Charles Bielle

François Ducray

Charles Mokhtari

Charles Dehais

Homa Adle-Biassette

Catherine Carpentier

Charles Chanut

Marc Polivka

Sylvie Poggioli

Shai Rosenberg

Franck Bielle

Karima Mokhtari

Caroline Dehais

Homa Adle- Biassette

Anaïs Chanut

Shaï Rosenberg

Marine Giry

Yannick Marie

Charles Duyckaerts

Marc Sanson

Pola Network

Dominique Figarella-Branger

Ahmed Idbaih
email: ahmed.idbaih@gmail.com

Christine Desenclos

Henri Sevestre

Angers

Philippe Menei

Audrey Rousseau

; Besançon

Joel Godard

Gabriel Viennet

Antoine Carpentier

; Bordeaux

Sandrine Eimer

Hugues Loiseau

; Brest

Phong Dam-Hieu

Isabelle Quintin-Roué

Jean-Sebastien Guillamo

Emmanuelle Lechapt-Zalcman

Jean-Louis Kemeny

Toufik Khallil

; Clichy

Dominique Cazals-Hatem

Thierry Faillot

Pomone Ioana Carpiuc

Richard ; Créteil

Caroline Le Guerinel

; Colmar

Claude Gaultier

Marie-Christine Tortel

; Dijon

Marie-Hélène Aubriot-Lorton

François Ghiringhelli

; Kremlin-Bicêtre

Clovis Adam

Fabrice Parker

; Lille

Claude-Alain Maurage

Carole Ramirez

; Limoges

Edouard Marcel Gueye

François Labrousse

; Lyon

Anne Jouvet

Olivier Chinot

; Montpellier

Luc Bauchet

Valérie Rigau

Dr Nancy : Patrick Beauchesne

Guillaume Gauchotte

; Nantes

Mario Campone

Delphine Loussouarn

Denys Fontaine

Fanny Vandenbos

; Orléans

Claire Blechet

Mélanie Fesneau

Paris : Jean

Yves Delattre

Selma Elouadhani-Hamdi

Damien Ricard

; Poitiers

Delphine Larrieu-Ciron

Pierre- Marie Levillain

; Reims

Philippe Colin

Marie-Danièle Diebold

; Rennes

Danchristian Chiforeanu

Elodie Vauléon

; Rouen

Olivier Langlois

Saint- Annie Laquerrière

Marie Janette

Motsuo Fotso

Michel Peoc'h ;

Saint-Pierre De La

Marie Andraud

Marie-Pierre Chenard

Georges Noel

; Suresnes

Dr Stéphane Gaillard

Elisabeth Cohen-Moyal

Emmanuelle Uro

Tumor cells with neuronal intermediate progenitor features define a subgroup of 1p/19q co-deleted anaplastic gliomas

Keywords: Anaplastic oligodendroglioma, 1p/19q co-deletion, neuronal intermediate progenitor, embryonic subventricular zone

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

Anaplastic diffuse gliomas form a group of primary malignant brain tumors with a significant clinical, radiological, histological and molecular intertumor heterogeneity. Historically and in WHO 2007, the histological diagnosis of these tumors was defined by morphological similarities between tumor glial cells and normal glial cells [START_REF] Louis | WHO classification of tumours of the central nervous system. 4ème Edition[END_REF]: anaplastic astrocytoma(A3)/glioblastoma(GBM), anaplastic oligodendroglioma (OD3) or anaplastic oligoastrocytoma(OA3) presenting astrocyte-like cells, oligodendrocyte-like tumor cells, or a mixed phenotype respectively. Because key mutations defining different oncogenic molecular pathways with high clinical relevance were identified, these tumors are now classified by WHO 2016 according to an integrated histomolecular diagnosis combining histological information (demonstration of diffuse glioma and grading criteria) and molecular information (presence or absence of key molecular alterations) [START_REF] Alentorn | Oligodendrogliomas: new insights from the genetics and perspectives[END_REF][START_REF] Labussiere | All the 1p19q codeleted gliomas are mutated on IDH1 or IDH2[END_REF][START_REF] Louis | WHO classification of tumours of the central nervous system[END_REF][START_REF] Sahm | Farewell to oligoastrocytoma: in situ molecular genetics favor classification as either oligodendroglioma or astrocytoma[END_REF].

The WHO 2016 integrated diagnosis of anaplastic oligodendroglioma IDH-mutant and 1p/19q codeleted (O3 id ) is a diffuse glioma with chromosome arms 1p/19q co-deletion, IDH (i.e.

IDH1 or IDH2 genes) mutation and one or more criteria of anaplasia (high mitotic activity, microvascular proliferation, and necrosis) [START_REF] Louis | WHO classification of tumours of the central nervous system[END_REF]. O3 id exhibit better prognosis and better chemosensitivity compared to other anaplastic diffuse gliomas [START_REF] Cairncross | Phase III trial of chemoradiotherapy for anaplastic oligodendroglioma: long-term results of RTOG 9402[END_REF][START_REF] Van Den Bent | Adjuvant procarbazine, lomustine, and vincristine chemotherapy in newly diagnosed anaplastic oligodendroglioma: longterm follow-up of EORTC brain tumor group study 26951[END_REF]. However, they ineluctably relapse and become resistant to anti-tumor treatments similarly to the other diffuse gliomas. O3 id frequently present the histological diagnosis of OD3 or OA3, express the "proneural" tumor signature [START_REF] Ducray | Anaplastic oligodendrogliomas with 1p19q codeletion have a proneural gene expression profile[END_REF] but the cell phenotype of this histomolecular entity is poorly understood.

Several recent works on human tumors and murine models of gliomas showed that oligodendroglial precursor cells (OPC) are the cells of origin and/or the tumor propagating cells in gliomas with oligodendroglial morphology [START_REF] Liu | Mosaic Analysis with Double Markers Reveals Tumor Cell of Origin in Glioma[END_REF][START_REF] Persson | Non-stem cell origin for oligodendroglioma[END_REF]. In contrast, tumor cells with neural stem cells (NSC) phenotype were rarely found in such tumors [START_REF] Beier | CD133 expression and cancer stem cells predict prognosis in high-grade oligodendroglial tumors[END_REF].

In embryo, neural stem cells (NSC) produce, first, neuronal precursors directly or via neuronal intermediate progenitors (NIP). After the glial switch, NSC become gliogenic progenitors and produce: (i) oligodendrocytes via OPC and, (ii) later, astrocytes via astrocyte precursors cells (APC) [START_REF] Kriegstein | The glial nature of embryonic and adult neural stem cells[END_REF]. Gene expression is highly dynamic during specification and differentiation of these lineages as showed by single cell analysis [START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF]. In the early neuronal lineage, the transcription factor INSM1 promotes neuronal fate and expansion of NIP and is downregulated in more differentiated neuronal cells [START_REF] Farkas | Insulinoma-associated 1 has a panneurogenic role and promotes the generation and expansion of basal progenitors in the developing mouse neocortex[END_REF][START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF]. ELAVL2 (embryonic lethal abnormal visual system (ELAV)-like neuron-specific RNA binding protein 2) is highly expressed in NIP [START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF] and promotes neuronal differentiation and mitotic arrest by regulation of the traduction of mRNA [START_REF] Akamatsu | Mammalian ELAV-like neuronal RNA-binding proteins HuB and HuC promote neuronal development in both the central and the peripheral nervous systems[END_REF].

The transcription factor SOX11 is involved neuronal differentiation from NIP to mature neuron [START_REF] Bergsland | Sequentially acting Sox transcription factors in neural lineage development[END_REF][START_REF] Chen | Orchestration of Neuronal Differentiation and Progenitor Pool Expansion in the Developing Cortex by SoxC Genes[END_REF][START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF]. We thus decided to investigate the phenotype of O3 id tumor cells in light of cell types reported during CNS development.

Material and Methods

Patients and tumors selection

Two cohorts of adult supratentorial high grade diffuse gliomas were established retrospectively:

(i) a training cohort from the Hôpitaux Universitaires La Pitié-Salpêtrière, and (ii) a validation cohort from POLA -prise en charge des tumeurs oligodendrogliales anaplasiques-network cohort. The training cohort included 33 newly-diagnosed cases: (i) 33 with available tumor tissue for immunohistochemistry, (ii) 23 with available transcriptome profiling data and (iii) 21 with enough tumor tissue for targeted expression profiling using RT-PCR. Six adult non tumor brain tissue samples (from epilepsy surgery) were used as non-tumor control. Informed consents of patients were obtained for review of medical records for researches purposes and molecular analysis of biological tissues. The POLA network validation cohort included 94 cases with available transcriptome profiling data previously reported [START_REF] Reyes-Botero | Contrast enhancement in 1p/19q-codeleted anaplastic oligodendrogliomas is associated with 9p loss, genomic instability, and angiogenic gene expression[END_REF]. Human fetuses without any neuropathological alterations were collected after legal abortion or spontaneous death. All procedures were approved by the ethics committee (Agence de Biomédecine; approval number: PFS12-0011).

