G Jauny

F Eustache

& Hinault

Thomas Hinault
email: thomas.hinault@inserm.fr

M/EEG dynamics underlying reserve, resilience and maintenance in ageing: A review

Keywords: Aging, Cognition, M/EEG, Dementia, Connectivity

Cognitive reserve and resilience refer to the set of processes allowing the preservation of cognitive performance in the presence of structural and functional brain changes. Investigations of these concepts have provided unique insights on the heterogeneity of cognitive and brain changes associated with aging. Previous work mainly relied on methods benefiting from a high spatial precision but a low temporal resolution, and thus the temporal brain dynamics underlying these concepts remain poorly known. Moreover, while spontaneous fluctuations of neural activity have long been considered as noise, recent work highlights its critical contribution to brain functions. Here, we synthesize the current state of knowledge from MEG (magnetoencephalography) and EEG (electroencephalography) studies that investigated the contribution of maintenance of neural synchrony, and variability of brain dynamics, to cognitive changes associated with healthy aging and the progression of neurodegenerative disease (such as Alzheimer disease). The reviewed findings highlight that compensations could be associated with increased synchrony of higher (>10Hz) frequency bands. Maintenance of young-like synchrony patterns was also observed in healthy older individuals. Both maintenance and compensation appear to be highly related with preserved structural integrity (brain reserve).

However, increased synchrony was also found to be deleterious in some case and reflect neurodegenerative processes. These results provide major elements on the stability or variability of functional networks as well as maintenance of neural synchrony over time, and their association with individual cognitive changes with aging. These findings could provide new and interesting considerations about cognitive reserve, maintenance, and resilience of brain functions and cognition.

Introduction

Understanding the evolution of cognition as we age is crucial, not only because it is intimately related to everyone's subjective experience, but to help describing and better understanding cognition itself. Cognitive aging is a highly variable phenomenon, characterized by a decline in cognitive abilities that might lead to higher risk of pathological aging in some individuals, while others are able to remain efficient in most everyday tasks until an advanced age [START_REF] Reuter-Lorenz | How Does it STAC Up? Revisiting the Scaffolding Theory of Aging and Cognition[END_REF]. Research on the variability of age-related changes across individuals aims at answering at several questions, such as the factors associated with preserved cognitive functioning with age (the "why" question), or what differs between individuals with preserved versus declined cognitive performance (the "how" question). While lifestyle activities associated with reduced risk of cognitive decline and pathological aging have been extensively investigated and specified (see Livingstone et al., 2020, for a recent review), a mechanistic understanding of the neural bases underlying individual differences with advancing age remains to be further developed. Achieving this goal requires the use of highly sensitive methods, and the investigation on brain activity with high spatial and temporal resolutions.

The concept of cognitive reserve has originally been proposed to improve our understanding of mechanisms underlying sustained cognitive performance in spite of agerelated and pathology-related brain changes [START_REF] Stern | What is cognitive reserve? Theory and research application of the reserve concept[END_REF]. Over the last two decades, this concept has undergone several changes and developments (see [START_REF] Cabeza | Maintenance, reserve and compensation: the cognitive neuroscience of healthy ageing[END_REF][START_REF] Stern | Whitepaper: Defining and investigating cognitive reserve, brain reserve, and brain maintenance[END_REF]Pascual-Leone & Bartréz-Faz, 2021). The current concepts of maintenance, resistance, and resilience have been proposed to specify the heterogeneity brain and cognitive changes in face of aging and neurodegenerative disease. During healthy aging, maintenance [START_REF] Nyberg | Memory aging and brain maintenance[END_REF] refers to the relative absence of brain changes with advancing age, while reserve [START_REF] Stern | What is cognitive reserve? Theory and research application of the reserve concept[END_REF] encompasses the compensatory processes allowing the preservation of cognitive performance in presence of structural and functional brain changes. The concept of reserve involves two complementary aspects: brain reserve (i.e. individual differences in brain size, number of synapses, etc.) and cognitive reserve (i.e. individual differences in the cognitive processes and brain networks recruited to perform a given task). With the progression of neurodegenerative disorders, resistance (Arenaza-Urquijo & Vemuri, 2018) defines the protection of brain reserve against alterations and the prevention of brain lesions and damages before their occurrence. Finally, resilience (Pascual-Leone & Bartréz-Faz, 2021) concerns the processes involved in the compensation of changes occurring with the development of neurodegenerative disorders, explaining various degrees of symptomatology in the face of an equal pathological load. Some degree of overlap may exist between these concepts. As an example, compensatory adjustments (e.g., increased frontal recruitment) might be implemented in presence of both age-and pathology-related changes, yet qualitative differences may also be observed between the adjustments implemented in response of healthy aging and pathology. A recent review of Pascual-Leone and Bartrés-Faz (2021) specified these concepts and emphasized the need for individually-based markers that could predict an individual's risk for disability and cognitive decline.

Neuroimaging studies have been central in the emergence and evolution of the concepts of reserve, maintenance, and resilience. Several decades of work aimed at investigating structural (i.e., grey matter, white matter) and functional (i.e., local activity, association between the activity of distinct brain regions) changes with age and pathology (e.g., [START_REF] Damoiseaux | Effects of aging on functional and structural brain connectivity[END_REF][START_REF] Spreng | The aging brain: functional adaptation across adulthood[END_REF]. Recent work revealed that these dimensions are closely related, with large-scale brain functional network relying on a structural architecture of white matter fibers (e.g., [START_REF] Hinault | Age-related differences in the structural and effective connectivity of cognitive control: A combined fMRI and DTI study of mental arithmetic[END_REF][START_REF] Suárez | Linking Structure and Function in Macroscale Brain Networks[END_REF]. Indeed, preserved brain integrity has been associated with preserved cognitive functioning. This work also identified compensatory adjustments in older adults (i.e., larger activations, bilateral recruitment) associated with similar cognitive performance to that of younger individuals (e.g., [START_REF] Cabeza | Maintenance, reserve and compensation: the cognitive neuroscience of healthy ageing[END_REF]. These studies mainly relied on high spatial resolution methods such as functional magnetic resonance imaging (fMRI), characterized by excellent spatial accuracy but low temporal resolution (in the order of seconds). Therefore, the temporal dynamics of brain networks and the influence of age and pathology on these dynamics remain poorly known. Investigating these dynamics with high temporal-resolution methods (in the order of milliseconds) such as magnetoencephalography (MEG) or electroencephalography (EEG) is important because higher cognitive functions such as memory and cognitive control that are most affected by age and pathology involve multiple cognitive processes in rapid successions and short durations (e.g., Courtney & Hinault, 2021).

Even when compensation may mask these changes in clinical or neuropsychological assessment, specifying dynamic network connectivity may reveal alterations of the stability of communications between brain regions, or delays in the fast succession of connectivity patterns, providing a better understanding of concepts of reserve, maintenance, resilience and resistance.

The brain generates its own temporal structure, that is critical to the ways in which signals are routed, combined and coordinated (e.g., [START_REF] Bao | Synchronization as a biological, psychological and social mechanism to create common time: A theoretical frame and a single case study[END_REF][START_REF] Voytek | Dynamic Network Communication as a Unifying Neural Basis for Cognition, Development, Aging, and Disease[END_REF].

Brain rhythms present the particularity of being observed across species (e.g., Buzaki 2006), which suggest a major evolutionary advantage of rhythmic communications (e.g., Miller et al., 2018). Brain rhythms are distinguished in different frequency bands (delta (1-4Hz), theta ). Magnetoencephalography and electroencephalography (M/EEG) methods enable the investigation of these rhythms and dynamic connectivity patterns in humans (e.g., [START_REF] Baillet | Magnetoencephalography for brain electrophysiology and imaging[END_REF]. Given the critical involvement of coordinated brain rhythms in higher-order cognitive processing, age-related changes in the dynamic of brain communications may act as a marker for cognitive decline in older adults. Such complex interplay across rhythms is highly sensitive to structural changes and the progression of neurodegenerative disorders (e.g., Courtney & Hinault, 2021;[START_REF] Gaubert | EEG evidence of compensatory mechanisms in preclinical Alzheimer's disease[END_REF], as even small changes of dynamic synchrony can lead to cognitive decline with aging (e.g., [START_REF] Hinault | Disrupted neural synchrony mediates the relationship between white matter integrity and cognitive performance in older adults[END_REF][START_REF] Hinault | Age-related differences in network structure and dynamic synchrony of cognitive control[END_REF]Kumral et al., 2021).

Here, we review EEG and MEG studies in healthy older individuals and in patients to identify elements that shed new lights on cognitive aging and pathology effects. We focus on three main patterns: 1) compensatory or resilience adjustments when brain dynamics are altered, 2) maintenance of these dynamics in the face of aging or pathology and 3) non-effective or maladaptive changes related to normal aging or pathology. These concepts have been extensively investigated with fMRI, we thus aimed at highlighting the complementary contribution of M/EEG findings. M/EEG can indeed detect between group differences in the initiation, maintenance, or interruption of brain communication at the sub-second level, which is therefore highly sensitive to early disruptions associated with age and pathology. In this review, we will first present studies contributing to these concepts in healthy aging before presenting work on pathological aging. Given the work conducted in pathological aging, we focused on Alzheimer's disease and his preclinical stage the Mild Cognitive Impairment (MCI).

