Marc-Antoine Georges
email: marc-antoine.georges@grenoble-inp.fr

Laurent Girin

Jean-Luc Schwartz

Thomas Hueber

Learning robust speech representation with an articulatory-regularized variational autoencoder

Keywords: Speech production, representation learning, variational autoencoder, articulatory model, speech enhancement

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Introduction

Motor and perceptuo-motor theories of speech perception involve internal motor simulation processes [START_REF] Liberman | The motor theory of speech perception revised[END_REF][START_REF] Schwartz | The Perception-for-Action-Control Theory (PACT): A perceptuomotor theory of speech perception[END_REF] which may be particularly recruited when perceiving speech in adverse (e.g. noisy) conditions [START_REF] Skipper | The hearing ear is always found close to the speaking tongue: Review of the role of the motor system in speech perception[END_REF]. Similarly, most computational models of speech motor control rely on an explicit access to motor representations, first when recovering the motor commands required to reach an acoustic target (inverse internal model), and then when simulating the acoustic consequences of articulatory gestures (direct internal model) [START_REF] Houde | Speech production as state feedback control[END_REF][START_REF] Guenther | A neural theory of speech acquisition and production[END_REF]. Inspired by human cognition and neurophysiology, the integration of motor/articulatory priors and constraints in automatic speech processing systems has motivated several studies, for increasing the robustness of automatic speech recognition (ASR) systems in noise [START_REF] Rose | The potential role of speech production models in automatic speech recognition[END_REF][START_REF] Castellini | The use of phonetic motor invariants can improve automatic phoneme discrimination[END_REF][START_REF] King | Speech production knowledge in automatic speech recognition[END_REF][START_REF] Mitra | Articulatory information for noise robust speech recognition[END_REF], for allowing a better control of text-to-speech (TTS) synthesis [START_REF] Ling | Integrating articulatory features into HMM-based parametric speech synthesis[END_REF], or for designing voice restoration and pronunciation training systems [START_REF] Schultz | Biosignal-based spoken communication: A survey[END_REF]. Modeling the complex relationships between phonetic targets, articulatory movements and speech acoustics is also essential to build a computational model of speech perception and production [START_REF] Laurent | The complementary roles of auditory and motor information evaluated in a Bayesian perceptuo-motor model of speech perception[END_REF][START_REF] Hueber | Evaluating the potential gain of auditory and audiovisual speech predictive coding using deep learning[END_REF].

With both these technological and fundamental research goals in mind, we deal in this paper with the automatic learning of latent representation from the raw speech audio signal. We focus on deep generative models and in particular on the variational autoencoder (VAE) model [START_REF] Kingma | Auto-encoding variational Bayes[END_REF][START_REF] Rezende | Stochastic backpropagation and approximate inference in deep generative models[END_REF] which can be seen as a probabilistic version of a deep autoencoder. The VAE was shown to be able to learn relevant latent representations by disentangling dimensions like speaker identity or phonetic features [START_REF] Blaauw | Modeling and transforming speech using variational autoencoders[END_REF][START_REF] Hsu | Learning latent representations for speech generation and transformation[END_REF]. This model has already been successfully used in a variety of speech processing applications, e.g. [START_REF] Hsu | Voice conversion from non-parallel corpora using variational auto-encoder[END_REF][START_REF] Bando | Statistical speech enhancement based on probabilistic integration of variational autoencoder and non-negative matrix factorization[END_REF][START_REF] Akuzawa | Expressive speech synthesis via modeling expressions with variational autoencoder[END_REF][START_REF] Leglaive | Semi-supervised multichannel speech enhancement with variational autoencoders and non-negative matrix factorization[END_REF]. In line with speech perception theory, we propose in this paper to introduce prior articulatory information in the representation learning process. This information is first derived from an articulatory model built from in-vivo recordings of a reference speaker. It is then transferred at training time via an additional regularization term in the loss function of the VAE. An overview of the proposed architecture is shown in Figure 1. With this model, we address the two following research questions: 1) Can prior articulatory knowledge speed up the speech representation learning process? 2) Can prior articulatory knowledge make the learned latent representation more robust to noise? To address those questions, we compared the proposed articulatoryregularized VAE to a conventional one in terms of convergence speed at training time and on a speech denoising task.

To the best of our knowledge, the introduction of prior articulatory constraints for representation learning has been proposed only in very few studies. In [START_REF] Turrisi | Improving generalization of vocal tract feature reconstruction: From augmented acoustic inversion to articulatory feature reconstruction without articulatory data[END_REF], a set of vocal tract variables derived from the articulatory phonology theory [START_REF] Browman | Towards an articulatory phonology[END_REF] is used to constrain the latent space of a (deterministic) autoencoder. The performance is evaluated by measuring the accuracy of the reconstructed articulatory features whereas in the present study we focus on the quality of the reconstructed speech signal. In [START_REF] Saha | Learning Joint Articulatory-Acoustic Representations with Normalizing Flows[END_REF], a normalizing flow technique is used to constrain the latent space of two autoencoders respectively processing articulatory and audio data. However, evaluation is mostly limited to qualitative evaluation. Therefore, the present study proposes the first VAE model regularized by articulatory prior knowledge and used to learn robust latent representation from the audio speech signal.