Pathology, Genetic and Transcriptomic analysis

Tumors of the training cohort were reviewed by two pathologists (FB and KM). Histological characteristics of tumors of the validation cohort were established during a central review described in a previous report [START_REF] Reyes-Botero | Contrast enhancement in 1p/19q-codeleted anaplastic oligodendrogliomas is associated with 9p loss, genomic instability, and angiogenic gene expression[END_REF]. Only histological diagnoses of OD3 or OA3 which are further called anaplastic oligodendroglial tumors (AOT) were selected for further studies. IDH1/2 mutational and chromosome arms 1p/19q statuses were determined as previously described [START_REF] Ducray | Anaplastic oligodendrogliomas with 1p19q codeletion have a proneural gene expression profile[END_REF][START_REF] Houillier | IDH1 or IDH2 mutations predict longer survival and response to temozolomide in low-grade gliomas[END_REF]. Tumors were then classified according to the WHO 2016 integrated diagnoses of (i) anaplastic oligodendroglioma, IDH-mutant and 1p/19q co-deleted (O3 id ), anaplastic astrocytoma IDH-mutant, glioblastoma IDH-mutant, glioblastoma IDH-wildtype and anaplastic oligoastrocytoma, NOS. The three last tumor types were gathered in a group termed "non 1p/19q codeleted AOT"). The RNA extraction and the gene expression profiling upon Genechip Human Genome U133 Plus 2.0 Expression array (Affymetrix, CA) were performed as previously described [START_REF] Ducray | Anaplastic oligodendrogliomas with 1p19q codeletion have a proneural gene expression profile[END_REF].

Reverse Transcription-PCR (RT-PCR)

Quantitative gene expression measurements, at mRNA level, were performed for 24 genes ( 22genes of interest and 2 control genes) using the « UPL assay design center » (Roche Applied Science®) (Supplemental Table 1). RT-PCR was performed as described previously [START_REF] Alentorn | Prevalence, clinico-pathological value, and co-occurrence of PDGFRA abnormalities in diffuse gliomas[END_REF].

Immunohistochemistry and staining scoring

Tissue sections were cut from formalin-fixed and paraffin-embedded (FFPE) tumor samples.

Sections were deparaffinized and rehydrated. For fluorescent immunolabeling, antigen retrieval was performed using pH=6.0 citrate buffer or pH=8.0 Ethylenediaminetetraacetic acid buffer and microwave heating. After blocking with fetal calf serum, sections were incubated with primary antibodies (Table 1). The following secondary antibodies were used: Alexa 488 Donkey anti-Mouse IgG, Cy3 Donkey anti-Rabbit IgG, Cy3 Donkey anti-Goat IgG (Jackson Immunoresearch Lab., Inc., Baltimore). Nuclei were labelled with 4',6-Diamidino-2-Phenylindole (DAPI).

Fluorescence microscope Axio Imager Z1 (Zeiss®) was used to acquire signal. The fluorescent immunolabeling markers (SOX9, INSM1, and marker of proliferation Ki-67) were quantified by counting single cells. For chromogenic immunolabeling, deparaffinization and immunolabeling of the sections were performed manually or by a fully automated immunohistochemistry system Ventana benchmark XT system® (Roche, Basel, Switzerland) using as chromogen: streptavidinperoxidase complex with diaminobenzidin, alkaline phosphatase with Fast Red (ultraView Universal Alkaline Phosphatase Red Detection Kit, Ventana®) or Vector Blue (Vector®). The chromogenic immunolabeling of markers (INSM1 for Insulinoma-associated 1, NFIA for Nuclear Factor I/A) were quantified by evaluating the ratio of the number of immunopositive cells out of the number of all tumor cells. The ELAVL2 and SOX11 immunolabeling were evaluated by a score ranging from 0 to 400 adapted from Hirsch et al [START_REF] Hirsch | Epidermal growth factor receptor in non-small-cell lung carcinomas: correlation between gene copy number and protein expression and impact on prognosis[END_REF]. The percentage of tumor cells at different staining intensities was determined by visual assessment: Score = (percentage area of weak labelling x 2) + (percentage area of moderate labelling x 3) + (percentage of intense labelling x 4). Micrographs were acquired with Axiocam ICc 1 camera and Axiovision 4.8.2 software (Zeiss®).

Computational biology analysis

Gene signatures of the different CNS cell types observed during development (i.e. lineages from NSC to neurons, oligodendrocytes and astrocytes) were retrieved from the literature (Supplemental Table 2, Fig. 1a) [START_REF] Kriegstein | The glial nature of embryonic and adult neural stem cells[END_REF]. A gene list was retrieved from study of NIP in the cerebral cortex [START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF] and only genes expressed in both subpallium and pallium of mouse embryo were selected to build a forebrain NIP signature. Human genes homologous to murine genes were identified using the software bioDBnet [START_REF] Mudunuri | bioDBnet: the biological database network[END_REF]. Gene Set Enrichment Analysis (GSEA) was performed with the JavaGSEA application using the following parameters: number of permutations = 1000, False Discovery Rate <0.25, permutations of phenotype [START_REF] Mootha | PGC-1alpha-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes[END_REF][START_REF] Subramanian | Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles[END_REF].

Hierarchical clustering was performed using Babelomics 4.3 with Self Organizing Tree Algorithm (SOTA) and correlation coefficient of Spearman [START_REF] Medina | Babelomics: an integrative platform for the analysis of transcriptomics, proteomics and genomic data with advanced functional profiling[END_REF]. As a preliminary step, tumor samples which co-segregate with non-tumor brain were excluded for the following analysis because they were considered as highly contaminated by non-tumor cells.

Statistical analysis

Discrete

Results

O3 id overexpress neurogenesis genes

In order to determine the cell phenotype of O3 id , we compared gene expression of O3 id to non 1p/19q co-deleted AOT (tumors with OD3 or OA3 histological diagnoses that do not fulfill the criteria of integrated diagnosis of O3 id ) in the training series. CNS cell lineage expression signatures obtained from previously reported expression arrays were compared between O3 id (n=13) versus non 1p/19q co-deleted AOT (n=10) using GSEA (Fig. 1a,b; Supplemental Table 3). Although not reaching statistically significant thresholds, the only enrichments observed in O3 id :were: (i) neuronal intermediate progenitor -NIP-, (ii) neuronal precursor, (iii) neuron, and (iv) OPC. By contrast, O3 id showed significant underexpression of gene lists related to NSC, mature oligodendrocytes and astrocytes.

Using quantitative RT-PCR, expression of markers of CNS cell lineages revealed significantly overexpression of Doublecortin (DCX, neuronal precursor marker) and underexpression of Nuclear factor 1 A-type (NFIA, glial marker) in O3 id (n=14) versus nontumor brain samples (n=6). In addition, NFIA was significantly underexpressed in O3 id compared to non 1p/19q co-deleted AOT (n=7) (Supplemental Fig. 1).

In the same line, immunolabeling showed that the ratio of NFIA-positive/total tumor cells was lower in O3 id than in non 1p/19q co-deleted AOT (0.33 versus 0.79 respectively, n O3id =14 and n=19 non 1p/19q co-deleted AOT , p=0.0007, Supplemental Fig. 1).

O3 id share features with embryonic subventricular zone containing NIP NIP are located in the embryonic subventricular zone (eSVZ) which is located between the ventricular zone (VZ) containing the NSC/apical progenitors and the intermediate zone (IZ) containing axonal processes and migrating neuronal precursors (Fig. 1c,d).

O3 id cells were morphologically closer to NIP (at gestational week 19 when corticogenesis is ongoing) than adult oligodendrocytes (Fig. 1e-g). Indeed, similarly to O3 id tumor cells, NIP have round nucleus, clear chromatin, several small nucleoli, and clear perinuclear halo.

O3 id share additional similar features with eSVZ from E15.5 mouse embryo cerebral cortex: (i) a rich anastomotic capillary network with "chicken wire" branching (31, 75) (Fig. 1hi), and (ii) a perinuclear dot expression staining pattern of the neuronal intermediate filament internexin alpha (INA), a positive-marker of neurons and their early precursors (43) and a negative marker of oligodendrocytes (Supplemental Fig. 2).

Finally, the most commonly mutated genes in O3 id are CIC, FUBP1, NOTCH2 and TCF12 [START_REF] Bettegowda | Mutations in CIC and FUBP1 contribute to human oligodendroglioma[END_REF][START_REF] Labreche | TCF12 is mutated in anaplastic oligodendroglioma[END_REF] were reported highly expressed in the eSVZ on mouse embryos in public atlas (Supplemental Fig. 3).

Two subgroups of O3 id were identified based on their expression of NIP genes

A hierarchical clustering of O3 id was thus performed based on genes committing to neurogenesis or to gliogenesis (NIP list and gliogenic progenitor list). Two subgroups of O3 id were identified. The NIP high sugbroup (n=7/13, 54%) contained O3 id exhibiting higher expression of NIP and OPC genes. The other O3 id were considered as the NIP low subgroup (n=6/13, 46%) and showed higher expression of genes associated with gliogenic progenitors, astrocytes and mature oligodendrocytes compared to NIP high subgroup (Fig. 2a,b).

Similarly to the results obtained in the training set, O3 id overexpressed gene lists of the neuronal lineage in the multicentric validation cohort including 73 1p/19q co-deleted AOT and 21 non 1p/19q co-deleted AOT (Supplemental Fig. 4; Supplemental Table 4). A NIP high subgroup (n=27/73, 37%) and a NIP low subgroup (n=46/73, 63%) of O3 id were identified (Supplemental Fig. 5).