We conclude with recommendations and future directions that could guide and stimulate future studies. Such endeavor could lead to new cognitive stimulations strategies targeting brain rhythms, and reduce the cognitive decline commonly associated with age.

Normal aging

Nineteen M/EEG studies including younger (20 years -30 years) and older (60 years -85 years) healthy participants have been selected, investigating cognitive performance and neural synchrony data (see table 1). We will describe here three of the most commonly used techniques. First, the Phase locking value (PLV; [START_REF] Lachaux | Measuring Phase Synchrony in Brain Signals[END_REF] measures whether the oscillatory phase of the activity of a group of neurons, in a certain frequency band, can transiently synchronize with those of another group of neurons. This transient phase-locking has been associated with communications between neural groups [START_REF] Fries | Rhythms For Cognition: Communication Through Coherence[END_REF]. A second technique similar to this is the Phase lag index (PLI; [START_REF] Stam | Phase lag index: Assessment of functional connectivity from multi-channel EEG and MEG with diminished bias from common sources[END_REF], which measures the asymmetry of the distribution of phase differences between two signals. Finally, coherence [START_REF] Nunez | EEG coherency I: statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales[END_REF] measures the associated of signals' amplitudes across brain regions. These measures and provides information about neural synchrony and the presence of functional connectivity between brain regions. The main results studied in this section are illustrated in Figure 1.A.

Compensation

In older individuals with similar levels of cognitive performance as younger individuals, previous MRI studies have shown that older individuals frequently engage additional brain regions, as described in the CRUNCH (Compensation Related Utilization of Neural Circuit Hypothesis. [START_REF] Reuter-Lorenz | Neurocognitive Aging and the Compensation Hypothesis[END_REF] model. This increased recruitment of brain regions has been associated with cognitive performance, and is referred to as compensation [START_REF] Cabeza | Maintenance, reserve and compensation: the cognitive neuroscience of healthy ageing[END_REF]. [START_REF] Angel | Individual differences in executive functioning modulate age effects on the ERP correlates of retrieval success[END_REF][START_REF] Angel | Two hemispheres for better memory in old age: Role of executive functioning[END_REF] investigated this phenomenon in EEG using ERP (Event-related potential). They revealed larger bilateral activity in older individuals with higher cognitive performance. M/EEG studies critically identified that an increased synchronization of fronto-parietal regions has been observed in older individuals showing preservation of cognitive functioning. [START_REF] Ariza | Evaluating the effect of aging on interference resolution with timevarying complex networks analysis[END_REF] asked healthy young and elderly participants to perform an interference-based working memory task in which participants were asked to memorize a face/sound pair (a face was displayed and associated with a semantic attribute). The pair was followed by an interference phase during which a known face with a question about that person was presented to them. Finally, a recognition phase in which participants were asked to tell whether the presented pairs were the same as those presented in the encoding phase. This study reported a global increase in alpha synchrony (measured by PLV) in older individuals compared to younger individuals, while both groups showed similar cognitive performance. This increased alpha synchrony has only been observed during the interference period, and has been interpreted as a compensatory mechanism in older individuals.

Using an inhibitory task, [START_REF] Hong | Age-related differences in the modulation of small-world brain networks during a Go/NoGo task[END_REF] showed that an increase in phase synchrony of the delta and theta frequency bands localized at the fronto-central and parieto-central areas reflected a compensatory phenomenon in healthy older individuals (see also Phillips & Takeda,2010, for similar findings in the gamma frequency band). Also, a posterior-anterior synchrony switch (increase of delta synchrony in anterior versus posterior position) was also found to be compensatory for a face emotion recognition task [START_REF] Aktürk | Age related differences in the recognition of facial expression: Evidence from EEG event-related brain oscillations[END_REF]. These compensatory phenomena are not only found in cognitive tasks, but also for motor tasks. [START_REF] Rosjat | Stimulus transformation into motor action: Dynamic graph analysis reveals a posterior-to-anterior shift in brain network communication of older subjects[END_REF], for example, showed increases in delta and theta synchrony (measured by PLV) in healthy elderly, in association with sustained motor performance at the same level as in young people (see also [START_REF] Rosjat | Aging-associated changes of movement-related functional connectivity in the human brain[END_REF].

Maintenance

Increased brain activity is not systematic and it is important to note that some individuals do not need to implement these compensations, possibly because of higher cognitive reserve levels [START_REF] Stern | Cognitive reserve[END_REF]. Lopez et al. (2014b), in a study comparing the global connectivity (with PLV and PLI) of older participants with higher or lower cognitive reserve, showed compensatory phenomena from the latter group only. Indeed, while cognitive performance was similar between low and high reserve participants, individuals with lower reserve showed increased in theta, alpha and beta synchrony in frontal, temporal and occipital regions. This suggests that some individuals show a more efficient network functioning and therefore do not need to engage a more extended brain network. Relatedly, [START_REF] Ho | Age-related changes of taskspecific brain activity in normal aging[END_REF] showed that lower theta and alpha synchrony levels (measured with coherence and phase-locking measures) in the parietal region, associated with similar performance than younger individuals.

Maintenance thus refers to the preservation of similar brain activity levels than younger individuals, allowing cognitive abilities to be relatively preserved with advancing age [START_REF] Nyberg | Memory aging and brain maintenance[END_REF]. MRI work showed, for example, that older individuals with little changes in functional activity during encoding, relative to younger adults, can sometime perform better than older individuals with larger activation changes (Duzel et al., 2011). Studies on this phenomenon are, to our knowledge, rare. [START_REF] Rondina | Age-related changes to oscillatory dynamics during maintenance and retrieval in a relational memory task[END_REF] investigated the preservation of brain dynamics with aging, using a spatial memory task where participants were asked to remember the spatial location of three objects seen separately. In the test phase, participants were then asked to determine whether the location of the objects was the same or different than in the memory phase. They revealed that older individuals showed a similar pattern of brain activations than young participants, with an increase theta band oscillatory activity in occipital regions, and a decrease in frontotemporal regions. The maintenance of this brain activity pattern was associated with similar cognitive performance between age groups. Also, in a visual attention task, young and older individuals showed a similar pattern of increased lower gamma frequency activity in the frontal region with increasing task difficulty [START_REF] Phillips | Frontal-parietal synchrony in elderly EEG for visual search[END_REF]. Moreover, [START_REF] Coquelet | The electrophysiological connectome is maintained in healthy elders: A power envelope correlation MEG study[END_REF] in working memory in order to determine whether proposed equation results (e.g., 8 x 4 = 36) were correct or incorrect. Preserved integrity of white matter fibers at a similar level to younger participants, in some older individuals, was associated with preserved functional synchrony in the alpha and gamma frequency bands, and similar cognitive performances between age groups.

In particular, the inferior fronto-occipital tract was associated to functional coupling between the inferior frontal gyrus and the occipital lobe. These results also illustrate the strong association with the preservation of brain reserve, which would enable such maintenance [START_REF] Stern | Cognitive reserve[END_REF].

Thus, the maintenance of functional synchrony with age (at rest and during task completion) is associated with the preservation of cognitive functions in healthy elderly individuals. This maintenance has mainly been observed between frontal and parietal regions. However, the preservation of this functional synchrony at a similar level to younger individuals is frequently associated with an increased synchrony in other brain regions. [START_REF] Liu | Age-related changes in oscillatory power affect motor action[END_REF] showed that a maintenance of delta and theta synchrony of central regions (measured with the PLI), in the absence of increased activity in other regions, was associated with decreased motor and cognitive performance. This suggests that maintenance is strongly linked to the presence of functional compensations. However, such increased brain activity could also be deleterious, reflecting network alteration and the presence of excitotoxic or neurodegenerative phenomena [START_REF] Hillary | Injured Brains and Adaptive Networks: The Benefits and Costs of Hyperconnectivity[END_REF].

Non-effective changes

With advancing age, changes in brain function can be compensatory (as discussed above), but may also turn out to be ineffective. In an EEG study (Toth et al., 2014), young and old healthy participants had to perform a working memory task consisting of remembering coloured squares at certain locations. During the test phase, these squares remained at the same locations but could change in colour. Participants had to determine whether squares were identical to those displayed during the encoding phase or not. Synchrony was determined with the PLI measure, and a specific decrease in theta synchrony between frontal and posterior sites was observed in healthy older adults compared to younger individuals (see also [START_REF] Li | Age-related inter-region EEG coupling changes during the control of bottom-Up and top-Down attention[END_REF].

Importantly, this theta synchrony decrease has been associated with lower cognitive performance. Also, increased high gamma synchrony in the left frontal region during a maze task (visual planning task) has been shown to be negatively associated with performance (Paul et al., 2005).

