K).

FIG. 1 HERE

This sample exhibits a square jump. Magnetic measurements with in-plane applied field indicate that the saturation magnetization is difficult to obtain, with a saturation field comprising between 1.2 and 2 teslas from RT to LT respectively (curves not shown). These results indicate that the out-of-plane direction is an easy magnetic axis for t Ox =40 s. For the oxidation time ranging from 15 to 60 s, a crossover for the anisotropy from in-plane to out-of-plane appears around t Ox =25 s. In the next part, we will research the possible reasons of this crossover, and the maximized outof-plane anisotropy close to t Ox ~40 sec as previously found in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF].

B. Structural characterizations by reflectivity

Fig. 2 displays a series of X-ray reflectivity curves for different oxidation times t Ox ranging from 15 to 60 s.

FIG. 2 HERE

XRR curves indicate that, for increasing t Ox , it appears clear Kiessig's fringes more and more pronounced and differently positioned. We note a progressive change of these curves with t Ox , indicating that a weak variation of the oxygen treatment remarkably changes the structure of semi tunnel junctions. XRR data are simulated using different appropriate stacking models. The main difficulty of the study resides on the fact that the layers thicknesses are very low. In order to evaluate the sensitivity of the XRR for sub-nanometer layers, we have simulated the reflectivity for different architectures (see Fig. 3): Pt/Al/AlO x without Co, Pt/Co 0.3nm /Al/AlO x and Pt/Co 0.6nm /Al/AlO x with a Co thin layer.

FIG. 3 HERE

Here, the fixed thicknesses Th were Th Pt =3 nm, Th Al =1.2 nm and Th AlOx =0.8 nm. The densities values were the bulk ones and the roughness was 0.2 nm at each interface. This architecture is corresponding to the low t Ox regime (non oxidized Co and partially oxidized Al). We note that a low Co thickness value significantly affects the curves. In the same way, we adopt the following architecture: Pt/Co/CoO/AlO x corresponding to the high t Ox regime (partially oxidized Co and fully oxidized Al). Table 1 lists the nominal values of density taken in the reflectivity models.

Table. 1 HERE

Firstly, we start the adjustment for the least oxidized sample (15 s). The reason lies on the architecture of the trilayer including only AlO x slab on the top with no a priori known thickness value. Taking into account the best set of parameters for t Ox =15 s as starting values, we were able to adjust subsequent oxidized sample data with the stack: Pt/Co/Al/AlO x . The procedure is iteratively repeated for the sample's series. Due to the large number of parameters in the model, density and thickness of Co and Pt layers were fixed to nominal values at the beginning of the simulation and released only for the final fit. The last point to consider in the fit analysis is the appearing of a CoO layer for higher t Ox values as mentioned above, inducing the stack Pt/Co/CoO/AlO x . It occurs with the full oxidation of the Al layer at a certain t Ox value noted t * Ox . The crossover oxidation time t * Ox is obtained at 40 s, this value being the best compromise between both architectures from the obtained fits.

We individually extract for each fitted curve, three fit parameters as mentioned above: thickness (Th), roughness (σ) and density (ρ) for each layer of the architecture. For improving the understanding of these results, we combine both ρ and Th for a considered layer, and we then define the following ratios R for Al The oxidation process is usually considered as homogeneous in the surface plane of the layers with a diffuse interface which is quantified by the roughness parameter.

Here, the values are high (see right panel in Fig. 4) comparatively to thicknesses in these slabs. The oxidation process could induce a degradation of the interfaces. Due to these high rms roughness and the low thickness, the density or composition profile is non abrupt. Consequently Co and O atoms can he bonded before a complete disappearance of the Al layer. This result is important for understanding magnetic results as detailed in the next part.