NIP high O3 id exhibit proliferating INSM + /SOX9 -tumor cells subpopulation

The following markers addressing different steps of the neuronal lineage were used: (i) INSM1 as a specific marker of NIP in the developing CNS, not expressed in the adult CNS (Supplemental Fig. 6) and which drives NIP specification and expansion [START_REF] De Smaele | An integrated approach identifies Nhlh1 and Insm1 as Sonic Hedgehogregulated genes in developing cerebellum and medulloblastoma[END_REF][START_REF] Farkas | Insulinoma-associated 1 has a panneurogenic role and promotes the generation and expansion of basal progenitors in the developing mouse neocortex[END_REF][START_REF] Lan | IA-1, a new marker for neuroendocrine differentiation in human lung cancer cell lines[END_REF], (ii) ELAVL2 as a marker of NIP promoting mitotic arrest and neuronal differentiation [START_REF] Akamatsu | Mammalian ELAV-like neuronal RNA-binding proteins HuB and HuC promote neuronal development in both the central and the peripheral nervous systems[END_REF][START_REF] Kawaguchi | Single-cell gene profiling defines differential progenitor subclasses in mammalian neurogenesis[END_REF], (iii) SOX11 as a marker of differentiation from NIP to neurons [START_REF] Bergsland | Sequentially acting Sox transcription factors in neural lineage development[END_REF][START_REF] Chen | Orchestration of Neuronal Differentiation and Progenitor Pool Expansion in the Developing Cortex by SoxC Genes[END_REF], and (iv) SOX9 as a marker of immature glial cells and OPC [START_REF] Kang | Sox9 and NFIA Coordinate a Transcriptional Regulatory Cascade during the Initiation of Gliogenesis[END_REF].

INSM1 immunostaining was positive in large tumor cells areas characterized by high cell density in NIP high subgroup tumors. In addition, association of nuclear INSM1 labeling with cytoplasmic IDH1 R132H labeling within the same cells demonstrated that O3 id tumor cells express INSM1 (n=2/2, Fig. 3a-c).

The proportion of tumor cells expressing INSM1 was significantly higher in NIP high O3 id compared to NIP low O3 id and to non 1p/19q co-deleted AOT (n NIPhigh =11, n NIPlow =16, n non 1p/19q co- deleted AOT =8 p=0.0163, Kruskall-Wallis) (Fig. 3d-f). expression showed higher expression of SOX11 and ELAVL2 (n=6, Supplemental Fig. 7).

NIP high O3 id clinico-patho-biological characteristics compared to NIP low O3 id Age, sex, brain location, mitotic activity, and INA expression were not significantly different between NIP high and NIP low O3 id tumors or patients (Table 2). Necrosis was significantly more abundant in NIP high subgroup versus NIP low subgroup (p=0.0034). Microvascular proliferation was significantly more frequent in NIP high subgroup versus NIP low subgroup with non adjusted p=0.0142. However, this difference was not significant if p is adjusted for multiple comparisons (threshold of significance p<0.0045). Chromosome arm 9p and chromosome arm 10q losses occurred at similar rates in both subgroups. The analysis of overall survival showed no statistically significant difference between NIP high and NIP low subgroups (n NIPhigh =34, n NIPlow =52, p=0.582, Supplemental Figure 8) but older age had a worse prognosis (n age<45y =38, n age>45y =48, p=0.013) and necrosis and microvascular proliferation showed a trend for shorter survival (n no necrosis =65, n necrosis = 21 , p=0.055, and n no microvascular proliferation =16, n microvascular proliferation =70 , p=0.074 respectively).

GSEA for GeneOntology lists found an enrichment in NIP high subgroup versus NIP low subgroup for genes involved in DNA metabolism, RNA metabolism, DNA methylation and histones methylation (Supplemental Table 5). GSEA for Oncogenic Signature lists found an enrichment in NIP high subgroup in both training and validation sets for genes associated with: (i) activation of Sonic Hedgehog, MYC, E2F1 and, (ii) inactivation of retinoblastoma and EZH2.

A significant increase of the ratio of INSM1+ tumor cells/total tumors cells was observed in a cohort of 8 O3 id compared to their paired newly-diagnosed 1p/19q co-deleted tumors (paired t test, p=0.03) (Fig. 4).

Discussion

Over the last years, significant advances have been accomplished in deciphering intertumor heterogeneity in anaplastic diffuse gliomas [START_REF] Suzuki | Mutational landscape and clonal architecture in grade II and III gliomas[END_REF]. In contrast, intratumor cell phenotypic heterogeneity has been less investigated. Transcriptomic classification of glioblastoma identified a "proneural" signature which is enriched in O3 id [START_REF] Ducray | Anaplastic oligodendrogliomas with 1p19q codeletion have a proneural gene expression profile[END_REF][START_REF] Verhaak | Integrated genomic analysis identifies clinically relevant subtypes of glioblastoma characterized by abnormalities in PDGFRA, IDH1, EGFR, and NF1[END_REF]. Nevertheless, the "proneural" signature associates genes of oligodendroglial and neuronal lineages and thus does not correspond exactly to the proneural specification program governing neuronal versus glial lineages in the normal CNS. Therefore, the current work was focused in deciphering the intertumor and intratumor heterogeneity of tumor cell phenotype compared to CNS lineages.

It has been recently demonstrated that the cell of origin of oligodendroglioma is OPC [START_REF] Liu | Mosaic Analysis with Double Markers Reveals Tumor Cell of Origin in Glioma[END_REF][START_REF] Persson | Non-stem cell origin for oligodendroglioma[END_REF] and it is admitted that oligodendroglioma cells mimic normal oligodendroglial lineage [START_REF] Louis | WHO classification of tumours of the central nervous system. 4ème Edition[END_REF]. Previous works reported neuronal features in O3 id supporting a neuronal specification of some AOT cells: (i) a rare neurocytic morphology [START_REF] Makuria | Oligodendroglioma with neurocytic differentiation versus atypical extraventricular neurocytoma: a case report of unusual pathologic findings of a spinal cord tumor[END_REF][START_REF] Mrak | Atypical extraventricular neurocytoma with oligodendroglioma-like spread and an unusual pattern of chromosome 1p and 19q loss[END_REF][START_REF] Mueller | 45-year-old male with symptomatic mass in the frontal lobe[END_REF][START_REF] Perry | Oligodendrogliomas with neurocytic differentiation. A report of 4 cases with diagnostic and histogenetic implications[END_REF], (ii) a rare gangliocytic morphology [START_REF] Horbinski | Isocitrate dehydrogenase 1 analysis differentiates gangliogliomas from infiltrative gliomas[END_REF][START_REF] Perry | Oligodendroglial neoplasms with ganglioglioma-like maturation: a diagnostic pitfall[END_REF][START_REF] Tanaka | Anaplastic oligodendroglioma with ganglioglioma-like maturation[END_REF][START_REF] Yamashita | Oligodendroglial ganglioglioma[END_REF], or (iii) frequent neuronal markers expression -e.g. INA in tumors with honeycomb "oligodendroglial" morphology [START_REF] Ducray | alpha-Internexin expression identifies 1p19q codeleted gliomas[END_REF][START_REF] Ducray | Anaplastic oligodendrogliomas with 1p19q codeletion have a proneural gene expression profile[END_REF][START_REF] Ducray | Diagnostic and prognostic value of alpha internexin expression in a series of 409 gliomas[END_REF] and see Supplemental Table 6 for the list of other neuronal markers expressed in AOT). The absence of neurocytic/gangliocytic histological variants in our series excludes that the enrichment of neuronal gene lists that we observed in O3 id corresponds to these rare variants. As most of the gene lists were inferred by homology with mouse cell types, our comparisons need to be improved in the future using characteristics of human neural lineages. The comparison of O3 id with the neuronal lineage opens new perspectives for investigating tumor biology. Genes recurrently mutated in O3 id (CIC, FUBP1, NOTCH2, TCF12) are expressed in murine embryonic cortical SVZ at E13.5. These genes could be involved in cortical NIP biology although such a role has not been reported. Indeed, at E13.5, only neurogenesis occur in the cortical SVZ whereas oligodendrogliogenesis will occur at birth [START_REF] Kessaris | Competing waves of oligodendrocytes in the forebrain and postnatal elimination of an embryonic lineage[END_REF]. As some tumor cells of O3 id have a NIP phenotype, embryonic SVZ could be a model to test a specific functional effect of these mutations in NIP. Nevertheless, we did not find association between CIC mutation and NIP high subgroup and CIC, FUBP1, NOTCH2, TCF12 could have roles in both neuronal and oligodendroglial lineages which require further studies. CIC and NOTCH2 are expressed in cerebellar neuronal precursor and NOTCH2 was shown to inhibit differentiation and to maintain proliferation [START_REF] Lee | CIC, a member of a novel subfamily of the HMG-box superfamily, is transiently expressed in developing granule neurons[END_REF][START_REF] Solecki | Activated Notch2 signaling inhibits differentiation of cerebellar granule neuron precursors by maintaining proliferation[END_REF]. Notch signaling had a tumor suppressor role in a murine glioma model: the decrease of Notch signaling in this murine model mimicked glioblastoma with primitive neuronal component [START_REF] Giachino | A Tumor Suppressor Function for Notch Signaling in Forebrain Tumor Subtypes[END_REF]. Our analysis revealed an enrichment of MYC and Shh signaling in the NIP high subgroup which may be involved in NIPlike tumor cells proliferation. MYC pathway was shown to promote neurogenesis in the chick embryo (83) and MYC amplification transform gliomas into glioblastoma with primitive neuroectodermal tumor-like component/GBM-PNET-like (59) termed glioblastoma with primitive neuronal component in WHO 2016 [START_REF] Louis | WHO classification of tumours of the central nervous system[END_REF]. MYC activity was shown to be increased in a subgroup of OD3 id by several mechanisms [START_REF] Kamoun | Integrated multi-omics analysis of oligodendroglial tumours identifies three subgroups of 1p/19q co-deleted gliomas[END_REF]. The extracellular signal Shh was shown to promote proliferation of bipotent (neuronal and oligodendroglial) embryonic progenitors (82).