In one of our studies (Jauny et al., 2022), we showed that maladaptive changes can be identified in resting-state activity. This study involved the Cam-CAN cohort (e.g., [START_REF] Shafto | The Cambridge Centre for Ageing and Neuroscience (Cam-CAN) study protocol: a cross-sectional, lifespan, multidisciplinary examination of healthy cognitive ageing[END_REF][START_REF] Taylor | The Cambridge Centre for Ageing and Neuroscience (Cam-CAN) data repository: Structural and functional MRI, MEG, and cognitive data from a cross-sectional adult lifespan sample[END_REF] and changes in synchrony (with the PLV measure) as well as directed connectivity (with the entropy transfer measure, which provides a directed connectivity measure) were investigated. We observed a greater variability in brain networks' synchrony over time relative to younger individuals, mainly for the Default Mode Network (DMN; this network is mainly activated when no task is proposed from the participant and plays a role in continuous environmental monitoring; [START_REF] Uddin | Towards a universal taxonomy of macro-scale functional human brain networks[END_REF] in the delta frequency band.

Moreover, we showed that older individuals showed a revered dominant direction in information transfer, relative to younger individuals, with a significant increase in the anterior to posterior direction of functional connectivity. These changes were correlated with a decline in cognitive performance on tests measuring working memory, attention and logical reasoning (also [START_REF] Sahoo | Lifespan associated global patterns of coherent neural communication[END_REF]. This reversal of the dominant information transfer direction could represent a failed compensation attempt. The increases in brain synchrony studied could also reflect excitotoxic processes [START_REF] Hillary | Injured Brains and Adaptive Networks: The Benefits and Costs of Hyperconnectivity[END_REF]Mai & Howell, 2019), with increased activity preceding neuronal loss. Indeed, older individuals showing these hyperconnectivity phenomena had decreased cognitive performance.

As we have seen in these different sections, changes in synchrony vary over time and with task difficulty, and increased synchrony is not always beneficial. These changes appear to be related to changes in the level of white matter fibers integrity [START_REF] Hinault | Disrupted neural synchrony mediates the relationship between white matter integrity and cognitive performance in older adults[END_REF][START_REF] Hinault | Age-related differences in network structure and dynamic synchrony of cognitive control[END_REF]. Indeed, with the presence of white matter lesions has been associated with decreased brain synchrony [START_REF] Wessel | Neural synchrony indexes impaired motor slowing after errors and novelty following white matter damage[END_REF]. In association with the influence of potentially preclinical excitotoxic processes, structural and functional changes could reflect the progression of neurodegenerative disorders.

Pathological Aging

In this part, we considered M/EEG study involving patients with Alzheimer's disease (AD) and its prodromal stage called MCI (Mild Cognitive Impairment). AD is the most common agerelated pathology and is characterized by memory and cognitive control impairment (involving inhibition, planification and mental flexibility; [START_REF] Baudic | Executive function deficits in early Alzheimer's disease and their relations with episodic memory[END_REF]. The investigation of early AD stages such as the MCI stage is of significant interest because some individuals will later develop AD while others will remain stable or develop other pathologies such as, for example, frontotemporal or vascular dementia (e.g. [START_REF] Perez-Gonzalez | Description and classification of normal and pathological aging processes based on brain magnetic resonance imaging morphology measures[END_REF][START_REF] Jongsiriyanyong | Mild Cognitive Impairment in Clinical Practice: A Review Article[END_REF]. The reviewed studies were selected based on the same criteria as in the previous section on normal aging (see table 1). The main results studied in this section are illustrated in Figure 1.B.

Resilience

In line with the reserve concept developed in healthy older individuals, resilience refers to the processes involved in coping with the development of neurodegenerative disorders and the associated brain changes (Pascual-Leone & Bartréz-Faz, 2021). Indeed, resilience allows, like reserve, the preservation of cognitive functions in spite of brain changes. Few studies have documented this phenomenon. [START_REF] Gaubert | EEG evidence of compensatory mechanisms in preclinical Alzheimer's disease[END_REF] compared resting state EEG data (phase synchrony calculated using PLV and PLI) from preclinical AD patients (at two AD progression stages), and control participants. They observed that the degree of neurodegeneration (measured by the level of amyloid beta load) impacted functional connectivity. Higher alpha functional connectivity in parieto-occipital sites was observed when amyloid load levels were low. This increase in alpha connectivity was interpreted as reflecting a compensatory phenomenon, as patients showed normal cognitive performance (measured by the Free and Cued Selective Reminding Test, assessing episodic memory). In presence of high amyloid loads, theta functional connectivity was decreased. It was suggested that amyloid deposits could negatively impact the extracellular environment, preventing compensatory adjustments. Moreover, Bajo et al. ( 2010) administered a memory task to healthy elderly MCI participants with similar performance levels than controls. They reported an increased interhemispheric gamma, beta, and alpha synchrony in MCI participants compared to controls. This increase in synchrony has been interpreted as reflecting compensatory adjustments in MCI individuals. The presence of interhemispheric activit is in line with the HAROLD (Hemispheric Asymmetry Reduction in Older; [START_REF] Cabeza | Aging Gracefully: Compensatory Brain Activity in High-Performing Older Adults[END_REF] model. Finally, an overall increase in theta synchrony has been reported in fronto-occipital and right parieto-temporal areas for MCI individuals during the performance of a mental arithmetic task thus allowing the maintenance of cognitive performance (Lopez et al., 2014a). These resilience phenomena have been reported in patients with MCI, but may not always be necessary. Indeed, Lopez et al., (2014b) showed that increases in synchrony were reduced in individuals with greater reserve.

Resistance

Resistance refers to the prevention of brain injury and damage before their occurrence (Pascual-Leone & Bartréz-Faz, 2021). AD is characterized by advanced brain and cognitive impairments, being the results of years of neurodegenerative processes, and therefore resistance phenomenon can no longer be observed. However, investigating the earlier stages of this disease, Lopez et al. (2014a) used a mental arithmetic task (mental subtraction) at two levels of difficulty (subtracting from one to one, being the easy level, and subtracting from three to three being the hard level). Both MCI patients and controls showed similar cognitive performance. Furthermore, lower synchrony at rest, and increased delta synchrony in frontal interhemispheric regions during task completion (measured with PLV), were similar across groups. Thus, there seems to be a maintenance of certain brain functions in early AD stages. However, such maintenance of specific brain communications was associated with compensatory increases in synchrony in other brain regions in MCI patients. The concept of resistance, alone, would therefore not allow the maintenance of cognitive performance in individuals at risk of developing a neurodegenerative disease. Furthermore, increased synchrony in individuals with MCI was initially associated with preservation of brain and cognitive functioning, but may also be a sign of disease progression [START_REF] Knyazeva | Evolution of source EEG synchronization in early Alzheimer's disease[END_REF].

Maladaptive changes

Despite the presence of maintained synchrony patterns and the ability of some individuals to compensate for disease-related brain damage, individuals with MCI also exhibit brain changes associated with impaired cognitive performance. For example, Caravaglios et al, (2016) showed that increases in beta synchrony in aMCI patients correlated with poorer performance on various neuropsychological tests (Trail making test, Rey Auditory Verbal Learning Test, Semantic Verbal Fluency). Maladaptive changes thus occur and could be due to disturbances in the integrity of white matter fibers. Altered white matter integrity has indeed been shown to result in decreased alpha synchrony in individuals with MCI, particularly in parietal regions [START_REF] Teipel | Regional networks underlying interhemispheric connectivity: an EEG and DTI study in healthy ageing and amnestic mild cognitive impairment[END_REF]. Synchrony analyses have also revealed decreased connectivity in frontal and parieto-temporal alpha and beta activity, especially in interhemispheric couplings, associated with impaired cognitive performance (digit verbal span task; [START_REF] Li | Dynamic cortical connectivity alterations associated with Alzheimer's disease: An EEG and fNIRS integration study[END_REF].

Thus, maladaptive changes appear to differ depending on AD progression level. [START_REF] Garn | Quantitative EEG markers relate to Alzheimer's disease severity in the Prospective Dementia Registry Austria (PRODEM)[END_REF] revealed that qEEG markers such as decreased delta synchrony in parietal regions could have a predictive role in AD severity. Indeed, synchrony measures could discriminate between SCD (Subjective Cognitive Decline; defined by a subjective complaint without cognitive impairment), MCI, and AD individuals [START_REF] Houmani | Diagnosis of Alzheimer's disease with Electroencephalography in a differential framework[END_REF]. Using measures of synchrony (bump model) and complexity (epoch-based entropy), the authors discriminated AD patients from SCD patients with high specificity (91.6% accuracy, 100% specificity and 87.8% sensitivity). Their results showed that AD patients showed increased EEG synchrony in the theta band on frontal and occipital region compared to SCD patients. These differences could be explained by the degradation or lower cognitive reserve in AD patients (Montemurro et al., 2021).