Methodology

Acoustic and articulatory data

The following experiments were conducted on two datasets. Each of these datasets is composed of parallel audio and electromagnetic articulography (EMA) recordings (sustained vowels, vowel-consonant-vowel sequences, french words and sen-tences). The first dataset, PB2007, consists of 1,109 items (15 minutes of speech) produced by a reference speaker (PB, male). EMA data were recorded using the Cartens 2D EMA system (AG200). Six coils were placed on the tongue tip, blade and dorsum, upper and lower lip and on the jaw (lower incisor). The acquired trajectories were low-pass filtered at 20 Hz and down-sampled from 200 Hz to 100 Hz. We denote by y an individual resulting vector of EMA data, of dimension 12. The second corpus, BY2014, 1 includes 925 items (45 minutes of speech) produced by another reference speaker (BY, male). Articulatory trajectories were recorded using the 3D NDI Wave system with 9 coils used (3 on the tongue, 4 on the lips, 1 on the jaw, 1 on the velum). They were low-pass filtered at 20 Hz and down-sampled from 200 Hz to 100 Hz. The 3D coordinates of the 9 EMA coils were finally projected on the midsagittal plane resulting in a 14-dimensional vector y.

As required by the LPCNet vocoder [START_REF] Valin | LPCNet: Improving neural speech synthesis through linear prediction[END_REF] which is used in this study to reconstruct an audio speech signal from the output of the VAE, each audio recording was converted into a sequence of 18 Bark-scale cepstral coefficients [START_REF] Schroeder | Objective measure of certain speech signal degradations based on masking properties of human auditory perception[END_REF], using a 20-ms sliding analysis window with 10-ms frame shift. The resulting vector of audio features is denoted x.

Building the articulatory model

For each of the two reference speakers, we first built an articulatory model using the general methodology originally proposed by [START_REF] Maeda | Compensatory articulation during speech: Evidence from the analysis and synthesis of vocal-tract shapes using an articulatory model[END_REF], slightly adapted in [START_REF] Serrurier | The tongue in speech and feeding: Comparative articulatory modelling[END_REF] in order to process EMA articulatory data. In the present study, we consider the six following articulatory parameters (represented in Figure 1): Jaw Height (JH), Tongue Body (TB), Tongue Dorsum (TD), Tongue Tip (TT), Lip Protusion (LP), Lip Height (LH), Velum (VL, for BY speaker only). Here "articulatory parameters" means that these parameters are interpretable in terms of articulatory control/function in speech production [START_REF] Maeda | From EMG to Formant Patterns of Vowels: The Implication of Vowel Spaces[END_REF]. The core principle is to extract the latent dimension of tongue and lip movements after removing the contribution of the jaw, using a so-called "guided-PCA". More precisely, the JH parameter (and the corresponding value for all the articulatory observations of the dataset) is defined as the first principal component (PC) of the jaw movement. The contribution of the jaw to the movement of the tongue is then estimated using a linear regression between JH values and the coordinated of the 3 EMA coils attached to the tongue. Once this contribution is estimated and removed, the parameters TB and TD are defined as the two first PCs of the joint movement of tongue dorsum and back. A linear regression between the TB and TD on one hand and the tongue tip coils on the other hand provides a residual movement of the tongue, freed from the contribution of the jaw, the tongue dorsum and the tongue back. The TT parameter is finally defined as the first PC of this residual movement. A similar procedure is used for extracting the LP and LH lip parameters and corresponding values for both datasets. For the BY2014 corpus, the VL parameter is simply defined as the first PC of the EMA coils attached to the velum. In summary, at the end of this guided PCA analysis, we have a linear transformation to go from a vector of EMA parameters y to an articulatory vector a = [JH, TB, TD, TT, LP, LH] (for the PB2007 dataset) or a = [JH, TB, TD, TT, LP, LH, VL] for the BY2014 dataset, and vice versa. For convenience in the following, we denote by a(x) the articulatory vector corresponding to the cepstral vector x. Because this set of parameters is reduced in size compared to 1 available online at http://doi.org/10.5281/zenodo.154083 EMA parameters, the articulatory information is "compressed" into a low-dimensional vector, which is appropriate for our later application of an articulatory constraint on the VAE latent space (which is also expected to be of low-dimension).