Shh and MYC signaling pathways thus appear as putative therapeutic targets to treat OD3 id with NIP high phenotype.

Based on gene expression profiling, we observed different phenotypes among AOT associated to the expression of the master genes controlling glial specification and to the tumor genotypes. SOX9 and NFIA together control a glial fate [START_REF] Deneen | The transcription factor NFIA controls the onset of gliogenesis in the developing spinal cord[END_REF][START_REF] Kang | Sox9 and NFIA Coordinate a Transcriptional Regulatory Cascade during the Initiation of Gliogenesis[END_REF][START_REF] Namihira | Committed neuronal precursors confer astrocytic potential on residual neural precursor cells[END_REF]. Maintained NFIA expression determines astrocytic fate by inhibiting SOX10. By contrast, NFIA downregulation in OPC allows SOX10-induced oligodendroglial specification [START_REF] Glasgow | Mutual antagonism between Sox10 and NFIA regulates diversification of glial lineages and glioma subtypes[END_REF]. SOX10 was previously shown to be expressed in all glioma subtypes, whereas NFIA expression was low in oligodendrogliomas and high in astrocytomas [START_REF] Bannykh | Oligodendroglial-specific transcriptional factor SOX10 is ubiquitously expressed in human gliomas[END_REF][START_REF] Ferletta | Sox10 has a broad expression pattern in gliomas and enhances platelet-derived growth factor-B--induced gliomagenesis[END_REF][START_REF] Glasgow | The miR-223/nuclear factor I-A axis regulates glial precursor proliferation and tumorigenesis in the CNS[END_REF][START_REF] Rousseau | Expression of oligodendroglial and astrocytic lineage markers in diffuse gliomas: use of YKL-40, ApoE, ASCL1, and NKX2-2[END_REF][START_REF] Song | Nuclear factor IA is expressed in astrocytomas and is associated with improved survival[END_REF]. We observed higher expression of SOX9 and NFIA, and significant enrichment of gene list related to astrocytes in non 1p/19q co-deleted AOT. These findings are consistent with SOX9 and NFIA controlling gliogenesis mainly along the astrocytic lineage in the integrated diagnosis of anaplastic astrocytoma, IDH-mutant. By contrast, OD3 id showed lower expression of SOX9 and sparse NFIA expression consistent with rarer astrocytic cells. We showed, for the first time to the best of our knowledge, the possibility to distinguish Its reliability waits for validation in larger series.

We described a new intertumor heterogeneity in OD3 id based on the NIP phenotype: NIP high and NIP low subgroups. The NIP high subgroup accounted for 54% and 37% of training set and validation set, respectively. The two subgroups could correspond to different cell of origin or oncogenic pathways but we did not observe significant differences in genetic alterations between both subgroups. The enrichment in the NIP high subgroup of lists involved in DNA methylation and EZH2 function suggests that methylation profiles could also distinguish the two subgroups and will require further studies. Alternatively, NIP high subgroup could result from the progression of NIP low subgroup as suggested by: (i) more frequent necrosis and microvascular proliferation in NIP high subgroup, and (ii) increase of INSM1 expression in relapses. The increase of the NIP high phenotype during tumor progression could result from tumor dedifferentiation and increased plasticity between glial and neuronal lineages. Differently, a small subpopulation of progenitorlike tumor cells that lack differentiation and harbor higher lineage plasticity could exist in the initial tumor and would increase during tumor progression.

Microvascular proliferation and necrosis were associated to shorter survival in OD3 id [START_REF] Figarella-Branger | Mitotic index, microvascular proliferation, and necrosis define 3 pathological subgroups of prognostic relevance among 1p/19q co-deleted anaplastic oligodendrogliomas[END_REF].

In our series, these parameters showed a non statistically significant trend for worse prognosis probably because of the limited number of cases. NIP high subgroup showed more frequent microvascular proliferation (94%) and necrosis (41%) than NIP low subgroup (26% and 12% respectively) but NIP high phenotype did not have prognostic value. We propose that NIP high phenotype is associated to more aggressive OD3 id rather than an independent prognostic factor.

!" #! # $ ! !" ! #! # $ % &' ( &) * ! !+ $ * , - !# ! ! ! !# ! ! ! % . / ! ! % 0 ) 012 3 % % ( 4
0 ) 012 , % 0'1 5 " $ ! 0'1 + 202 5 $ 202 + % 6 7 !,$ " $ ! ! 6 7 !,$ ! % $ 7 ! % ( 7 $ % 2 ! $ # $ ! + $ $ $ $ # ! $ $ " + " 8 5 " ! $ " + " 8 9 ! $ ! : + $;5 $ ! 5 ! ! " <! ! !$ 9 $;5 $ ! $ : )"" # ! = !,$ !,$ ! > 012 5 ! ! > !# !# 5 > ! > > + + $ =
" ! #$ % ! $ % & $ ' ' & & ! ( ( % )$ ) $ ( )$ '( ) $ )$ (& ) $ ) * ' + ) ) * ) ( ) * ( !
- <6 - = , 0 ( ! 7>' ! > )2 7>!&# >777 7>2"' "/)) * 7>//' > !& 7>"/! 7>'7! 7>&!' )!! 3 7>"/2 >72& 7>" ' 7>2&) 7>&'& !/!! 7>"7) >77' 7>##) 7>2!# 7>'") " 7/ 7>"!! 7>'#/ 7>227 7>&'! 7>)!' !2") ! 7>"!& 7>&& 7>&!/ 7>&2& 7>)27 )'& ! 6 6 30 - ; - <6 - = , 0 ( ! 7>/27 >#'' 7>7! 7> /) 7>7)" ")#/ " 7>/"2 >#") 7>7!/ 7> /! 7> &! ") ' 3 > 7>##7 >#"' 7>7"# 7> 7! 7> &! # / ! 7>'#& >#"! 7>7 # 7>7'! 7> '! !&/2 # 7>2&/ >#!! 7>7"7 7>7&" 7> ) !') 7>2/ ># / 7>7 ! 7>72/ 7>!7 " !/ 7>/' >#7 7>7#& 7>72' 7>!!2 " &' 3 > ! 7>/"' >"!" 7> /# 7> !& 7>"/' "&# 3 > " 7>"/# >!&2 7> // 7> 2/ 7>##& #!'/ 3 ! 7>##/ >!!! 7>722 7>! " 7>//# )& 3 " 7>"7# >7'" 7>!)7 7>"& 7>&27 "/#7 7>/2! >72 7>#7# 7>"& 7>&'' #/)7 7>"#" >727 7>""" 7>"## 7>&'' !)'' "> % 6 $ - > 6
- <6 - = , 0 ( 7>#!! >!/! 7> '' 7>& " 7>/## !!!# * 7>2!2 > )! 7>!'/ 7>#)7 7>2#/ 7#/ ! 7>&&/ > ) 7>!)2 7>"!& 7>2#/ !!&2 7>"&" 7>)7) 7>/2& 7>2'& 7>) ! !#&2 ! 7>""2 7>&#7 7>&&& 7>'7& 7>)&! !!&# ! 6 6 30 - ; - <6 - = , 0 ( 7>#&# >"!2 7>7&7 >777 7>")" "!&2 7>#'# >" ' 7> ) 7>2#& 7># "7'2 ! 7>#"# >!!& 7>!72 7>&#' 7>//' "&#" # 7>/ ! > 2' 7>!)) 7>&2/ 7>2// "&7/ ! 7>2#" > #& 7>"") 7>2&' 7>2'& !"! 3 " 7>" " >7!& 7>") 7>'') 7>' " ""/7 3 > ! 7>#") >7 ) 7>#/! 7>&'2 7>'! ##77 3 > 7>"!) >7 ' 7>##2 7>2') 7>'! #!)! 3 > " 7>!)' >77' 7>#!2 7>2"' 7>'" #!') " 7>""/ 7>''/ 7>2"/ 7>'7 7>) # "&7/ 3 ! 7>"2" 7>''# 7>& ! 7>&"7 7>) # !// 7>")/ 7>'22 7>2)! 7>&7# 7>)!/ !777 3 7>"#" 7>'#2 7>2)! 7>2'& 7>)#" "#2 7>#7) 7>&7" 7>'"7 7>'/" 7>)&2 # ! #> % 6 $ - - > 6

  INSM1 and SOX9 immunolabeling mainly excluded each other showing their expression by two distinct tumor cell populations: INSM1+/SOX9-NIP-like cells and INSM1-/SOX9+ OPC-like cells (Fig. 3g-j). Interestingly, INSM1+ and SOX9+ tumor cells both proliferate (Fig. 3k-n, data not shown). ELAVL2 and SOX11 immunolabeling showed expression by a majority of tumor cells with heterogeneous level in a majority of OD3 id . Assessment of the expression by Hirsch score showed a non statistically significant higher expression of SOX11 and ELAVL2 in NIP high versus NIP low tumors (n NIPhigh =12, n NIPlow =16, mean score SOX11 NIPhigh =273 ±46, mean score SOX11 NIPlow = 248 ±74, SOX11 p=0.53; mean score ELAVL2 NIPhigh = 206 ±104, mean score ELAVL2 NIPlow = 177 ±95, ELAVL2 p=0.43, Mann-Whitney test). Tumor areas with INSM1

  Fig.6). In addition, the neuronal phenotype of some tumor cells was confirmed by INSM1

  1p/19q co-deleted and non 1p/19q co-deleted AOT by the ratio of NFIA+ tumor cells with high sensitivity and specificity. Although loss of ATRX identified most of IDH-mutant non 1p/19q codeleted tumors, NFIA could help detection of ATRX maintained, non 1p/19q co-deleted tumors.