Discussion

Results reviewed here highlight the importance of considering the temporal dynamics of brain activity, and synchronized brain communications, to our understanding of cognitive reserve, resilience and maintenance in healthy and pathological aging. Dynamic connectivity patterns must display both stability and flexibility as a function of the cognitive process involved, and task context. While the stability of dynamics in the network engaged is important to process relevant information, flexibility is required to adjust to goal changes and to inhibit the processing of irrelevant information (e.g., [START_REF] Voytek | Dynamic Network Communication as a Unifying Neural Basis for Cognition, Development, Aging, and Disease[END_REF]. Cognitive decline during healthy and pathological aging can result from impairments of such dynamic network activity. While further investigations remain necessary, the present review summarizes current work on the association of sustained, increased or altered neural synchrony across brain regions, with cognitive preservation or decline.

While reserve has been associated with increased frontal synchrony in the theta and alpha bands [START_REF] Ariza | Evaluating the effect of aging on interference resolution with timevarying complex networks analysis[END_REF][START_REF] Hong | Age-related differences in the modulation of small-world brain networks during a Go/NoGo task[END_REF], resilience has been associated with increased alpha, beta and gamma synchrony (e.g., [START_REF] Bajo | Functional Connectivity in Mild Cognitive Impairment During a Memory Task: Implications for the Disconnection Hypothesis[END_REF]. It is important to note that not all changes are associated with a relative preservation of cognitive performance. Indeed, maladaptive changes have also been reported, such as the increased delta synchrony in posterior regions (Jauny et al., 2022). Findings suggest that (a) the neural mechanisms involved in both reserve and resilience could be partly similar, and (b) resilience could involve a stronger involvement of higher frequency bands relative to reserve. This difference could be determined by the degree of preservation of the structural network integrity, which is modulated by the pathology progression, leading to different compensation levels. Yet, whether differences across reserve and resilience are mainly of quantitative nature, or also qualitative, remains to be further clarified.

Maintenance-related patterns were also observed in healthy older individuals, with a relative absence of impairments in fronto-parietal communication dynamics associated with preserved cognitive performance [START_REF] Hinault | Disrupted neural synchrony mediates the relationship between white matter integrity and cognitive performance in older adults[END_REF], 2021[START_REF] Rondina | Age-related changes to oscillatory dynamics during maintenance and retrieval in a relational memory task[END_REF]. The brain's structure-function interplay appears to be at the heart of the heterogeneity associated with maintenance during aging (Courtney & Hinault, 2021;Jauny et al., 2022). Indeed, maintenance was observed with preserved dynamics in the relative absence of integrity loss. Conversely, reserve-related adjustments are a necessity in presence of reduced structural integrity. The inability of any of these two mechanisms will lead to cognitive decline. Additional longitudinal studies remain necessary to further specific the concepts of maintenance and resistance mechanisms. Another open question for future research lies in the distinction between hyperactivation or hyperconnectivity resulting from (a) failed compensatory attempts, although that some degree of network reorganization has been implemented, and (b) excitotoxic processes associated with the progression of neurodegenerative disorders. Direct investigations, associated with longitudinal follow-up, will be necessary to further clarify this distinction.

While these findings are promising, they only reflect a fraction of M/EEG aging studies.

Future studies in the field could integrate the following recommendations to further address the contribution of brain dynamics. First, while resting-state measurements are indicators of the potential for brain networks' reorganization in cognitively challenging situations, they cannot always inform on their actual implementation and association with specific cognitive processes.

Although few studies were conducted to address these issues, we expect that dynamic stability and flexibility of task-related networks could provide critical elements regarding subsequent cognitive changes and the effect of cognitive stimulation programs. In line with recent questioning in the field (e.g., [START_REF] Finn | Movie-watching outperforms rest for functional connectivity-based prediction of behavior[END_REF], it also appears critical to question whether restingstate recording can precisely measure elements of cognitive reserve. Although changes can be observed in brain activity at rest, specific task-related delays in the implementation, maintenance or interruption of communications across brain regions could be highly sensitive to age and pathology effects. Recent work [START_REF] Babiloni | Resting-state electroencephalographic delta rhythms may reflect global cortical arousal in healthy old seniors and patients with Alzheimer's disease dementia[END_REF]Guntenkin et al., 2021) highlighted the clinical value of investigating oddball-related brain activity to detect pathology effects. Finally, from an epidemiological perspective, future studies should also consider middle-aged individuals (40-60 years) to clarify the association between changes in brain dynamics and later cognitive trajectories. Indeed, age-related brain changes occur throughout life, and changes in older individuals (> 65 years) may be the result of earlier brain changes.

Also, it appears critical that future studies include a more diverse population, especially in terms of education level (de Olivera et al., 2018;[START_REF] Ashby-Mitchell | Proportion of Dementia Explained by Five Key Factors in Jamaica[END_REF]. Indeed, most of the reviewed studies considered populations with a high level of education, which limits the investigation of reserve and resilience mechanisms.

Many studies relied on methods that are blind to temporal changes, such as amplitude comparison following averaging of large time periods. This facilitates data analyses but could lead to missing important information. Hidden-Markov models [START_REF] Tibon | Transient neural network dynamics in cognitive ageing[END_REF] or multiscale entropy [START_REF] Mcintosh | Spatiotemporal Dependency of Age-Related Changes in Brain Signal Variability[END_REF] enable the specification of time-varying connectivity states, which could further our understanding of the heterogeneity of cognitive aging. Finally, the majority of the reviewed studies involved sensor-based analyses and brain connectivity methods, such as coherence analyses. While the reviewed work reveals important patterns associated with resilience and maintenance, they are prone to volume conduction effects (e.g., [START_REF] Brunner | Volume conduction influences scalp-based connectivity estimates[END_REF] and suffer from low spatial accuracy. A more generalized use of nonbiased connectivity estimates (e.g., Allouch et al., 2020), associated with source reconstruction of M/EEG activity, could clarify some open questions and replicate the currently reported findings. This would also enable the investigation of the same networks and regions of interest as previous fMRI work [START_REF] Pascual-Leone | Human Brain Resilience: A Call to Action[END_REF], to specify their time course and dynamics.

Brain connectivity changes observed in M/EEG could differentiate individuals according to pathology stages [START_REF] Houmani | Diagnosis of Alzheimer's disease with Electroencephalography in a differential framework[END_REF] in a non-invasive manner. These data could also help predicting pathology progression. Specifying rhythmic brain communication changes with age and pathology could also guide direct modulations of brain rhythms through targeted stimulations. Recent work, such as [START_REF] Reinhart | Working memory revived in older adults by synchronizing rhythmic brain circuits[END_REF], revealed the feasibility of short-term interventions using tACS (transcranial Alternative Current Stimulation; application of a low intensity current to the brain with electrodes in order to synchronize or desynchronize brain oscillations) on working memory performance in healthy older adults. Improved working memory performance (up to 50 min post-stimulation) has been reported in healthy older adults following frontotemporal theta stimulation relative to a sham condition. Several points, such as the long-term benefits of these interventions, together with the optimal number of sessions, remain to be specified. Such knowledge could lead to new specific and neurophysiologically grounded intervention targeting disrupted brain communications and enhancing rhythms associated with successful compensation, suggesting an intense development of this research field in the coming years.

  investigated MEG phase synchrony at rest and reported a maintenance of the electrophysiological connectome with age. Coquelet and colleagues observed similar patterns between age groups in the alpha and beta frequency bands. The maintenance of synchrony in the beta band was positively correlated with the maintenance of cognitive performance in older individuals. This functional maintenance seems to critically depend on the maintenance of the underlying structures of the brain networks. Hinault et al. (2020) investigated the structurefunction relationship between Diffusion Tensor Imaging (DTI) and EEG data of neuronal synchrony (PLV) of young and old healthy participants. Authors used an arithmetic task, in which participants had to maintain, or update, arithmetic operations (addition, multiplication)

Figure 1 :

 1 Figure 1: Illustration of the main results of this study: Each point represents a brain region and each color a frequency band (orange: delta; blue: theta; yellow: alpha; green: beta, pink: gamma). (A): Normal Aging. This row of three brains summarizes the main results found in this review (change in synchrony in different regions for different frequency bands relative to younger individuals) for the notions of compensation, maintenance and non-effective changes in normal aging. (B): Pathological Aging. This row of three brains summarizes the main results found in this review (change in synchrony in different regions for different frequency bands, relative to healthy controls) for the notions of resilience, resistance and maladaptive changes in pathological aging. Using BrainNet-viewer tool.