The VAE model

The seminal VAE model introduced in [START_REF] Kingma | Auto-encoding variational Bayes[END_REF][START_REF] Rezende | Stochastic backpropagation and approximate inference in deep generative models[END_REF] is defined by:

p θ (x, z) = p θ (x|z)p(z), (1)
where p(z), the prior distribution of the latent vector z, is a multivariate standard Gaussian distribution, p θ (x|z) is the (conditional) likelihood function of the observed variable x, and the dimension L of z is (possibly much) lower than the dimension F of x. The parameters of p θ (x|z) are provided by a deep neural network (DNN), called the decoder network, that takes z as input. θ represents the parameters of this decoder network (e.g., the weights and biases of a multi-layer perceptron). In the present work, p θ (x|z) is a conditional Gaussian distribution with diagonal covariance matrix.

Because the relationship between z and x is highly nonlinear, the posterior distribution p θ (z|x) is not analytically tractable. It is thus approximated with a parametric variational distribution q φ (z|x), a.k.a. the inference model, whose parameters are provided by another DNN (called the encoder network, with weights φ and input x). A usual choice, that we follow here, is to set q φ (z|x) as a conditonal Gaussian distribution with diagonal covariance matrix. The parameters {θ, φ} are then jointly estimated by maximizing a lower bound of the data log-likelihood function, called the Variational Lower Bound (VLB), given by (for one single data vector):

L(φ, θ, x) = E q φ (z|x) log p θ (x|z) -DKL q φ (z|x) p(z) , (2)
and evaluated on a training dataset (DKL denotes the Kullback-Leibler divergence). The left term of the VLB represents the reconstruction accuracy of the encoding-decoding process and the right term is a regularization term that ensures some degree of "disentanglement" of the latent vector entries [START_REF] Kingma | Auto-encoding variational Bayes[END_REF]. Maximization of the VLB is done by combining stochastic gradient descent with sampling techniques.

The articulatory-regularised VAE (AR-VAE)

In the present work, each vector x is a vector of Bark-scale cepstral coefficients, of dimension 18, extracted from the audio signal as described in Section 2.1. The dimension of z will be specified later. To force the latent space of the VAE to fit the articulatory space, we added a third term to the above VLB using the same regularization technique as in [START_REF] Roche | Make that sound more metallic: Towards a perceptually relevant control of the timbre of synthesizer sounds using a variational autoencoder[END_REF] (itself inspired from [START_REF] Esling | Generative timbre spaces with variational audio synthesis[END_REF]):

L(φ, θ, x) = E q φ (z|x) log p θ (x|z) -DKL q φ (z|x) p(z) + α E q φ (z|x) R(z, a(x)) . (3)
The new regularization term R(z, a(x)) ensures that for each speech frame the first entries of the latent vector z remain close to the corresponding entries in the vector of articulatory parameters a(x) defined in Section 2.2. In our experiments, we implemented this regularization term with the mean squared error (MSE): R z, a(x)

= z1:N -a(x) 2 , (4)
where z1:N denotes the subvector made of the N first latent values, with N = 6 or 7 depending on the dataset. This term can be interpreted in statistical modeling terms as an additional Gaussian prior on z1:N with mean vector a(x) and an arbitrary fixed variance. In practice, the two expectations in (3) are replaced with estimates based on Monte Carlo sampling of z (using the well-known reparameterization trick, just as in the seminal VAE [START_REF] Kingma | Auto-encoding variational Bayes[END_REF]). Finally, α is a weighting factor monitoring the weight of the articulatory regularization term, and that will be varied in our experiments.

Implementation

We implemented the proposed articulatory-regularized VAE model with the following architecture: The encoder was composed of 4 fully connected hidden layers (256, 128, 64 and 32 neurons) and the decoder had the same, but reversed, composition. The size of the latent space was 12 (i.e., the size of the output layer of the encoder) when the model was trained on the PB2007 corpus (including 6 articulatory-regularized dimensions), and it was 14 when the model was trained on the BY2014 corpus (including 7 articulatory-regularized dimensions). Note that half of the z entries are articulatoryconstrained, hence they are forced to encode the information in cepstral vectors that is strongly correlated to the articulatory parameters, and the other half are let free to encode "everything else" (e.g., speech source information). The hyperbolic tangent activation function was used for each hidden layer. Model training was done using backpropagation with Adam optimizer, on mini-batches of 32 observations (pairs of x and a(x) vectors). For each experience, the datasets were randomly partitioned with 80% of the data used for training and the remaining 20% used for testing. The implementation was done using the PyTorch toolkit [START_REF] Paszke | Pytorch: An imperative style, high-performance deep learning library[END_REF].

Experiments

Model learning speed and accuracy

We first tested if the introduction of articulatory constraints could speed up the training process. To that purpose, for each of the two datasets, and for each value of α taken in {0, 0.1, 0.25, 0.5, 1} we trained 10 AR-VAE models (with a different initialization each time) during 60 epochs (note that an AR-VAE with α = 0 is equivalent to a conventional VAE). At each epoch, we computed the reconstruction error defined as the MSE between the reconstructed and true cepstral coefficients, on the test set. For each value of α (and for each dataset), we finally built a smooth version of the learning curve by averaging the reconstruction loss on the test set, over the 10 models. These learning curves are presented in Figure 2a. First, we observe that almost all AR-VAEs converge faster than the conventional VAEs (i.e. the blue dashed line is almost always above the other lines). Then, as summarized in Figure 2b, the best final performance is obtained with the proposed AR-VAE on both datasets (i.e. with α = 1 for PB2007 and with α = 0.25 for BY2014). Therefore, adding articulatory constraints does improve representation learning, both in terms of convergence speed and accuracy.