Finally, our

  work identifies novel intertumor and intratumor tumor cell heterogeneities in OD3 id based on the presence of tumor cells with NIP phenotype. These findings will help the understanding of OD3 id biology and open new therapeutic avenues considering neuronal cell lineage. 82. Yung SY, Gokhan S, Jurcsak J, Molero AE, Abrajano JJ, Mehler MF (2002) Differential modulation of BMP signaling promotes the elaboration of cerebral cortical GABAergic neurons or oligodendrocytes from a common sonic hedgehog-responsive ventral forebrain progenitor species. Proc Natl Acad Sci U S A.99(25):16273-8. 83. Zinin N, Adameyko I, Wilhelm M, Fritz N, Uhlen P, Ernfors P, Henriksson MA (2014) MYC proteins promote neuronal differentiation by controlling the mode of progenitor cell division. EMBO Rep.15(4):383-91.

Figure 1 .

 1 Figure 1. Expression of cell lineage signatures according to 1p/19q co-deletion status in

Figure 2 .

 2 Figure 2. Hierarchical clustering of tumors according to the expression of genes of the

Figure 3 .

 3 Figure 3. INSM1 immunolabelling in anaplastic oligodendroglial tumors a-c, three sections of the same anaplastic oligodendroglial tumor of the NIP high subgroup were

Figure 4 .

 4 Figure 4. INSM1 expression in newly-diagnosed tumors and their relapse.

Figure 1 123x241mm

 1 Figure 1 123x241mm (300 x 300 DPI)

  variables with normal distribution were compared between two groups by two-tailed t test; other discrete variables were compared by Mann-Whitney test. Discrete variables were compared between three or more groups by Kruskal-Wallis test; post-hoc pairwise comparisons were performed by Wilcoxon rank sum test or by Mann-Whitney test. Qualitative variables were compared by Chi-square test if expected values were superior to 5, if not by Fisher exact test. A Bonferroni correction was used when a multiple comparison was performed. Survival analysis was performed by Kaplan-Meier method and log-rank test.

Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology !

								!
	"	"	# $	%&# ' ( #	&% # $	&
	"	"	(	%)	)*(	)		*
				+ ,-	-		.	/ 0
	"	"		%).1	-		.	/ 0
				)2%	)*	, )	*
				.34$		$	.	/ 0
				.34	#	( ,	. "	!
		5	"		"" !	! "

Page 43 of 62 Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK

						Brain Pathology
								!"
	##	##						"
	!	$	%		#			&'
	(							&'
					%			!&
		%						!)
	*+	,	-	.	*+		/!
	00 !	0		$	%%	%	!	"
	01	0						22
	3	4	5	3				"
	6							&2
	*	%						!7
	3 * !	3			%	!		!
								&#
	3 /	3	8	/8	%			"/
	30							'"
	0	0 $			$			"!
	3(!	,	%	3( !				"
	3()	,	%	3( )				2
	, ,"			-	%		"	#
	, &	,	%	& .				/#
	9 4 !# 9 %	4				!#
	4 ,	4 5 $	$ $	%		&"
	,:	, ,	5					"

Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK

Acknowledgements

This work was supported by The Institut Universitaire de Cancérologie (IUC), ONCOMOLPATH (AP-HP). We are grateful to the staff of Neuropathology Department for technical assistance.

This work is funded by the French Institut National du Cancer (INCa) and part of the national program Cartes d'Identité des Tumeurs® (CIT) http://cit.ligue-cancer.net/ funded and developed by the Ligue Nationale contre le cancer. The research leading to these results received fundings from the programs "Investissements d'avenir" ANR-10-IAIHU-06 and ANR-11-INBS-0011 (NeurATRIS: Translational Research Infrastructure for Biotherapies in Neurosciences), from Fondation ARC pour la recherche sur le cancer (n°PJA 20151203562) and from Association pour la Recherche sur les Tumeurs Cérébrales (ARTC).

Funding

Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology 175x215mm (300 x 300 DPI) Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology 156x194mm (300 x 300 DPI) Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology 165x127mm (300 x 300 DPI) Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology 169x139mm (300 x 300 DPI) Brain Pathology Editorial Office, Blackwell Publishing, Oxford, UK Brain Pathology 161x178mm (300 x 300 DPI)

Supplementary Material

Supplementary material (supplemental figures) is available.

Supplemental Figure Legends

Supplemental Figure 1. RT-qPCR and immunohistochemistry for lineage markers of central nervous system in anaplastic oligodendroglial tumors. a, schematic representation of embryonic central nervous system lineages. Neural stem cells produce neurons, becomes gliogenic progenitors after the glial switch and then produce oligodendrocytes and astrocytes. b,c, RT-qPCR in anaplastic oligodendroglial tumors (AOT) with or without 1p/19q co-deletion, and in control (non tumoral cerebral tissue). b, genes correspond to markers of the different cell types: embryonic stem cells (cyan), NSC (blue), neuronal precursors (green), gliogenic progenitors (yellow), oligodendroglial lineages


F Bert

D Bono

P Mendels

F Ladieu

F Duc

J.-C Trombe

P Millet

Ground state of the Kagomé-like S=1/2 antiferromagnet, Volborthite Cu 3 V 2 O 7 (OH) 2 2H 2 O

Keywords: numbers: 75.30.Cr, 75.50.Lk, 76.60.-k

Volborthite compound is one of the very few realizations of S=1/2 quantum spins on a highly frustrated kagomé-like lattice. Low-T SQUID measurements reveal a broad magnetic transition below 2 K which is further confirmed by a peak in the 51 V nuclear spin relaxation rate (1/T1) at 1.4 K±0.2 K. Through 51 V NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% correspond to a well defined short range order, possibly of the √ 3 × √ 3 type. While the freezing involve all the Cu 2+ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.

In the quest for novel states of condensed matter, frustration has emerged as a key concept [START_REF] Ramirez | Handbook on Magnetic Materials[END_REF]. In magnetic systems, competitive interactions resulting from the geometry of the lattice, especially for corner sharing networks, can lead to a macroscopic entropy at T=0 K and could favor a novel spin liquid state. Theoretically, Heisenberg S=1/2 antiferromagnet on a 2D kagome lattice is predicted to lead to such an exotic quantum state [START_REF] Misguich | Frustration in Two-Dimensional Quantum Antiferromagnets[END_REF][START_REF] Mila | [END_REF]. Actually very few real systems approach this model. So far, the Cr 3+ (S=3/2) kagomé bilayer compounds SrCr 9p Ga 12-9p O 19 (SCGO) and Ba 2 Sn 2 ZnGa 10-7p Cr 7p O 22 (p < 0.97) have been the experimental archetypes of Heisenberg frustrated antiferromagnets. In this context, the recent rediscovery of Volborthite Cu 3 V 2 O 7 (OH) 2 2H 2 O [5,6] is a major step towards a realization of the theoretical model. The magnetic lattice of this natural antiferromagnet consists of quantum S=1/2 (Cu 2+ ) spins sitting at the vertices of well separated (7.2 Å) kagome-like planes. The lattice displays a monoclinic distortion, possibly yielding two Cu-Cu interaction constants J 1 = J 2 , which does not seem to impact on the characteristic fingerprints of frustration. Indeed, despite strong antiferromagnetic interactions (J ≃ 90 K), no transition towards an ordered state has been detected down to 1.8 K, neither in susceptibility nor in heat capacity measurements [6]. Instead, a maximum in both these quantities is observed around 20 K, probably reflecting the enhancement of short range correlations, and defines a new low energy scale as a result of frustration [7,8]. Besides, as in kagomé bilayers [4], muon spin relaxation (µSR) experiments detected no sign of static spin freezing but rather temperature independent spin fluctuations persisting down to 50 mK, indicative of a fluctuating quantum GS [9]. Only in one ESR study the existence of an internal field was evidenced at 1.8 K which was interpreted as short range order [10].

In this Letter, we show, for the first time, that volborthite undergoes, around 1.3 K, a transition to a frozen state which we characterize using 51 V NMR as a local probe of magnetism. Note that, so far, NMR investigation of the GS in the kagomé bilayers had proved to be impossible because of a wipe out of the NMR intensity at low T [11]. The volborthite powder samples were prepared by refluxing an aqueous suspension of V 2 O 5 and a basic copper (II) carbonate salt Cu(OH)2-Cu(CO3) for several days. No spurious phase was detected in X-ray measurements. SQUID and NMR measurements above 2 K and µSR experiments on these samples [12] were similar to the above described published data.