Table 1 :

 1 Summary table of the resultsAn overall increase in theta synchrony was reported in the right fronto-occipital and parieto-temporal regions for the MCI group, as well as an increase in delta synchrony in the interhemispheric frontal regions. All this would allow the MCI group to have similar cognitive performance to the healthy elderly group Resistance

	726
					Healthy Aging
	Lead author	Publication date	Measure	Method	Task	Participants (age)	N	Results
					Compensation
						Young healthy adults		The global increase in alpha synchrony is
	Ariza et al.	2015	MEG	PLI	Working memory	(21.88) Older healthy adults	9 11	positively correlated with the maintenance of cognitive performance in
						(64.45)		the elderly group
	Aktürk et al.	2020	EEG	Coherence	Facial expressions recognition task	Young healthy adults (24) Older healthy adults (62.07)	15 15	Increased delta, theta, and alpha synchrony in frontal position in healthy elderly would allow maintenance of cognitive performance compared to the young
								Increased delta and theta phase
				Phase		Young healthy adults	23	synchronization in the fronto-central and
	Hong et al.	2016	EEG	synchronization	Go/NoGo	(21.4)		parieto-central areas is associated with
				analysis		Older healthy adults (61)	18	the maintenance of cognitive
								performance for the elderly group
								Increased gamma synchronization in the
	Phillips & Takeda	2010	EEG	PLV	Visual search	Older healthy adults (68)	14	fronto-parietal position is positively correlated with cognitive performance in
								the elderly group
								Maintenance of the increase in delta
						Young healthy adults (22-	21	synchronization in the elderly (similar to
	Rosjat et al.	2018	EEG	PLV	Finger tap	35) Older healthy adults (60-		the young group) could enable the maintenance of cognitive performance in
						78)	31	this same group compared to the young
								group

EEG: Electroencephalography; MEG: Magnetoencephalography; PLI: Phase Lag Index; PLV: Phase Locking Value; TE: Transfer Entropy

Author Contributions Statement

GJ: Investigation, Writing; FE: Supervision, Review; TH: Conceptualization, Supervision, Writing, Review.

Conflict of Interest Statement

The authors report no declarations of interest.


A Bailly

P Bouvier

S Grenier

T Hajlaoui

M Gaudin

A Y Ramos

M Chaker

L Laversenne

Interplay between boron doping and epitaxial relationships in VO 2 films grown by laser ablation

Keywords: Boron-doped VO 2 films, Epitaxial growth, Metal-to-insulator transition, Temperature-dependent measurements, X-ray diffraction, Raman spectroscopy

In this contribution, the effect of boron doping on the functional and structural properties of VO 2 thin films is investigated. Temperature-dependent measurements were performed on pure and boron-doped (0.5 and 1.3 at.%) VO 2 films grown on Al 2 O 3 (0001) by Reactive Pulsed Laser Deposition. Increasing the boron concentration leads to a noticeable decrease of the transition temperature (by ∼ 12°C), accompanied by a significant modification of the hysteresis loop shapes. The phase transition occurs at ca. 73 °C in the undoped film, while it drops down to ca. 60 °C in the film containing the highest boron amount. The undoped sample exhibits the best resistivity contrast (about 4 orders of magnitude) with a relatively narrow hysteresis cycle (∼ 6 °C). The most doped sample has a broad and significantly reduced resistivity contrast (less than 3 orders of magnitude). Raman spectroscopy and high-resolution X-ray diffraction were performed to elucidate the nature of the involved phases and their structure. A correlation was found between increasing the boron concentration and the formation of two peculiar in-plane epitaxial relationships; the VO 2 films evolving from one to the other. We also evidenced the presence of the transient M2 phase in the most doped sample.

Introduction

Vanadium dioxide in its bulk form exhibits a reversible insulator-metal transition (IMT) at a critical temperature T IMT of 68°C. The drastic change of the electrical resistivity goes along with a crystallographic phase transformation, changing from the insulating monoclinic M1 phase below T IMT to the metallic tetragonal R (rutile) phase beyond. The optical transmittance in the infrared range is also strongly affected, as VO 2 reversibly switches from transparent below T IMT to opaque above it. Based on these peculiar optical and electrical thermally-driven changes, many applications are targeted, such as : thermochromic windows Zhou et al. [START_REF] Zhou | Vo2 thermochromic smart window for energy savings and generation[END_REF], optical fibers [START_REF] Nouman | Vanadium dioxide based frequency tunable metasurface filters for realizing reconfigurable terahertz optical phase and polarization control[END_REF] or passive radiators [START_REF] Hendaoui | Enhancement of the positive emittance-switching performance of thermochromic vo2 films deposited on al substrate for an efficient passive thermal control of spacecrafts[END_REF]. For these developments, VO 2 films are usually deposited on amorphous or crystalline substrates. In this latter case, the possible existence of specific epitaxial relationships between the VO 2 film and the substrate provides invaluable opportunities to tailor the film properties via strain engineering [START_REF] Muraoka | Metal-insulator transition of vo2 thin films grown on tio2 (001) and (110) substrates[END_REF].

Chemical doping of VO 2 is another strategy to tune its electrical and optical properties. The objectives of elemental doping are twofold: i) electronic, by increasing a carrier concentration and ii) structural, by inducing atomic cell distortions. The nature of the dopant element (size and valence) plays a crucial role [START_REF] Cui | Thermochromic vo 2 for energy-efficient smart windows[END_REF]. Numerous studies report on the influence of substitutional doping with high-valence metallic cations, such as W, Re or Mo. Experimental studies related to doping with light elements are instead very scarce. Actually, introducing such light elements into the VO 2 structure is experimentally challenging since they are either too light (as B) or too volatile (as N and C), which explains why most studies deal with heavier elements. Hydrogenation induces the formation of the metallic R phase at temperatures much lower compared to pure VO 2 , even at room temperature depending on the hydrogen concentration [START_REF] Wu | Hydrogen-incorporation stabilization of metallic vo2(r) phase to room temperature, displaying promising low-temperature thermoelectric effect[END_REF][START_REF] Zhao | Hydrogen-doping stabilized metallic vo2 (r) thin films and their application to suppress fabry-perot resonances in the terahertz regime[END_REF][START_REF] Chen | Sequential insulator-metal-insulator phase transitions of Vo 2 triggered by hydrogen doping[END_REF]. For boron-doped VO 2 , the insulator-metal transition was theoretically investigated by Density Functional Theory (DFT) calculations [START_REF] Wan | Density functional theory study of m-doped (m = b, c, n, mg, al) vo2 nanoparticles for thermochromic energy-saving foils[END_REF][START_REF] Zhang | Boron-tuning transition temperature of vanadium dioxide from rutile to monoclinic phase[END_REF]. It was demonstrated that the boron atoms sit in interstitial positions within the VO 2 lattice and that a strong decrease of the transition temperature should be expected. B-doped VO 2 samples were obtained in different forms following various synthesis techniques: boron incorporated by diffusive doping into nanobeams and nanoparticles [START_REF] Alivio | Postsynthetic route for modifying the metal-insulator transition of vo2 by interstitial dopant incorporation[END_REF], thin films doped by ion implantation [START_REF] Ufert | Doping of vo2 thin films by ion implantation[END_REF], nanoparticles obtained by hydrothermal synthesis [START_REF] Zhou | Reducing transition temperature and diluting brown-yellow color of vo2 films via embedding ag particles periodic arrays[END_REF]. Some coworkers in the present study recently reported on the evolution of the insulator-metal transition of VO 2 films doped with low amounts of boron (up to 1.6 at. %) [START_REF] Hajlaoui | Metal-insulator transition temperature of boron-doped vo2 thin films grown by reactive pulsed laser deposition[END_REF]. The B-doped VO 2 films were synthesized by Reactive Pulsed Laser Deposition (RPLD) on Si(100) substrates. The IMT temperature is drastically reduced due to the boron doping (∼ 31 °C / at. %), characterized by interstitial atoms in the VO 2 lattice. The transition temperature T IMT even drops down to 17.5 °C for 1.6 at. % of boron. The 4 + valence of the vanadium atoms is kept, whatever the boron concentration; but the incorporation of boron into the VO 2 lattice tends to stabilize the R phase at much lower temperature compared to bulk VO 2 . In the present paper, the effect of the two factors (B doping and epitaxial growth) on the functional and structural properties of RPLD-synthesized VO 2 films on Al 2 O 3 (0001) is investigated. The temperature-dependent measurements highlight the evolution of the phases nature and their epitaxial relationships, as a function of the boron concentration and temperature.

Experimental details

Sample synthesis

Pure and boron-doped VO 2 films have been synthesized using PLD on c-oriented sapphire substrates (Al 2 O 3 (0001)) by ablating vanadium and mosaic vanadium/boron targets [START_REF] Hajlaoui | Metal-insulator transition temperature of boron-doped vo2 thin films grown by reactive pulsed laser deposition[END_REF]. A KrF excimer laser beam (wavelength of 248 nm and pulse duration of 25 ns) was focused on the targets at a repetition rate of 10 Hz. Sapphire substrates were used due to their lattice parameter that allows the epitaxial growth of VO 2 films (mismatch ∼ +4 %) as well as for their high resistivity, making them appropriate for resistivity measurements of the deposited films. During deposition, the targets were placed at a distance of 6.5 cm in front of the substrate, while the laser beam was focused on the target forming a 1.65 mm 2 spot size that results in a laser fluence of 2 J.cm -2 on target. To improve the uniformity of both target ablation and films thicknesses, the laser beam was scanned across the target and both substrate and targets were maintained in a rotating motion during deposition. To achieve well-crystallized and epitaxial films, the substrate temperature and the background oxygen pressure were kept at 500 °C and 30 mTorr, respectively. The final film thickness was in the range 80-100 nm. The boron concentration was determined by X-ray Photoelectron Spectroscopy (XPS), with an accuracy of ± 0.1 at. %, and boron atoms have been shown to sit in interstitial positions [START_REF] Hajlaoui | Metal-insulator transition temperature of boron-doped vo2 thin films grown by reactive pulsed laser deposition[END_REF]. Three samples are studied hereafter: pure VO 2 and VO 2 doped with 0.5 at. % and 1.3 at. % of boron. They are respectively called B0, B05 and B13.