C. Discussion

In the present study, we have studied the oxidation time dependence in XRR data in semi tunnel junctions. This method of XRR analysis permits to obtain the structural evolutions provoked by the oxidation front of the oxygen plasma. In our Pt/Co/AlO x trilayers, the oxygen atoms progressively penetrate in the material in a non uniform way, as indicated by the values of thickness and roughness. The effect of the oxidation process on fitted XRR data has been seen in [START_REF] Asgharizadeh | Ruthenium nano-oxide layer in CoFe-Ru-CoFe trilayer system: An x-ray reflectivity study[END_REF] where the authors have shown the change of the electron density profile for CoFe/Ru/CoFe and CoFe/RuO x /CoFe thin layers.

In our trilayers, the extracted quantities from fitted XRR data corroborate the magnetic measurements at fixed temperature in the range (4.2-293K). From our magnetic measurements, an out-of-plane easy axis is seen for t Ox >25 s whereas the in-plane easy axis is obtained for lower t Ox . This crossover at t Ox ~25 s has previously been seen in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF] at room temperature. The authors have interpreted these results by the substantial amount of oxygen atoms at this interface which induces a strong perpendicular magnetic anisotropy PMA, overcoming the in-plane anisotropy of the Co layer. The present results confirm this hypothesis. Due to the roughness of layers, the Co layer is very close to the AlO x one for t Ox ~25-30 s. This is why we observe that this value is lower than t* (40 s, see Fig. 4) where a CoO layer appears in the structure. The thermal evolution of magnetic properties for out-of-plane measurements will be discussed now in the light of our structural characterizations.

For t Ox <25 s the easy magnetic axis is in the plane of the Co layer and a weak thermal dependence appears in the magnetic data. In addition, there are no oxygen atoms at interfaces of the Co layer as deduced from XRR data. Hence, only the interfacial anisotropy coming from Pt/Co and Co/Al, which favour an in-plane anisotropy, contributes to the total interfacial anisotropy. Perpendicular magnetic anisotropy of the Co layer for low oxidation times is only observed for higher Pt thickness (~ 5 nm) and a Ta buffer layer [START_REF] Carvello | Sizable room-temperature magnetoresistance in cobalt based magnetic tunnel junctions with out-of-plane anisotropy[END_REF].

For t Ox above 25 s, it appears a noticeable variation of EHE with T. This crossover coincides with the emergence of the perpendicular easy axis at RT as observed in reference [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF]. In this t Ox regime, XRR data clearly show the presence of oxygen atoms at the top of the Co layer. As a result, we have to consider an additional interfacial anisotropy, K(Co/Oxygen). This might be at the origin of the PMA.

For t Ox >40 s, XRR analysis reveals a CoO layer, and the persisting out-of-plane anisotropy as observed in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF] at RT. Indeed, the additional magnetic coupling between Co and CoO becomes non-negligible in the high t Ox regime. Consequently, the strong increase of H c when decreasing T could be explained by the thermally induced increase of the antiferromagnetic pinning strength, as in [START_REF] Tripathy | Probing the exchange bias in Co/CoO nanoscale antidot arrays using anisotropic magnetoresistance[END_REF] for Co/CoO nanostructures. A forthcoming work will focus on the T dependence of the magnetic properties on Pt/Co/AlO x trilayers for different t Ox [12]. Our results indicate that the magnetic interaction is proportional to t Ox in the 25-60 sec range. CoO favouring in-plane anisotropy, the optimization of PMA (40 sec), see in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF], is explained by the compromise between both precedent regimes.

To our knowledge, it does not exist a systematic study combining structural analysis and temperature dependent magnetic properties for a series of oxidized multilayers. Only, fixed temperatures (LT and/or RT) have been used in the literature ( [START_REF] Lacour | Magnetic properties of postoxidized Pt/Co/Al layers with perpendicular anisotropy[END_REF], [START_REF] Yoon | Effect of localized antiferromagnetic phases at interfaces between AlOx insulating barriers and Co50Fe50 electrodes in magnetic tunnel junctions[END_REF] and [START_REF] Lu | A magnetometry study of Co oxidation in Co/MgO bilayers grown by sputtering[END_REF]). In these papers, no systematic structural studies with t Ox , explaining the magnetic results, have been reported contrary to the present study.