The low T static susceptibility of volborthite is presented in Fig. 1 (top panel). Below 2 K, the separation between the field cooled (FC) and zero field cooled (ZFC) susceptibilities reveals a spin freezing process. At 1.2 K, "ageing" effects [START_REF] Vincent | Complex Behaviour of Glassy Systems[END_REF] have been observed (not shown here) which ascertains the glassy nature of the GS. At variance with textbook spin glass transition, the FC susceptibility does not level off below the transition and the hardly detectable broad maximum on the ZFC branch occurs below the FC/ZFC separation [START_REF]0.1 K, is due to few ppm magnetic impurities in the grease used to ensure thermalization[END_REF]. This suggests a rather broad distribution of freezing temperatures as, for instance, in super-paramagnets where spin clusters get progressively blocked on lowering T.

To address the important issue of the intrinsic character of this glassy low-T phase, the susceptibility of two zinc substituted samples is also reproduced in Fig. 1. Zn atoms enter Volborhtite lattice without noticeable distortion. Since Zn 2+ is non-magnetic, the Zn/Cu substitution results in diluting the kagome magnetic lattice. The freezing temperature T g , defined here as the temperature of the ZFC maxima, are plotted in the inset of Fig. 1 as a function of the magnetic lattice dilution and compared to the same data for SCGO compounds [11]. In marked contrast with SCGO, T g for Volborthite is strongly affected by dilution. This reminds us of the drastic reduction upon dilution of the dynamical plateau value seen in µSR experiments [12] and suggests that the bilayer topology likely better accommodates defects than the single layer one in volborthite. Nonetheless, in both systems, the random dilution of the magnetic network reduces T g and hence simple magnetic dilution as a source of disorder cannot explain, alone, the spin-glass like transition.

Microscopic insight into this ground state is provided by our low-T 51 V NMR experiments. The non-magnetic V 5+ ions are situated above or below the center of the stars which constitutes the kagomé lattice. They thus probe symmetrically the magnetism of six Cu 2+ ions belonging to the same hexagon through an hyperfine coupling, estimated to be A ≃ 7.7 kOe from susceptibility versus NMR shift measurements (see Ref. [12]) above 90 K in agreement with the value estimated in Ref. [6].

The nuclear spin lattice relaxation has been measured by the saturation-recovery method and fitted to a sum, with T-independent coefficients, of four exponential terms with relaxation rates proportional to 1/T 1 as expected for a S=7/2 nuclear spin [START_REF] Narath | [END_REF] in the case of partial saturation of the NMR line. The divergence of 1/T 1 at 1.4 K±0.2 K (Fig. 3, inset) is a strong evidence that the vanadium probe indeed feels a transition in agreement with our susceptibility measurements. Following the analysis of Ref. [9] of the zero field µSR relaxation rate below 1 K (λ = 5 µs -1 in our sample [12]), we get 3.5 MHz for the copper spin fluctuation rate. From the hyperfine coupling A, we would then expect the corresponding 51 V 1/T 1 to be ≃ 20 ms -1 , much higher than the value actually measured. This suggests that spin fluc- tuations, seen in µSR, are efficiently filtered by the nuclear probe. We shall come back to this point later. Characteristic 51 V (γ/2π = 11.1923 MHz/T) NMR spectra measured at ν 0 = 20.733 MHz, below 5 K, are presented in Fig. 2. At these low T, the quadrupolar splitting of the S=7/2 vanadium NMR line is masked by a large magnetic broadening which reflects the width of the field distribution at the vanadium site. On lowering T, the NMR line broadens drastically around 1.5 K and then saturates below 0.6 K. At a lower 12.548 MHz irradiating frequency, we checked that this saturation is field independent, and therefore reflects, as expected, a frozen field distribution in the GS. Upon closer inspection of the T-dependence of the lineshape, we note first the appearance of a broad background feature below 1.5 K. In order to track qualitatively this broad component we chose rather arbitrarily to plot the half width at 1/5 th of the maximum in Fig. 3. Then the main central line, which width is roughly the width at half maximum of the spectra (open symbols in Fig. 3), starts to broaden rapidly and below 1 K, its lineshape changes from lorentzian-like to gaussian-like. The two distinct features, broad background and central line, in the low-T spectra suggest that the NMR line, below 1.5 K, is no more homogenous but results from at least two different types of magnetic environments of vanadium. This is probably related, as well, to the progressive freezing observed in macroscopic susceptibility. It is an important finding of this study as it demands a special magnetic ordering in the GS leading to two different V sites.

We now focus on the T=0.35 K spectra (Fig. 4) in the well established GS of volborthite. By comparison of the integrated intensity with T > 2 K data, we checked that all sites are detected at this low-T and we therefore probe the bulk properties of the sample. The top and bottom spectra have been obtained in the same condi- tions except for a different duration τ in the pulse sequence π/2 -τ -π/2. This contrast procedure allows us to separate the two components of the spectrum. They indeed prove to have different spin-spin relaxation times T 2 which we determined by standard T 2 measurements at H = 1.845 T and H = 1.955 T.

In the long time spectrum (top panel), the slowly relaxing (T 2 = 105 µs) broad background clearly stands out, without the fast relaxing (T 2 = 60 µs) gaussianlike component and appears to be rectangular shaped. An unshifted narrower line also appears on this spectrum. However, because of its much longer T 2 = 240 µs, it eventually represents less than 1% of the total sample and probably arises from some small impurity phase. The rectangular lineshape is a clear signature of the presence of one well defined frozen field H f at the vanadium site arising from the neighboring copper moments. The resonance condition writes H 0 = 2πν 0 /γ = H + H f where H is the applied field. Due to powder distribution, H f is randomly oriented with respect to H. In the limit H f ≪ H 0 one would expect a rectangular lineshape with cut-offs at H 0 ± H f . An exact derivation of the NMR line P (H) yields

P (H) = (H 2 0 + H 2 -H 2 f )/(4H f H 2 ) ( 1
)
for |H -H 0 | < H f . The component labelled "ordered" in Fig. 4 is a fit with such a model with H f = 0.16 T and a narrow distribution (0.02 T HWHM) of this frozen field. The solid line in the top panel is a global fit to the NMR line, including the impurity phase. In order to produce a well-defined amplitude of the frozen field at the vanadium site, short-range order of the six neighboring Cu 2+ moments must exist. In a classical picture, the energy is minimized on the kagomé lattice, when the spins are at 120 • from each other on each triangle. Following most of the theoretical works [15], we assume a √ 3 × √ 3 type The solid lines are fits to the data and result from the sum of three components (dashed, dashed-dotted and dotted lines) as explained in the text. Inset: scheme of the proposed √ 3 × √ 3 local order responsible for the ordered component (dashed line). The vector at the center of the hexagon stands for the resulting frozen field at the vanadium site.

short range order, sketched in the inset of Fig. 4, which corresponds to alternating chiralities (+ and -signs) on neighboring triangles. Such a short range order indeed leads to a well defined H f = 3H Cu resulting field at the vanadium site, where H Cu is the frozen field arising from each Cu 2+ . On the contrary, a uniform chirality order (q = 0) would lead to a null field at the vanadium site which cannot reproduce our NMR data. In addition, the classical √ 3 × √ 3 order favors local collective excitations made of a coherent out-of-plane rotation of the six spins belonging to a same hexagon as depicted in the inset of Fig. 4. It is remarkable that such excitations, which cost zero energy, do not affect the resulting field at the vanadium site, neither by hyperfine nor dipolar coupling, and are, therefore, "filtered" out at the symmetric vanadium site. This could explain why we measured a small 1/T 1 which, besides, decreases at low temperature, as in usual static phases, whereas, in µSR experiments, muons which sit in less symmetric positions, still feel a strong dynamics which persists below T g [9,12]. From H f and the hyperfine coupling constant, we get 0.41µ B for the frozen Cu 2+ moment contributing to this slow relaxing component. This small value, compared to 1µ B expected for a spin 1/2, demonstrates that zero point quantum fluctuations strongly affect the volborthite GS.

In the bottom panel, combining the formerly discussed slow relaxing components with a frozen gaussian-like component ("disordered" label) results in the solid line which reproduces well the short time experimental spectra. Taking into account the different T 2 values, we evaluate the corresponding sample fractions, in the limit τ → 0, to be ≃80% for the gaussian like component and ≃20% for the rectangular-shaped one. A gaussian-like frozen component is easily obtained provided that the Cu 2+ frozen moments belonging to a same hexagon are randomly oriented as in the case of a spin glass. In this random picture, we extract also a small 0.44µ B value for the frozen copper moment consistent with the previous one. A gaussian like component could also come from several frozen field values, smaller than in the √ 3 × √ 3 case and slightly distributed, arising from various other spin configurations. A crude illustration of this scenario can be obtained if one assumes a random distribution of the chiralities on the kagomé lattice. One finds then that 4% of the hexagons are in the √ 3 × √ 3 configurations while the other configurations lead to either H f = 0 (54%) or H f = √ 3H Cu (41%). Our experimental value already indicates that, within this classical framework, the √ 3 × √ 3 configuration has to be favored by some mechanism. An exact quantum calculation of the possible states in a finite kagomé spin 1/2 cluster would certainly allow a better quantitative understanding of this gaussian-like component in this scenario. At the nanoscopic scale of the NMR probe, it is difficult to decide whether these two vanadium sites in the GS reveal different domains or appear as a mixture in a single phase. However, both configurations freeze at approximatively the same temperature and, for both, we found a similar frozen fraction of the Cu 2+ moments. Both arguments favor an original single phase description.