Robustness to noise

We then tested the performance of the proposed AR-VAE on a speech denoising task. To that purpose, a babble noise was added to each audio speech signal with different signal-to-noise ratios (SNR) (no noise, 10dB, 5dB and 0dB). Sequences of acoustic feature vectors (i.e. 18 Bark-scale cepstral coeffi- cients) were extracted from the noisy audio signals with the same method used previously. For each dataset, both VAE and AR-VAE were trained to reconstruct the non-noisy version of each acoustic feature vector from its noisy counterpart. For the AR-VAE, we first compared different values of the α parameter for this denoising task. For concision, we report here only the results with α = 1 which provided the best performance among the tested values. As for the first experiment, we trained 10 different VAEs/AR-VAEs (with a different initialization each time) and averaged the results over the 10 runs. The reconstruction error on the test dataset is shown in Figure 3. These results show that the proposed AR-VAE outperforms the conventional VAE on the denoising task, for all considered SNR. The performance difference is more pronounced for lower noise levels.

Since the absolute value of the reconstruction loss (which is in an arbitrary unit) is difficult to interpret, we then conducted further evaluations to assess the quality of the denoised speech. First, we evaluate its phonetic content. To that purpose, for each sentence of the test set, and for each considered SNR, we re-synthesized a speech signal using the LPC- Net neural vocoder fed by the cepstral coefficients reconstructed by the VAE/AR-VAE, together with the original pitch parameters (period and correlation, extracted from the clean speech sound). 2 The resulting speech signals were sent to a Hidden Markov Model (HMM) based phonetic decoder, trained on the original (clean) speech signals of the training set (left-to-right 3 emitting states context-independant HMM-GMM, trained using the HTK toolkit and a standard procedure, no language model used). The decoding accuracy (which takes into account insertion and deletion errors) are presented in Figure 4. Again, the AR-VAE outperforms the VAE, by a large margin (up to 10%) when processing clean speech, and by a smaller one when processing noisy speech.

Finally, we assessed the perceptive quality of the reconstructed speech signal using a MUSHRA test during which participants had to rank a set of audio stimuli by their similarity with a reference sound on a scale from 0 to 100 [START_REF] Itu | Method for the subjective assessment of intermediate quality level of audio systems[END_REF]. We first randomly selected 20 short sentences from the BY2014 corpus (preferred to the PB2007 corpus because of the presence of data on the velum). For each sentence, we generated 6 audio stimuli: a low anchor built by adding babble noise to the original audio speech signal with an SNR of 0dB and re-synthesized (i.e. vocoded) with LPCNet, a hidden reference built by resynthesizing the original signal with LPCNet, a third stimulus built by first encoding-decoding the original signal either with the conventional VAE or with the proposed AR-VAE, and then 2 Several sound examples are available at https://georges. ma/p/ar-vae synthesizing an audio signal with LPCNet, and four other stimuli built following the same principle but after having first added noise to the original signal with three levels of SNR (10dB, 5dB and 0dB). We recruited 23 native French speakers online via the Prolific Academic platform [START_REF] Palan | Prolific.ac-a subject pool for online experiments[END_REF]. Results are reported in Figure 5. To assess the statistical significance of the difference between the MUSHRA scores, we first conducted a Kruskal-Wallis ranksum test which showed a significant effect of the SNR factor (p < 0.05). Then a post-hoc Dunn test validated a statistically significant increase of performance from VAE to AR-VAE for clean audio (p < 0.001) and for noisy audio with SNR = 10dB, and showed no significant difference between the two models for SNR = 5dB and SNR = 0dB (i.e. very noisy inputs).

Discussion and perspectives

The two experiments reported in Section 3 suggest that articulatory constraints improve the learning of speech representations in a VAE. This study opens interesting perspectives for assessing the combined role of articulatory knowledge and auditory processes in the elaboration of internal representations of speech signals. While the efficiency of such articulatoryconstrained VAE appears clearly in terms of spectrum reconstruction, it remains to explore how the corresponding representations are structured and whether they are able to integrate the concept of articulatory/motor invariance [START_REF] Liberman | Perception of the speech code[END_REF] inside phonetic representations. We will particularly focus on the way articulatory information in the present VAE could improve the representation of plosive place of articulation, known to depend on the availability of articulatory/motor information [START_REF] Barnaud | COSMO SylPhon: A bayesian perceptuo-motor model to assess phonological learning[END_REF].