X-ray diffraction

The X-ray diffraction (XRD) experiments were performed with two distinct setups. The room-temperature (RT) specular scans were recorded with a D8 Advance X-ray diffractometer (Bruker), with Cu K α1 radiation (λ = 1.54056 Å), in a Bragg-Brentano θ /2θ geometry, equipped with a Johansson monochromator and a linear Lynxeye detector. Reciprocal space mapping and temperature-dependent XRD measurements were performed with a high-resolution X-ray diffractometer (SmartLab, Rigaku Corp.) equipped with a 9 kW rotating Cu anode and a 5-circle goniometer, in a parallel beam mode. The oven used for temperature cycles (Anton Paar; accuracy ±1°C) was capped with a carbon dome, flushed and then swept by a slight nitrogen flux to avoid sample oxidation. Extrinsic thermal effects were counteracted by systematically checking the sample surface alignment with respect to the incident X-ray beam and optimizing the measured reflections at each temperature. The experimental set-up and the scan types performed are thoroughly described in a previous paper [START_REF] Bailly | Three-phase metal-insulator transition and structural alternative for a vo2 film epitaxially grown on al2o3[END_REF]. Crystalline phase identification was also done by recording specular θ /2θ scans. In this case, a 2-bounce Ge(220) crystal was used for monochromatization on the Cu K α1 emission line. Finally, a specific configuration allows to record the diffraction signal arising from lattice planes perpendicular to the sample surface. The in-plane epitaxial relationships of the VO 2 films with respect to the Al 2 O 3 (0001) substrate can thus be determined. In this case, the Ge monochromator was removed to increase the count rate and the grazing incidence angle was fixed to ∼ 0.3°.

Raman spectroscopy

Unpolarized Raman scattering experiments have been performed in a backscattering geometry with the final stage of a Horiba T64000 spectrometer using a 1800 grooves.mm -1 grating (blazed at 500 nm) and rejecting the Rayleigh line with an edge dichroic beamsplitter (LP02-514RE-25 RazorEdge, Semrock). This allowed to measure a relative wavenumber range of 100 to 750 cm -1 . The entrance slit was 100 µmwide providing a spectral resolution of 0.7 cm -1 . The spectrometer was calibrated in wavenumber by using the 520.6 cm -1 phonon of a Si(100) reference wafer. A continuous argon laser beam (Spectra Physics, λ = 514.5 nm) was focused onto the VO 2 film into a spot of 2 to 4 µm in diameter, using a long-distance lens (Olympus ×50 magnification). The laser power was adjusted to 0.25 mW in front of the lens to ensure a good signal and to avoid any thermal effect that could trigger the insulator-metal transition. The sample temperature was cycled by using a temperature-controlled stage (Linkam, THMS 600 controller) in the range 25°C -85°C. The sample chamber was swept with argon to avoid a phase transformation towards V 2 O 5 or V 6 O 13 , often observed when VO 2 is heated in air [START_REF] Vilanova-Martínez | Laser heating induced phase changes of vo2 crystals in air monitored by raman spectroscopy[END_REF]. The spectral parameters (wavenumber, half-width at half maximum and area) were obtained from the decomposition of each spectrum with several Lorentzian peaks and a linear background using the Fityk software [START_REF] Wojdyr | Fityk: a general-purpose peak fitting program[END_REF]. The accuracy on the wavenumber values was estimated to be ± 0.2 cm -1 .

Fourier transform infrared spectroscopy

The Fourier transform infrared (FT-IR) spectroscopic measurements were performed at the CARMALIM platform (IRCER Laboratory, University of Limoges). A Thermo Fischer Scientific spectrometer (Nicolet 6700), equipped with a specular reflection accessory (Harrick Scientific ERA 12°), was used. The temperature was cycled using a Peltier sample stage with a LFI-3751 temperature controller and the reflectivity was collected at a wavelength of 3 µm. The background level was calibrated on a c-oriented bare sapphire substrate.

Results and discussion

Morphological and electrical properties

The four-point probe resistivity measurements, as well as Scanning Electron Microscopy (SEM) images of the VO 2 films, are shown in Fig. 1. Boron doping clearly affects the grain morphology: the higher the boron concentration, the smaller the grains. We observe that the incorporation of boron effectively decreases the transition temperature averaged between heating and cooling cycles. T IMT drops from 72.6 °C (+/-0.1 °C) for the undoped sample to 62.3 °C and 60.5 °C for the 0.5 at.% and 1.3 at.% borondoped samples, respectively. However, increasing the boron concentration in the films induces a significant decrease of the resistivity contrast (from more than 4 orders of magnitude to less than 3), as well as a broadening of the hysteresis width (6 °C, 8 °C and 18 °C for the B0, B05 and B13 samples, respectively). Overall, there is no simple trend of the electric properties with respect to the B doping in these films.

The evolution of the transition temperature with the amount of boron inserted in the VO 2 lattice might seem surprising as T IMT does not decrease linearly with the increase of the boron concentration. We also note that the transition temperatures of our samples are substantially higher than the ones already reported in the literature [START_REF] Alivio | Postsynthetic route for modifying the metal-insulator transition of vo2 by interstitial dopant incorporation[END_REF][START_REF] Zhou | Reducing transition temperature and diluting brown-yellow color of vo2 films via embedding ag particles periodic arrays[END_REF][START_REF] Hajlaoui | Metal-insulator transition temperature of boron-doped vo2 thin films grown by reactive pulsed laser deposition[END_REF], except Ufert et al. who do not observe any effect of boron doping on the transition temperature [START_REF] Ufert | Doping of vo2 thin films by ion implantation[END_REF]. Several parameters are known to influence T IMT , such as the synthesis technique and conditions (impacting among other things the vanadium valence state and the amount of intrinsic point defects), the existence of strains in the material (induced by epitaxy or doping) and the eventual addition of a dopant element. In the case of boron doping, it was recently suggested that thermal and time histories might play a crucial role as interstitial boron atoms could diffuse in the VO 2 lattice, leading to a gradual modification of both T IMT and resistivity [START_REF] Bradicich | Probing relaxation dynamics and stepped domain switching in boronalloyed vo2[END_REF] (and references therein).

Identification of the VO 2 phases through the IMT

Temperature-dependent Raman spectroscopy was used to identify the VO 2 phases appearing during the insulator-metal transition. The Raman spectra of the B13 sample recorded upon heating from 25°C to 80°C are reported in Fig. 2. When increasing the temperature, we observe a progressive disappearance of the monoclinic phase Raman signature toward an almost featureless spectrum, revealing the transition to the high temperature metallic rutile phase. The Raman spectra recorded for the B0 and B05 samples behave qualitatively the same and are therefore not shown.

The VO 2 monoclinic M1 (point group: C 5 2h ) and the rutile R (point group: D 14 4h ) phases exhibit very different Raman signals. The M1 phase is characterized by 18 Raman active modes (9 A g and 9 B g ) [START_REF] Schilbe | Raman scattering in vo2[END_REF][START_REF] Schilbe | Lattice dynamics in vo2 near the metalinsulator transition[END_REF][START_REF] Chou | Vanadium oxide nanowire phase and orientation analyzed by raman spectroscopy[END_REF][START_REF] Zaghrioui | Polarized raman scattering of large crystalline domains in vo2 films on sapphire[END_REF][START_REF] Shibuya | Polarized raman scattering of epitaxial vanadium dioxide films with low-temperature monoclinic phase[END_REF]; some of which being very intense such as A g (1) at 194 cm -1 , A g (2) at 225 cm -1 , A g (3) at 310 cm -1 and A g [START_REF] Wu | Hydrogen-incorporation stabilization of metallic vo2(r) phase to room temperature, displaying promising low-temperature thermoelectric effect[END_REF] at 620 cm -1 . The R phase exhibits broad Raman modes (at 140 cm -1 , 450 cm -1 , 655 cm -1 and 850 cm -1 for B 1g , E g , A 1g and B 2g , respectively) [START_REF] Srivastava | Raman spectrum of semiconducting and metallic vo 2[END_REF][START_REF] Gervais | Lattice dynamics of oxides with rutile structure and instabilities at the metal-semiconductor phase transitions of nbo 2 and vo 2[END_REF] that are hardly measurable because of its metallic nature. The monoclinic M2 phase (point group: C 3 2h ) was first examined by Raman spectroscopy in chromium-doped VO 2 [START_REF] Marini | Optical properties of v 1-x cr x o 2 compounds under high pressure[END_REF]. This phase is expected to display as many Raman modes as the M1 phase, but with an upshift of A g (1) (to 201 cm -1 ) and A g (2) (to 228 cm -1 ), as well as a downshift of A g (3) (to 296 cm -1 ) [START_REF] Jones | Nano-optical investigations of the metalinsulator phase behavior of individual vo2 microcrystals[END_REF][START_REF] Strelcov | Doping-based stabilization of the m2 phase in free-standing vo2 nanostructures at room temperature[END_REF][START_REF] Goncharuk | Electronelectron correlations in raman spectra of vo2[END_REF]. Similar wavenumber shifts were interpreted as an effect of the oxygen stoichiometry [START_REF] Parker | Raman scattering from vo 2 single crystals: A study of the effects of surface oxidation[END_REF]. The establishment of the M2 phase presence is often based only on Intensity (arb. u.) 700 600 500 400 300 200