The disorder of the GS is a challenge to our understanding of highly frustrated magnets, given that volborthite is probably the purest model system known so far. From a comparison with Zn diluted samples, we estimated an upper limit of 1% spin vacancy like defects in the pure volborthite sample. Theoretical works [16,17] have put forward the possibility of an intrinsic "topological" spin glass state arising from frustration alone contrary to usual spin glasses where both frustration and disorder are responsible for glassiness. Alternatively, in Ref. [18], it was argued that a small amount of disorder could induce a spin glass like state provided that a coherent RVB background couples very efficiently the de-fect centers. This scenario naturally explains the simultaneous occurrence of the glassy-like transition and the dynamical plateau in µSR experiments and is consistent with our finding of a two component NMR signal, arising from vanadium nuclei far and close to a defect.

In conclusion , volborthite which presents all the well established signatures of a spin liquid, namely no freezing at T ≃ θ CW and a dynamical plateau at T → 0, allows, for the first time, a detailed NMR local investigation of the GS. This enabled us to study the internal field configurations and their dynamics. Further, this opens new avenues for refined theoretical calculations which are necessary to reveal the influence of the possible dissymmetry of the interactions and the actual texture of the GS.

  FIG.1: SQUID dc susceptibility in Cu 3(1-x) Zn3xV2O7(OH)2 2H2O measured after two cooling protocols, with (open symbols) and without (full symbols) a 100 Oe applied field. Inset: comparison of Tg versus S=0 impurity dilution rate in volborthite and SCGO bilayer compounds.

FIG. 2 :

 2 FIG.2: 51 V NMR spectra measured at 20.733 MHz as a function of the applied field. For clarity, the spectra have been normalized to their maximum value. The vertical arrow shows the position H0 of the unshifted reference line.

5 FIG. 3 :

 53 FIG. 3: Half widths of the NMR spectra measured at 1/2 (HW1/2, open symbols) and 1/5 (HW1/5, full symbols) of the maximum height. Inset : T -dependence of the 51 V spin-lattice relaxation rate (1/T1) measured at the maximum intensity of the spectra (H=1.85 T). Lines are guides for the eye.

FIG. 4 :

 4 FIG.4: 51 V NMR spectra measured for two different delays τ at T=0.35 K. Note the different scales in the top and bottom panel. The solid lines are fits to the data and result from the sum of three components (dashed, dashed-dotted and dotted lines) as explained in the text. Inset: scheme of the proposed √ 3 × √ 3 local order responsible for the ordered component (dashed line). The vector at the center of the hexagon stands for the resulting frozen field at the vanadium site.


Even Entem

Loic Barthe

Marie-Paule Cani

Michiel Van De Panne

From Drawing to Animation-ready Vector Graphics

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.

Closure computation in a transition region: a) Contours of the transition region are in this case described by a silhouette contour at the bottom and a red suggestive contour at the top. b) All the closure curves corresponding to pairs of one sample point from the contour and the suggestive contour extremity are computed and their plausibility is evaluated for closing the rightmost sub-part. Curves that intersect contours are eliminated. c) The same closing procedure is applied to the other region, therefore the suggestive contour's T-junction is used instead of its extremity. d) Resulting closure curves.

Our metric is based on a part-aware surface metric for shape analysis [1]. It de nes a distance between visibility pro les from neighbor points of view inside the shape. It is computed as the sum of the squared di erences in visibility distance of an angularly uniformly sampled set of rays. Outliers (occlusions) are smoothed using weighting terms. Our points of view being uniformly sampled, we avoid the noise produced by variable relative errors in the 3D technique.

Contour drawings are commonly used for shape depiction. However they remain di cult to edit or manipulate.

Some algorithms have been proposed to build 3D representations from Computer Aided Design sketches. Other methods tackle free-form drawings, but are generally dedicated to speci c kinds of shapes. While state of the art techniques can beautify, complete hidden contours, complete cusps as in SmoothSketch [2] and segment contour shapes, the problem of complex internal silhouette contours and expressive strokes remains challenging.

We show a novel technique to structure clean-line drawings of smooth shapes into a manipulable representation. Our contribution is an algorithm taking into account complex internal silhouette contours by combining the two usual kind of approaches: contour and region.

Given a clean-line drawing of a smooth free-form shape, segment it into a set of simple and smooth 2D shapes adapted for edition and animation.

We propose a 2D part-aware metric measuring the relative salience along the medial axis of 2D shapes, that is loosely inspired by the 3D metric in [1].

We cluster medial axis parts using this metric. We then de ne the area between each pair of contours corresponding to a cluster as a transition zone.

Processing possible transition zones in a speci c priority order enables us to achieve a recursive extraction of sub-regions, which handles the challenging case of trees of inner silhouette contours. The closure of identi ed sub-regions is performed by minimizing the curvature cost of the pair of closing cubic Bezier curves. Extremities and tangents are constrained by the type of transition zone. The relative depth between sub-regions is inferred from the information around T-junctions.

The structure and layering information we obtain can be used to represent, edit and animate the input sketch in a meaningful way. The purely expressive strokes are not handled when located in the closure area. An ambiguity remains between bulgy and at areas that is hard to formalize even perceptually. As future works we would like to tackle these limitations and provide a user-friendly interface for our technique. It would include an assisted positioning of skeleton joints and we could allow the deformation of each part using medial-axis-based manipulators.

Pipeline

Results

  From drawing to animation-ready vector graphics Even Entem a,b , Loïc Barthe b , Marie-Paule Cani a , Michiel van de Panne c a Université Grenoble-Alpes, LJK, Inria b Université de Toulouse, IRIT c University of British Columbia


F Ladieu
email: ladieu@drecam.cea.fr

F Bert

V Dupuis

J Hammann

The relative influences of disorder and of frustration on the glassy dynamics in magnetic systems

The magnetization relaxations of three different types of geometrically frustrated magnetic systems have been studied with the same experimental procedures as previously used in spin glasses. The materials investigated are Y 2 Mo 2 O 7 (pyrochlore system), SrCr 8.6 Ga 3.4 O 19 (piled pairs of Kagomé layers) and (H 3 O)Fe 3 (SO 4 ) 2 (OH) 6 (jarosite compound). Despite a very small amount of disorder, all the samples exhibit many characteristic features of spin glass dynamics below a freezing temperature T g , much smaller than their Curie-Weiss temperature θ . The ageing properties of their thermoremanent magnetization can be well accounted for by the same scaling law as in spin glasses, and the values of the scaling exponents are very close. The effects of temperature variations during ageing have been specifically investigated. In the pyrochlore and the bi-Kagomé compounds, a decrease of temperature after some waiting period at a certain temperature T p reinitializes ageing, and the evolution at the new temperature is the same as if the system were just quenched from above T g . However, as the temperature is raised back to T p , the sample recovers the state it had previously reached at that temperature. These features are known in spin glasses as rejuvenation and memory effects. They are clear signatures of the spin glass dynamics. In the Kagomé compound, there is also some rejuvenation and memory, but much larger temperature changes are needed to observe the effects. In that sense, the behaviour of this compound is quantitatively different from that of spin glasses.

(Some figures in this article are in colour only in the electronic version) It was usually thought that both disorder and frustration were necessary to obtain spin glass dynamics (see, for example, [1-3]). However, several frustrated but non-disordered antiferromagnets, rather than condensing into a spin liquid state as theoretically expected,

were found to enter a glassy state below a well defined freezing temperature. As in usual spin glasses, below this temperature T g their dynamic response to a small magnetic field becomes very slow and depends on the time t w spent below T g ('ageing'; see, for example, [1][2][3]). The question thus arises whether these glassy materials are really similar to standard spin glasses. We have addressed this question by investigating three examples of such antiferromagnets using the same experimental procedures as previously used in the detailed study of the dynamical properties of spin glasses. The three examples correspond each to a different topology of the frustrated spin network. The first one is Y 2 Mo 2 O 7 ('YMO'), where the spins (S = 3/2) are on a three-dimensional (3D) pyrochlore lattice [4,5]. The second one is SrCr 8.6 Ga 3.4 O 19 , ('SCGO'), where the spins are located on bi-layers of 2D Kagomé lattices, each bi-layer being well separated from the others [6,7]. The third one is a jarosite compound (H 3 O)Fe 3 (SO 4 ) 2 (OH) 6 , where the spins (S = 5/2) are located on genuine 2D Kagomé layers, with small interlayer couplings [8].

At high temperature, all three compounds exhibit a Curie-Weiss behaviour with a large negative value for the Curie-Weiss temperature θ , indicating strong antiferromagnetic interactions between spins. The values of θ are much larger than the observed freezing temperatures T g . The ratio |θ |/T g is of order 10 for the (3D) YMO sample [4], about 140 for SCGO [6], and about 60 for the (2D) Kagomé sample [9]. This reveals that frustration plays a key role in the low-T physics.

Below T g a clear separation between zero field cooled (ZFC) and field cooled (FC) magnetizations is found. This is a standard indication suggesting that the low-temperature phase is a spin glass phase. The spin glass transition is further confirmed by other measurements:

(i) in the Kagomé sample an analysis of the critical dynamics was carried out over 10 decades in frequency (including Mössbauer experiments) and it yielded the critical exponents usually found in standard spin glasses [10]; (ii) in YMO [4] it was shown that the nonlinear susceptibility diverges at T g , as expected for spin glasses.