Another question concerns the way articulatory regularization provided by the articulatory data available for a given speaker could enable this speaker to better process the speech utterances of other speakers. For this aim, we will explore how the regularized VAE performs in a denoising experiment involving multiple speakers. We will also study other VAE architectures in which articulatory-acoustic data for the speaking agent and acoustic-only data for other agents could be learnt together in articulatory-constrained VAE variants.

Finally, the precise developmental schedule along which a child develops her production and perception skills and learns the sounds of her language and the corresponding articulatory trajectories will shed interesting light on some algorithmic choices that should be made in further developments of such articulatory/motor constrained acoustic VAEs.

Conclusion

In this paper, we show how articulatory knowledge can help construct internal representations of auditory speech stimuli, by applying an articulatory regularization to VAEs encoding speech features, enforcing them to adopt mixed articulatoryacoustic representations in their latent space. The additional term in the training loss function enforcing a part of the latent space to follow articulatory parameters appears to improve learning efficiency, both in terms of learning speed and accuracy, and also improve reconstruction performance in a denoising VAE.

Acknowledgement

This work has been partially supported by MIAI @ Grenoble Alpes (ANR-19-P3IA-0003). The authors would like to thank Pierre Badin and Julien Diard for fruitful discussions.

Figure 1 :

 1 Figure 1: Schematic view of the proposed articulatoryregularized variational autoencoder.

Figure 2 :

 2 Figure 2: a.: Evolution of the reconstruction loss on the test set during training. For better visualization, each learning curve is fitted by an exponentially decreasing function b.: Final performance after convergence at epoch 40 on the test set.

Figure 3 :

 3 Figure 3: Reconstruction loss (mean ± standard deviation) of the conventional VAE and the proposed AR-VAE on the test set for the speech denoising task.

Figure 4 :

 4 Figure 4: Accuracy (mean ± standard deviation) of an HMMbased phonetic decoder when processing speech signals denoised by the conventional VAE and the proposed AR-VAE (with α = 1).

Figure 5 :

 5 Figure 5: MUSHRA scores obtained for each level of noise and for the conventional VAE (α = 0) and the proposed AR-VAE (with α = 1). For the sake of clarity, we omit the anchor and reference scores. *** and * are significant (p < 0.001 and p < 0.05), and NS are non-significant differences.


Dr Maurizio Vignolo
email: maurizio.vignolo@spin.cnr.it

Dr Gianmarco Bovone

Marco Capra

Federico Loria

Cristina Bernini

Dr Bertrand Vileno

Dr Loïc Mager

Dr Bertrand Donnio

Dr Mircea V Rastei

Dr Jean-Louis Gallani
email: gallani@ipcms.unistra.fr

Dr Jean-Paul Kappler

Magnetism: Another Idiosyncrasy of Boron?

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Boron is a peculiar element. It is not a product of nucleosynthesis unlike most elements,1,2 it cannot exist in water as an ion,3 it is considered essential to life even though its role remains unclear,4,5 it possesses a great many allotropes.6 Boron and its derivatives have found countless uses throughout history, from the embalming of mummies to the doping of semi-conductors, through the fabrication of glassware and neutron shielding. There is even a city named Boron in California, the site being the world's largest source of borax. Not so many elements can boast being the eponym of a city. Boron is diamagnetic in its bulk form but is ubiquitous in the NdFeB magnets found nowadays in smartphones, generators and hard drives.7 Calculations predict that 2-D boron, "borophene", could become superconducting below 20K.8,9 Even though there are numerous studies reporting the influence of boron doping/alloying on the magnetic properties of a variety of materials,10 there seems to be very few dealing with the magnetic properties of pure Boron,11,12,13,14 in particular we failed to find a recent one or one dealing with nanoparticles.

We have examined the magnetic properties of four batches of particulate Boron: two commercial samples and two lab-made samples. Surprisingly, all samples displayed soft ferromagnetism at room temperature.

Results and Discussion

We synthesized (samples BL8 and BL14) and purchased (samples PVZ and HCS) Boron particles in order to prepare MgB2 which is then subsequently used for the fabrication of superconducting wires and tapes. When used in this context, it has been shown that adding Carbon to the materials increases the upper critical field Hc2 without loosing too much on the critical temperature Tc. Carbon atoms and clusters are thought to act as pinning centers for the flux lines. The samples involved in this study therefore have a carbon content ranging from 0.8wt.% to 6.0wt.%. See Supplementary information (S1, S2, S3) for details on the synthesis, composition and other information.