IV. CONCLUSION

We have shown that the oxidation time t Ox remarkably changes the structure of Pt/Co/AlO x . For t Ox <25 seconds, the Co layer contains a weak quantity of oxygen atoms at least localized on the top Al protective layer. It becomes a mixture of "Co-CoO layer" with a fully oxidized Al at higher t Ox (≈ 40 s). Consequently, the perpendicular anisotropy found in [START_REF] Rodmacq | Influence of thermal annealing on the perpendicular magnetic anisotropy of Pt/Co/AlOx trilayers[END_REF] at RT is explained by the presence of oxygen at the interface between Co and AlO x . It will be interesting to study the coordinance of Co atoms as a function of both t Ox (as well as the annealing temperature) using x-ray absorption methods.

ACKNOWLEDGMENT

This work was supported in part by the Ministère des affaires étrangères from France.

  [(1)] and AlO x [(2)]: R Al = ρ Al ·Th Al / ( ρ Al ·Th Al + ρ AlOx ·Th AlOx ) (1) and R AlOx =1-R Al . (2) The reason is to take into account into the density in the extracted quantity of atoms. The ratios of Co and CoO are defined in the same way. The evolutions of R Al and R AlOx are shown in top-left panel in Fig. 4(a). FIG.4 HERE The oxidation time dependences of ratios for the (Al, AlO x ) couple clearly indicate that oxygen penetrates progressively inside the Al layer when t Ox increases. The behaviors of Co and CoO ratios [bottom-left panel in Fig. 4(b)] follow the same tendency. These results show a change from a mixed phase of Al and AlO x to a pure AlO x , followed at t Ox =t* Ox ~40 s by a change from a quasi pure Co to mixed Co, CoO phase for longer oxidation times. Concerning the roughness, it follows the same tendency as the thickness of the corresponding element [top-right (c), bottom-right (d) panels of Fig. 4 for {Al,AlO x } and {Co,CoO} couples respectively].

FIG. 1 :

 1 FIG. 1: EHE normalized data as a function of out-of-

FIG. 4 :

 4 FIG.4: Ratios [see the text, (1) and (2)] from fits in Fig.

FP-01 5 1,

 5 R Al and R AlOx vs t ox [top-left panel, (a)]; R Co and R CoO [bottom-left panel, (b)] vs t ox . Roughness σ of layers deduced from fits in Fig. 1 vs t ox : for Al and AlO x , [topright panel, (c)]; for Co and CoO [bottom-right panel, (d)]. The dashed lines (25 s) show the anisotropy crossover from in plane to perpendicular by increasing t ox , whereas the straight lines (40 s) indicate the appearance of CoO.

plane applied magnetic field H at different temperatures for Pt 3 nm /Co 0.6 nm /AlO x oxidized during t Ox =40 s. The arrows show the magnetization reversal at 4.2K.

	intensity)	points : data solid line : fit	t	Ox
	Log (relative				45" 30" 35" 50" 60" 55" 40" 25"
					15"
	4	8	12	16
			(degrees)
	FIG. 2: X-

ray reflectivity data (circles) with fits (solid lines) for Pt/Co/AlO x oxidized during t Ox in the range 15- 60 seconds. (Curves are shifted vertically for the sake of clarity). Table1: Nominal values of density taken in the reflectivity models compounds AlO x

				Al CoO Co	Pt	SiO2	Si
	density
			3.98 2.7 6.43 8.9	21.44	2.2	2.33
	(g/cm 3	)
		intensity)
		Log (relative	Pt/Al/AlO Pt/Co x 0.3 nm /Al/AlO
			4	8	12	16
				(degrees)

x Pt/Co 0.6 nm /Al/AlO x FIG.

3: Simulations of the reflectivity for different architectures: Pt/Al/AlO x , Pt/Co 0.3 nm /Al/AlO x and Pt/Co 0.6 nm /Al/AlO x where the thicknesses Th are: Th Pt =3 nm, Th Al =1.2 nm and Th AlO x =0.8 nm. The densities are the bulk values and the roughness is 0.2 nm for each interface. (Curves are shifted vertically).