In addition, both in YMO [5] and in the Kagomé sample [11], neutron diffraction experiments do not detect any long range ordering. The amount of disorder is very small in all these materials. In YMO the main source of disorder might be a small percentage of Mo-Mo bonds whose lengths are slightly different from the standard one [5]. In SCGO an obvious source of disorder could arise from the nonstoichiometry of the compound which leads to a Cr coverage of the magnetic sublattice of x = 8.6/9 = 95%, i.e. to an amount of disorder of 5%. However, since it was shown that T g is an increasing function of x [6], one expects a spin glass phase even in the stoichiometric compound. Thus, the imperfect coverage of the magnetic sublattice does not seem to trigger the spin glass phase. Last, in the Kagomé sample [9], the coverage of the Fe network is higher than 97%, leading, as in the two other compounds, to an upper bound of a small percentage of disorder.

To further investigate the spin glass phase in these samples, we first performed thermoremanent magnetization (TRM) experiments. In the measurements described here, the sample is quenched from above T g to T m = 0.7 × T g in a magnetic field of H = 50 Oe. After a certain waiting time t w at T m , the field is switched off and the magnetization M is recorded as a function of time t. The results are shown in figure 1. They look very similar to those of standard spin glasses, displaying a very slow t w dependent relaxation. The larger t w , the slower the relaxation, and the larger the remanent magnetization at a given time t. This indicates that more and more spin correlations develop as time t w becomes larger [1][2][3]12]. From top to bottom: YMO, SCGO, Kagomé samples. The longer the waiting time t w , the slower the relaxation when the magnetic field is switched off. Just as in standard spin glasses, the ageing magnetization M(t, t w ) -A(τ 0 /t) α can be scaled (see the insets) as a function of λ/t µ w , where As can be seen in figure 1, the whole set of TRM experiments yields results very similar to those of spin glasses. Moreover, applying the standard scaling procedure used in spin glasses, (see, for example, [2]) allows a perfect scaling of all the M(t, t w ) data on a unique curve. This is obtained by fitting the relaxation curves to an expression with two additive terms. The first one is a stationary (t w independent) power law relaxation A(τ 0 /t) α which is predominant at very small times. The second term is a function F(t, t w ) of t and t w . This function is found to scale as t/t µ w at short t with µ being an exponent close to 1. In this short t region, t w is approximately the age of the system, i.e. the time spent at the measuring temperature. At larger t, the real age must be taken as t + t w ; in other words, the system continues to age as one measures its relaxation. It can then be shown that the correct scaling variable should be rewritten as λ/t µ w , where

λ = t w [(1 + t/t w ) 1-µ -1]/[1 -µ], i.e.
λ = t w [(1 + t/t w ) 1-µ -1]/[1 -µ].
Note that one recovers λ/t µ w t/t µ w for t t w , as expected. The insets of figure 1 show the plots of the function F versus this reduced variable for the present samples. The scaling is shown to apply quite well. Setting the microscopic attempt time to τ 0 = 10 -12 s, one finds fitting parameters very close to those of the standard spin glasses (see the caption of figure 1), especially for the ageing exponent µ which is slightly below 1, indicating the usual 'sub-ageing' phenomenon.

Beyond these standard TRM measurements which are performed at constant temperature (after the initial quench), experiments involving temperature variations during ageing below T g usually reveal very striking characteristic features in standard spin glasses [13,14]. For example, it is now well established that ageing at any T p < T g has no apparent effect on the state at all other temperatures sufficiently different from T p . This was found, for instance, in ZFC experiments in which modified cooling protocols were applied [13,14]. While in the usual ZFC protocol the system is cooled (at a constant cooling rate) in zero field from above T g down to the lowest temperature, in the modified protocols, the cooling is interrupted at some temperature(s) T p and resumed after some waiting time t w . In both cases, a small dc field is applied at the lowest temperature reached, and the magnetization is recorded while the system is heated up at a constant rate. The ZFC magnetization, as measured in the modified protocol, clearly showed marked singularities ('dips') centred around the temperature(s) T p . Far enough from T p , it recovered the values of the usual (reference) ZFC magnetization (see [13,14]). This showed that ageing at T p during t w did not affect the system at a temperature T different from T p . It also implied that the system kept the memory of ageing at T p while it was at lower temperatures and was able to retrieve the aged state previously reached at T p . These results proved that in spin glasses different spin correlations are building up at different temperatures, and that the correlations built up at any temperature remain imprinted at lower temperatures. In these experiments, the width of the dips gives an idea of the 'temperature selectivity' of the spin correlations. The results of such ZFC experiments are displayed in figure 2 for the three considered compounds. In this figure, the differences between the modified ZFC and the reference ZFC data are plotted as a function of temperature. Clear singularities are observed around the various chosen values of T p exactly as in spin glasses. The (3D) YMO sample as well as the SCGO material present narrow dips characterized by a value δT /T g = 0.17 ± 0.03 very close to the values found in standard spin glasses: for instance, δT /T g = 0.16 ± 0.03 in the CdCr 1.7 In 0.3 S 4 Heisenberg spin glass for comparable t w , while δT /T g = 0.21 ± 0.03 in the Fe 0.5 Mn 0.5 TiO 3 Ising spin glass. This is in contrast with the results on the Kagomé (2D) compound, where δT /T g = 0.39 ± 0.05 is remarkably larger.

The 'temperature selectivity' has been studied more quantitatively by measuring the effect at some temperature T of ageing at a slightly smaller temperature T -T . This experiment yields a TRM measurement with the following procedure: (i) after field cooling from above T g to T , the sample is kept for a short time t 1 = 500 s at constant T , (ii) it is then further cooled to T -T and aged during t 2 = 9000 s before being reheated to T where it stays for another short time (iii) last, the field is switched off and the TRM curve is recorded.

t 3 = t 1 , -2,0 0,0 0 1 2 3 4 T
From these experiments, an effective time t eff 2 can be defined such as to superimpose the measured TRM with a purely isothermal TRM recorded at temperature T with waiting time t 1 + t eff 2 + t 3 . In other words, t eff 2 is a measure of the effect at T of ageing at T -T for a time t 2 . The actual quantitative results for the presently studied materials are reported in In contrast to SCGO and YMO data, which fall within the standard spin glass area, the Kagomé data are well above this region, with a very small slope. figure 3 and compared to those obtained in [15] for the CdCr 1.7 In 0.3 S 4 Heisenberg spin glass and for the Fe 0.5 Mn 0.5 TiO 3 Ising spin glass. The results for YMO and SCGO are clearly in agreement with those of spin glasses: the slopes of t eff 2 /t 2 versus T for these two systems are indeed within the values delimited by the Heisenberg and Ising cases. As for the Fe-jarosite, the effective time t eff 2 does not vary much with the change of temperature. The system ages almost as quickly at T -T as at T , and builds up the same pattern of spin correlations at both temperatures.

The conclusion of this investigation is that, in spite of their very small amount of disorder, the two frustrated antiferromagnets, the YMO pyrochlore and the bi-Kagomé SCGO, behave exactly as standard spin glasses. The Fe-jarosite Kagomé compound, though presenting many similarities in terms of the existence of a freezing temperature and the presence of ageing effects, has quite different dynamical properties as a function of temperature. It appears, indeed, in figure 3 that t eff 2 remains very close to t 2 even for larger T , meaning that ageing at T -T contributes significantly to the age of the system at T . The behaviour is not very temperature selective, implying that the pattern of the spin correlations is not very temperature dependent. The two-dimensional character of the jarosite compound may be at the origin of the observed differences with the two other materials [16].

Figure 1 .

 1 Figure 1. Thermoremanent magnetization experiments out at T = 0.7 × T g (see the text).From top to bottom: YMO, SCGO, Kagomé samples. The longer the waiting time t w , the slower the relaxation when the magnetic field is switched off. Just as in standard spin glasses, the ageing magnetization M(t, t w ) -A(τ 0 /t) α can be scaled (see the insets) as a function of λ/t

  t w . The best fit gives parameters very close to those found in standard spin glasses. For YMO µ = 0.85, α = 0.05, A = 0.3; for SCGO µ = 0.85, α = 0.10, A = 1.35; for the Kagomé sample µ = 0.90 and A 0.0.

Figure 2 .

 2 Figure 2. Memory dip experiment (see text): M ref is measured in a standard ZFC experiment, while M(T ) corresponds to the experiment where the cooling was interrupted for a time t w at a temperature T p (marked by the dotted lines). From top to bottom: YMO, SCGO, Kagomé samples. The width of the memory dip is quite small in YMO and in SCGO (just as in standard spin glasses). It turns out to be much larger in the Kagomé sample.

Figure 3

 3 Figure 3. t eff 2 /t 2 plotted versus T / T (see text): the data for Fe 0.5 Mn 0.5 TiO 3 and CdCr 1.7 In 0.3 S 4 are plotted as examples of, respectively, an Ising spin glass and an Heisenberg spin glass. The steeper the slope in this plot, the more 'temperature-selective' the ageing (solid line: prediction assuming that ageing occurs via thermal activation with an activation energy independent on T ).In contrast to SCGO and YMO data, which fall within the standard spin glass area, the Kagomé data are well above this region, with a very small slope.

Acknowledgments

Many thanks to A S Wills (Edinburgh University, UK) for giving us the Kagomé sample, to N Blanchard (LPS, Orsay, France) and to G Collin (LLB, CEA Saclay) for preparing the SCGO sample previously studied by NMR by Ph Mendels (Orsay University, France), and to J Greedan (McMaster University, Canada) for giving us the YMO sample. The technical help of L Le Pape is greatly acknowledged.