We have performed SQUID magnetometry on the four different samples in powder form. Figure 1 displays the raw magnetization curves of all samples, at 300K. The central parts ("minor cycles") are shown in Figure 2 in order to give more details on remnant magnetization and coercive field. Depending on sample history the first magnetization curve is not always visible but since the samples are not magnetic in the traditional sense, i.e. with domains and walls, the first magnetization curves bear no particular signifiance. Figure 1. Magnetization curves of the samples, at 300K. No correction for the diamagnetism of the sample holder or dotriacontane were applied (i.e. raw data)

The magnetic response at room temperature is essentially diamagnetic but soft ferromagnetism is obviously present, as can be clearly seen in the low-field region of the curves. A small remnant magnetization and a modest coercivity are visible for all samples. Boron electronic structure is 1s22s22p1, it is a semi-conductor with a bandgap ranging between ca. 0.60eV to 2.6eV, depending on the allotrope. It conducts electricity at high temperature but is insulating at low temperature. Not being a paramagnetic element and lacking conduction electrons, pure Boron cannot sustain regular para-or ferro-magnetism in its bulk form. It is therefore rather surprising to observe a deviation from diamagnetism. This being said, one has to observe that many other elements or materials seem to "become magnetic" when prepared in the form of nanoparticles (e.g. Au, Ag, Cu,…), we shall discuss this point more hereafter. We have further characterized the samples by recording the behavior of the magnetization upon cooling and field-cooled / zero-field-cooled (FC/ZFC) magnetization curves. A representative example is given in figures S4 and S5, all samples displayed very similar behaviors.

For all samples, the curves are featureless, showing only a monotonous increase of the magnetic moment upon decreasing the temperature. The magnetic susceptibilities do not follow a proper Curie or Curie-Weiss law, as seen in figure S6, though some linearity can be found over limited portions of the temperature range. More, the ZFC curves do not have the characteristic form usually observed with magnetic nanoparticles, there is no evidence at all of a blocking temperature. These measurements imply that the observed magnetism does not stem from para-or ferro-magnetic impurities. This is in contradiction with the measurements of reference 14 where the authors not only observe a monotonous non-saturating magnetic moment as a function of the applied field, and a susceptibility which follows a proper Curie law. Like ours their samples were carbon doped but, contrary to ours, they were crystalline. A final evidence that the magnetism is not brought by 3d elements is the absence of specific spectral lines in the energy-dispersive x-ray spectroscopy (EDX) spectra, as illustrated in figure S3 (though traces are detected).

Last, magnetization curves were recorded at 4K, they are given in figure S7. At this temperature the diamagnetic contribution becomes dominated by the para-and ferro-magnetic components. Ferromagnetism remains soft, the curves looking very much like paramagnetism Brillouin curves and the opening of the hysteresis cycles being quite modest.

The coercive fields and remnant magnetizations are summarized in Table 1. For all samples the remnant magnetization is equal or larger at low temperature. The behavior of the coercive fields is more puzzling. The coercive field of sample PVZ is larger at 4K -as usually observed in magnetic materials-but samples BL8, BL14 and HCS all display a surprising increase of their coercive field with temperature. We are tempted to ascribe this to an increased number of electrons in the conduction band when the temperature is risen. Even though ubiquitous in modern days as part of NdFeB magnets, Boron is not a material commonly encountered in magnetism. There have been many studies devoted to borides but boron itself has not been much investigated. This is probably due to the facts that it is still difficult to prepare reasonably pure Boron samples and that there are at least 14 known allotropes for crystalline Boron, each with a peculiar electronic structure. A glimpse on the complexity of Boron physical properties can be obtained in the book edited by V.I. Matkovich.15 A paramagnetic susceptibility has been observed in amorphous Boron above room temperature and been ascribed to thermal excitation of localized centres.12 Crystalline -rhombohedral Boron has been found diamagnetic below room temperature by Matyáš.11 Tsiskarishvili et al. observed a paramagnetic ESR signal between 100 and 450K, which they ascribe to the presence of holes captured on trapping levels.13

Magnetic materials usually comprise 3d and/or 4f metals such as Fe, Ni, Co, Sm, Gd, etc. but more original magnetic alloys exist which do not make use of paramagnetic elements, such as TiBe2 or ZrZn2. Nanoparticles of Au, Ag, Cu have also been found to deviate from the diamagnetic nature of the elements bulk form,16,17 with the origin of the magnetism still being debated. Beyond systems which are metallic and made from paramagnetic elements, magnetism in materials can also arise from a variety of reasons which could be dubbed as extrinsic. Room-temperature ex nihilo ferromagnetism has been observed in CdSe nanoparticles18 and attributed to the formation of holes in the material due to the electron transfer caused by the bonding to the capping ligands. Magnetic moments were of the order of a few 10-2emu/gram at room temperature and coercive fields lay around ~100G between room temperature and 4K. A similar observation has been reported for ZnO nanoparticles, with the same explanation put forth. 19 Moments are weaker by at least one order of magnitude, with no or a very small opening of the hysteresis cycle. All these materials are semiconductors. Pure sodium chloride NaCl, which is ionic and insulating, has also been found to display some ferromagnetism at room temperature, the explanation offered being that surface Cl deficiencies bear a magnetic moment and neighboring vacancies couple ferromagnetically.20 Along this line, since massive Boron is insulating and diamagnetic it seems reasonable to correlate the appearance of magnetism with either a surface effect or the size effect which occurs for most materials when prepared in nanoparticle form. Regarding the latter, suffice it to look at the original optical properties displayed by semiconductors such as CdTe or PbSe when they form so-called "quantum dots". Still, given the rather large size of our Boron particles, more micro than nano, this size effect is probably not at the origin of the observed magnetism. (Figure S1 gives representative SEM images of the samples.)