Wavenumber (cm -1 ) 25°C 35°C 45°C 50°C 55°C 58°C 60°C 62°C 64°C 66°C 68°C 70°C 75°C 80°C B13 (heating) A g (1)
A g (2)

A g (3) the observation of the 640 cm -1 Raman peak [START_REF] Zhang | Direct correlation of structural domain formation with the metal insulator transition in a vo2 nanobeam[END_REF]. However, this mode is much broader than the low wavenumber modes and it is located in a wavenumber region where at least three peaks of the M1 phase are also present. For these reasons, we consider that this unique criterion is not strong enough to draw an unambiguous conclusion. We believe that the temperature evolution of the low wavenumber Raman modes of VO 2 (which involve mainly vanadium displacements) is more accurate for studying the appearance of the transient M2 phase, even though this frequency range is in practice more difficult to access (spectrometer cut-off generally around 200 cm -1 ). The temperature dependence of the integrated total area of the monoclinic Raman modes (A g (1) + A g (2)) is shown in Fig. 3 along with the electrical resistance measured simultaneously between two tungsten probes inside the Linkam heating stage. The observed hysteresis loops are typical of the first-order insulator-to-metal transition. In the case of B13, it is interesting to note that the Raman intensity of the (A g (1) + A g (2)) modes does not exactly follow the electrical resistance measured concomitantly during the heating step, unlike the undoped or weakly doped samples (B0 and B05). The "excess" in the Raman intensity progressively vanishes while approaching the IMT.

The reflectivity in the mid-infrared region at 3 µm is shown in Fig. 3 (bottom right), while cycling the samples between RT and 90 °C. The transition from the insulating to the metallic state is illustrated via the change of the reflecting properties with tempera- ture. Close to room temperature, the incident beam is poorly reflected by the surface of the VO 2 films which appear to be almost transparent at this specific wavelength and the pure VO 2 sample exhibits a sligthly higher reflectivity. When increasing the temperature, the films gradually get metallic, leading to an increase of the reflectivity. Whatever the temperature, the B13 sample is much less reflective than the two other samples. Qualitatively, the width and amplitude of the hysteresis observed for each sample are similar to the general trend described by the electrical measurements.

Fig. 4 shows the temperature dependence of the A g (1, 2, 3) phonon wavenumbers of the monoclinic M1 phase measured in the B0, B05 and B13 samples, as well as for a reference bulk VO 2 single-crystal. The crystal displays the classical wavenumber temperature downshift which is the typical behavior expected from anharmonic effect [START_REF] Balkanski | Anharmonic effects in light scattering due to optical phonons in silicon[END_REF]. In the temperature range explored during our measurements (25 to 85°C), the wavenumber temperature dependence can be described by a linear function as indicated by the full black line in Fig. 4. It is worth noticing that the Raman modes of the Al 2 O 3 (0001) substrate measured at 441 and 586 cm -1 through the VO 2 films show the same linear downshift when the temperature increases (not shown).

Up to roughly 10-15°C before the transition to the rutile phase, the three A g (1, 2, 3) Raman modes measured in the films display the same linear downshift of their wavenumber. However, when approaching the IMT, the B13 sample differs from the less doped ones (B0 and B05). We observe that the A g (1) and A g (2) Raman modes shift , A g (2) and A g (3) phonons as a function of temperature, for the three films and a bulk VO 2 single-crystal (SC). Full and dashed lines are guides for the eyes. The M2 phase is evidenced in the case of the B13 sample at ∼ 65°C, through an upshift of the A g (1) and A g (2) phonon wavenumbers.

in the opposite direction compared to what is expected considering only the temperature effect. The fact that these two modes shift upwards, whereas the A g (3) mode shifts downwards, suggests that the monoclinic M2 phase is present before the transition to the rutile phase. The appearance of the M2 phase also supports the observation made earlier in Fig. 3, regarding the gap observed between the Raman intensity and the electrical resistance. The Raman intensity of the (A g (1) + A g (2)) modes does not allow to differentiate the M1 and M2 phases because both exhibit intense Raman signatures in this energy range. Only the dependence of these two modes on temperature allows to confirm the presence of the M2 phase. This was already proposed in a previous work dealing with an undoped VO 2 film and involving some of the co-authors of the present article [START_REF] Bailly | Three-phase metal-insulator transition and structural alternative for a vo2 film epitaxially grown on al2o3[END_REF]. This is also well explained by Okimura et al. who observed that the 195 cm -1 , 224 cm -1 and 620 cm -1 phonon modes of the M1 phase display a phonon hardening above a given temperature, whereas the corresponding phonon modes of the M2 phase exhibit a standard behavior due to the lattice thermal expansion (see Figure 4 in Ref. [START_REF] Okimura | Temperature-dependent raman and ultraviolet photoelectron spectroscopy studies on phase transition behavior of vo2 films with m1 and m2 phases[END_REF]). The convergence of the M1 phase Raman wavenumbers towards the ones of the M2 phase indicates that the low temperature M1 phase transforms to the rutile one via a transient structure similar to the M2 phase. The same upshifts of the 195 cm -1 , 225 cm -1 and 620 cm -1 phonons were described as a fingerprint of the T-M2 transformation in [100]-oriented single crystalline nanobeams on r-cut sapphire substrates with temperature [START_REF] Chang | Probing the photothermally induced phase transitions in single-crystalline vanadium dioxide nanobeams[END_REF]. These upshifts were also interpreted as a transformation to a triclinic cell as a bridge between M1 and M2 monoclinic phases in individual, homogeneous VO 2 single crystalline microbeams grown on a silicon substrate [START_REF] Atkin | Strain and temperature dependence of the insulating phases of vo2 near the metalinsulator transition[END_REF]. The authors proposed that, regardless the VO 2 film strain state, the monoclinic M2 structure is an ubiquitous phase for the transition to the rutile phase. The M2 phase formed prior to the IMT was also proposed based on the same wavenumber shifts for VO 2 films of different thicknesses deposited on c-cut sapphire substrates [START_REF] Nazari | Finite size effect on the phase transition of vanadium dioxide[END_REF]. Using the phenomenological Landau model, Tselev et al. [START_REF] Tselev | Symmetry relationship and strain-induced transitions between insulating m1 and m2 and metallic r phases of vanadium dioxide[END_REF] explained that the M1 and M2 phases are two different ways to respond to the same instability of the rutile lattice. Consequently, while M1 is the stable lower-symmetry phase of unstrained VO 2 in ambient conditions, a small perturbation can stabilize the M2 phase with respect to the M1 phase or bring the M1, M2 and R phases to coexist. In our case, it is interesting to notice that the A g (1) Raman modes (at 193-195 cm -1 ) observed for the three samples are positioned at a slightly higher wavenumber than that of the relaxed bulk VO 2 crystal (∼ 192 cm -1 ); the B13 sample showing the biggest upshift. The A g (2) Raman mode of B0 and B13 is positioned at roughly the same wavenumber as in the relaxed VO 2 crystal (224 cm -1 ), whereas it is positioned at a slightly lower wavenumber for B05. The A g (3) mode position (∼ 309 cm -1 at 25 °C) is less affected, when comparing the films and the single crystal. These wavenumber positions are due to epitaxial strains created in the films. The Raman modes respect symmetry constraints and can therefore be considered as a fingerprint of the stress field stored in the films due to in-and out-of-plane strains imposed by the substrate.

Growth and in-plane orientations

The growth orientation of the VO 2 films and their epitaxial relationships with respect to the Al 2 O 3 (0001) substrate were determined by temperature-dependent X-ray diffraction at room temperature and by cycling the samples up to 90°C.