Three samples, BL8, BL14 and HCS have a rather ill-defined morphology, with jagged particles, looking like ground glass. On the contrary sample PVZ turns out to be much more regular, with rather spherical particles, even if the size dispersion looks rather large. Interestingly, this sample has the second highest Boron content (94.2%) and it also displays the most ferromagnetic-like curves, even if its remnant magnetization is the lowest. Its coercive field reaches a value of 1000Oe at 4K. We find it tempting to correlate the reinforcement of magnetism (in the sense of more ferromagnetic-like) to the regular morphology of the particles and the better purity.

Given the nature, size and morphology of the particles we envision two possible origins for the magnetism: giant orbital paramagnetism or oxygen vacancies, both relevant in the presence of bandgaps.

Giant orbital paramagnetism, a peculiar form of magnetism not based on interacting spins, also called "d-zero magnetism" by J.M.D. Coey has been invoked to explain the magnetic properties of porous alumina.21,22 It originates in the influence of zero-point fluctuations of the vacuum electromagnetic field on bound electrons which stabilizes a collective ground-state energy, leading to novel effects such as ferromagnetism at room temperature for quasi-two-dimensional systems. Still, being field-induced, it is not a rigorous ferromagnetism. The effect is most likely to be observed at the surface of materials with low electron density and high dielectric constant. 23 The coherent orbital character of the dilute electronic assembly is almost temperature independent since it is a ground state. While it is difficult to totally rule out the possibility that some giant orbital paramagnetism be present, our results are nevertheless at odds with the findings of Coey since, contrary to his, our magnetization curves at 4K and 300K do not superimpose.24

Let us now consider the other possibility, defects and vacancies. Oxygen and Carbon are present in all our samples so some oxides and/or carbides are possibly present. Defects and vacancies can give rise to some magnetism, as it has been observed for e.g. Cerium oxide. 25 If F-centers (oxygen defects with two trapped electrons) and F+ centers (oxygen defects with one trapped electron) are indeed present in significant amounts, the samples should exhibit some luminescence in the visible spectrum. We could not detect luminescence in the samples examined with a sensitive spectrofluorimeter.

F-centers usually are paramagnetic. A simple test is to perform electron spin resonance (ESR) measurements. As for the luminescence, all samples exhibit an ESR signal, as seen in figure 3. Signals are actually quite strong. We cannot, of course, unequivocally assign the ESR response to the sole Fcenters.

Interestingly, each sample has a specific lineshape. While HCS and PVZ sample exhibit lines which could be described as "simple", BL8 and BL14 possess more complex ones. BL8 has a rather broad lineshape, BL14 clearly displays two superimposed responses. A broad lineshape usually implies that some magnetic coupling between sites is present. It is therefore surprising that HCS and BL8 samples have quite different lineshapes when their magnetic behaviour is quite similar (see figs. Magnetically ordered clusters of electron spins localized at oxygen vacancies would be expected to behave super-paramagnetically whereas our FC-ZFC curves do not evidence any blocking temperature. It is therefore not clear why some measurements would imply a certain amount of coupling between magnetic centers whereas other would not.

In one ESR study on amorphous Boron, Tsiskarishvili et al.13 report an ESR study of amorphous Boron. Just like ours, their samples had a noticeable amount of Oxygen (2%) and Carbon (figure not given). They observe in particular an ESR signal comprising two components having nearly the same g factor. No picture of the lineshape is provided nor the values of g but one could probably find similarities with our lineshapes, especially that of sample BL14. Their conclusion is that the magnetism is intrinsic and results from holes trapped on very shallow trapping levels just above the valence band. In another study14 on crystalline β-Boron they report that two ESR signals having g=2.00 and g=4.28 were observed, the latter being ascribed to Fe3+ impurities. We did not observe a signal corresponding to g=4.28. The role of Carbon doping is unclear but it is suggested that Carbon atoms could act as donors substituting Boron atoms in the lattice,14 even though no clear dependence between the magnetism and the Carbon content could be found.

The question of how magnetic centers diluted in an insulating or a large bandgap material can become coupled is not a simple one. Given the weakness of the moments and the average distance between them, dipolar coupling can most certainly be ruled out. Direct or indirect magnetic coupling mechanisms (i.e. electron mediated) between magnetic moments are not at all evident for the stabilization of the long-range ferromagnetic order since Boron is insulating. Ferromagnetism in insulators has already been observed in materials such as MgO,22 ZnO26 or HfO2,27 to name but a few. In these undoped materials, the magnetic centers are generally vacancies of the metallic element. The ferromagnetic coupling between magnetic centers is then mediated by the 2p orbitals of oxygen. In the case of Boron, which is 2p1, such a coupling can probably be ruled out. The only possibility left is that impurities create a conduction band within the Boron bandgap. The question of impurities conduction band is well known28 and, for example, doping the aforementioned oxides with metals or other impurities such as N or C is known to create localized energy bands that can then either sustain carriers mobility or facilitate the coupling with the host conduction band. 29 We therefore propose that a similar process is at work in the Boron particles, with either Mg, O or C acting as impurities, simultaneously creating magnetic centers and enabling their ferromagnetic coupling.

Conclusion

We have studied the magnetic properties of Boron particles and observed soft ferromagnetism from 4K up to 300K. Samples synthesized in different places with different methods all exhibit similar behaviors. We suggest that the magnetism does not originate on Boron itself but is related to impurities and dopants which are present in the material while in the same time a surface effect could also play a role in the magnetic behavior.

Experimental Section

Materials and methods

Boron particles synthesis : The PVZ nanoB (98.5 wt.% in purity) sample, produced by diborane thermal decomposition, was purchased from Pavezyum Kimya, Advanced Chemicals, Instanbul -Turkey. 30 The HCS micrometric B powder (grade I: min. 95 wt. % in purity ), prepared by magnesiothermal reduction, was acquired from H. C. Starck GmbH.31 Instead, BL8 and BL14 were prepared at CNR-SPIN lab of Genoa (Italy) following the European Patent described in references 32, 33, 34. Briefly, the B nanostructuration process can be summarized as follows. In order to obtain pure nanoB, B2O3 (≥ 98% in purity, purchased from Sigma-Aldrich, now Merck) was solubilized in hot deionized water and then atomized into liquid nitrogen (LN2). The solid phase (H2O-B2O3) was freeze-dried to sublimate water and the so-obtained nanoB2O3 was reduced to elemental nanoB following the magnesiothermal reaction of the Moissan's Process. The same procedure was adopted to prepare BL14, in this case a nominal 6 wt. % hemoglobin was dissolved in H2O together the B2O3, more and newer details are provided in reference 35, in particular from superconducting point of view.

Electron Paramagnetic Resonance (EPR) investigations: Continuous-wave EPR investigations were performed at room temperature using EMXplus X-band spectrometer (Bruker Biospin GmbH, Germany) equipped with a high-sensitivity resonator (4119HS-W1, Bruker). This setup was used to record conventional field-swept spectra of each powder of nanoparticles (ca. 50 mg) introduced into 4 mm outer diameter quartz tubes (Wilmad-Labglass). The principal experimental parameters values were a modulation amplitude of 2G, a microwave power of ca. 1.8 mW, a time constant of ca. 40 ms and a conversion time of ca. 150 ms. The g factor was calibrated using Bruker strong pitch standard of known g factor 2.0028.

SQUID magnetometry : Magnetometry has been performed with a Quantum Design MPMS3 magnetometer. The nanoparticles were simply hand-pressed into a standard gelatin container and pure molten dotriacontane wax was poured on top in order to mechanically stabilize the powder. Both gelatin container and dotriacontane were previously magnetically tested in the SQUID and returned only a weak diamagnetic signal (χdia ~ -1.3×10-4emu.g-1). As substracting this diamagnetic contribution did not change much the shape of the curves nor did it affect the discussion, we have chosen not to remove it from our data.

Figure 2 .

 2 Figure 2. Hysteresis cycles of the samples at low fields, at 300K. No corrections for the diamagnetism of the sample holder or dotriacontane were applied (i.e. raw data). Depending on sample history the first magnetization curve is not always visible.

  2 and S7). Sample PVZ, which is close to displaying a ferromagnetic behaviour, also has a simple narrow ESR lineshape. A tentative deconvolution of the ESR lineshapes is given in figureS8.

Figure 3 .

 3 Figure 3. Room temperature experimental EPR spectra (black line) of BL8, BL14, PVZ and HCS Boron nanoparticles, together with respective simulations attempts (red line) (see SI for details on spectral deconvolution).

Table 1 .

 1 Remnant magnetization and coercive field of all samples.

		T = 300K	T = 4K
		Remnant	Coercive	Remnant	Coercive
		magnet.	field (G)	magnet.	field (G)
		(emu/gram)		(emu/gram)
	BL8	3.510 -4	1000	3.410 -4	42
	BL14	7.910 -4	700	1.810 -3	75
	PVZ	7.310 -6	350	1.110 -3	1030
	HCS	1.610 -4	320	1.910 -4	28

Acknowledgements

We thank J. Faerber and C. Leuvrey for their help with the EDX measurements. Funding from Agence Nationale de la Recherche is acknowledged, grants OH-RISQUE SMARAGD (14 OHRI 0008 01) and BLANC METABIP (12 BS10 00301). Keywords: Boron • magnetism • particle

Supplementary information