Growth orientations

The specular θ /2θ scans recorded at room temperature (Fig. 5) show clear diffraction peaks from the VO 2 films and the (0001)-oriented Al 2 O 3 substrate. The diffraction peaks of the VO 2 films are located at 2θ ∼ 40°and 86°. These positions are associated to the (020) and (040) reflections of the monoclinic M1 phase, corresponding to [010]oriented VO 2 films. This conclusion is supported by the measurement of the (220) and its equivalent reflections, featuring an azimuthal six-fold symmetry (not shown) as a consequence of three in-plane epitaxial variants from the three equivalent orientations of VO 2 (010) planes with respect to the (0001) Al 2 O 3 basal plane [START_REF] Chen | Vo2 multidomain heteroepitaxial growth and terahertz transmission modulation[END_REF] (see also section 3.3.2 below). This growth orientation is often observed for epitaxial VO 2 films synthesized on Al 2 O 3 (0001) [START_REF] Théry | Role of thermal strain in the metal-insulator and structural phase transition of epitaxial vo2 films[END_REF][START_REF] Okimura | Changes in lattice parameters of vo2 films grown on c-plane al2o3 substrates across metal-insulator transition[END_REF][START_REF] Okimura | In situ x-ray diffraction studies on epitaxial vo2 films grown on c-al2o3 during thermally induced insulator-metal transition[END_REF][START_REF] Wong | Epitaxial variants of vo2 thin films on complex oxide single crystal substrates with 3m surface symmetry[END_REF][START_REF] Wu | Single-crystalline epitaxy and twinned structure of vanadium dioxide thin film on (0001) sapphire[END_REF], meaning that the V-V zig-zag chains lie in the surface plane. No additional diffraction peaks are observed indicating that no other vanadium oxide phases are present at room temperature. The insets of Fig. 5 highlight the difference between sample diffraction peaks: while B0 and B05 exhibit a similar, single peak shape, B13 reflections have at least two components. At ∼ 86°, B0 and B05 behave similarly with temperature, whereas B13 keeps its multi-component peak shape, even in the high temperature metallic phase (Fig. 6).

The behavior of these reflections with temperature is nonetheless qualitatively the same: the Bragg angle shifts towards lower values while heating the samples; an effect mainly dominated by the occurrence of the insulator-metal transition.

Let's first discuss the results obtained for the B0 and B05 samples. We know from Raman spectroscopy that both samples exhibit a typical M1 -→ R transition with heating. Fitting the (040) M1 reflection (Fig. 5) gives the b unit-cell parameter along the growth direction: 4.513 Å for B0 and 4.508 Å for B05. These values compare to the theoretical one for bulk VO 2 (4.538 Å), indicating a slight compressive strain along the growth direction of -0.55% for B0 and -0.66% for B05. These values are consistent with the ones already reported for films of a similar thickness [START_REF] Jian | Continuous tuning of phase transition temperature in vo2 thin films on c-cut sapphire substrates via strain variation[END_REF][START_REF] Théry | Structural and electrical properties of large area epitaxial vo2 films grown by electron beam evaporation[END_REF]. Given the transformation relationships between the M1 and the R phases [START_REF] Marezio | Structural aspects of the metal-insulator transitions in cr-doped vo2[END_REF], the high-temperature reflection therefore corresponds to the (400) R of the rutile tetragonal phase.

Figure 7 shows the evolution of the d hkl spacing with increasing temperature of the (040) M reflection for the three samples. The occurrence of the IMT is clearly visible on the d hkl values through an increase over the temperature range investigated. Finally, the (400) R Bragg peak positions were found be equal to 86°for B0, 86.03°for B05 (1.1294 Å and 1.1291 Å in terms of d spacing). It corresponds to a R lattice parameters of 4.518 and 4.516 Å, respectively, confirming the contraction in the out-of-plane direction (∼ -0.8% compared to the bulk R phase [START_REF] Rogers | An x-ray diffraction study of semiconductor and metallic vanadium dioxide[END_REF]). Regarding the B13 sample, the (040) M reflection was fitted with two components, peaking at 85.88°and 86.50°(at RT). Figure 7 therefore shows the evolution with temperature of the two corresponding d hkl spacings. The occurrence of the IMT is clearly visible through a more drastic increase of the d hkl in the temperature region of interest.

The existence of a multiple-component peak in the case of the B13 sample would call for more investigations to be understood. However, we can draw some conclusions and propose hypotheses. First, we dismiss the possibility of an inhomogeneous introduction of boron in the VO 2 lattice leading to a strain gradient in the film thickness. Such inhomogeneous insertion was the case reported by Jia et al. [START_REF] Jia | 3d local manipulation of the metal-insulator transition behavior in vo2 thin film by defect-induced lattice engineering[END_REF] showing similar diffraction spectra for 100 keV Ne + -implanted VO 2 films grown by PLD on Al 2 O 3 (0001). The implantation of Ne + ions led to an important lattice expansion in the direction perpendicular to the substrate and even gave rise, for the highest Ne + fluence, to a splitted diffraction peak with a component clearly shifted to lower Bragg angles. This Ne + concentration gradient in the film thickness induced a two-step insulator-metal transition, which is not observed in the B13 sample. However, the experiment of Jia et al. is quite different from ours where boron is incorporated at much smaller energy, simultaneously with the VO 2 growth.

Instead, we raise the hypothesis that the high-angle reflection follows the behavior of lattice parameter with the boron doping: at room temperature we measured 86.1°for B0, 86.2°for B05 and then 86.5°for B13. This reflection would be a M1 phase with a b lattice parameter that decreases with increasing boron concentration. This M1 phase Turning to the lower angle reflection, which is more intense, it also has a very interesting behavior with temperature: it exhibits a very strong displacement at the transition, with an angular shift between room and high temperature about twice as large compared to B0 and B05 (∼ 0.36°compared to 0.12°and 0.18°for B0 and B05). In fact, this displacement is of the same order than for undoped bulk VO 2 . This looks like the behavior of a phase nearly free to expand out of plane, yet somehow oriented by the substrate. We believe that the situation we observe is more likely the consequence of combined strain and composition effects. In the 85.5°-86.5°angular range, several hkl reflections might appear (see Tab. 1), but we definitely know from our Raman measurements that the M2 phase is present in the case of the B13 sample. We might thus assume that this low-angle contribution corresponds to the signature of the M2 phase somehow stabilized by strain effects. Despite the uncertainty remaining on the lower angle reflection assignment, two conclusions can be drawn: i) the corresponding interplanar spacings, d hkl , are systematically smaller than the theoretical ones, indicating a compressive strain along the out-of-plane direction, and ii) the axis corresponding to the V-V dimer chains always lie in the film surface plane.

In-plane epitaxial relationships

In a previous work, we reported on two possible in-plane epitaxial relationships for a [010] M1 -oriented VO 2 film on Al 2 O 3 (0001) [START_REF] Bailly | Three-phase metal-insulator transition and structural alternative for a vo2 film epitaxially grown on al2o3[END_REF]. These two structural models were designated as diagonal and on-axis. The main difference in these two is the inplane orientation of the VO 2 film, aligning either on the These models can be disentangled by recording the (200) M1 and (002) M1 in-plane reflections close to the Al 2 O 3 (1120) reflection. In the case of the diagonal model, a triplet and a doublet are respectively expected for these peculiar reflections, whereas it will give rise to a doublet and a singlet in the case of the on-axis model. We recorded a reciprocal space map (RSM) at room temperature for the pure VO 2 (B0) and 1.3 at. % Bdoped VO 2 (B13) samples (Fig. 8). The presence of a triplet and a doublet points to the diagonal model in the case of the B0 sample, as already observed for a thicker pure VO 2 film on Al 2 O 3 (0001) [START_REF] Bailly | Three-phase metal-insulator transition and structural alternative for a vo2 film epitaxially grown on al2o3[END_REF]. On the contrary, the B13 sample has an on-axis arrangement, as indicated by the doublet and singlet of its RSM. Figure 8 also shows the (200) M1 and (002) M1 reflections recorded at room temperature for the three samples. The 0.5 at. % B-doped sample shows the same signature as pure VO 2 (triplet and doublet), therefore pointing to a diagonal arrangement. The peaks width (roughly inversely proportional to the grains lateral size) gradually increases with the boron concentration: 2.5°, 3.2°and 4°for B0, B05 and B13, respectively. It confirms that the grain size decreases when the boron amount increases, in good agreement with the SEM images.

Conclusions

Boron-doped VO 2 films were successfully grown on Al 2 O 3 (0001) by Pulsed Laser Deposition. We highlighted that boron insertion globally induces a decrease of the transition temperature, but a trade-off has to be found between the reduction of T IMT and optimum functional properties. Indeed, although 0.5 at. % of boron improves the overall properties, further increasing the boron amount to 1.3 at. % leads to a hysteresis broadening. At this concentration, Raman spectroscopy evidences the presence of the M2 phase in addition to the M1 phase before the transition temperature, while X-ray diffraction reveals that this sample has a different in-plane epitaxial orientation with respect to the sapphire substrate. In the out-of-plane direction, this sample also exhibits a peculiar signature underlying the co-existence of the two phases (with one being nearly free to expand out of plane, yet somehow oriented by the substrate). The qualitatively different behaviors observed for the three films suggest that boron doping might help in tuning the functional properties according to the final application.

4

 4

Figure 1 :

 1 Figure 1: (Top) SEM images of the pure and boron-doped VO 2 samples. From left to right: undoped VO 2 (B0), doped with 0.5 at. % of B (B05) and 1.3 at. % of B (B13). (Bottom) Electrical resistance as a function of temperature.

Figure 2 :

 2 Figure 2: Raman spectra of the B13 sample recorded upon a heating step. The three VO 2 A g modes of interest for our purpose have been indicated and the main Raman modes of the Al 2 O 3 (0001) substrate are indicated by dashed lines.

Figure 3 :

 3 Figure 3: (a) to (c) Raman doublet area (left vertical scale) and electrical resistance (right vertical scale) as a function of temperature for different doping concentrations; (d) Reflected intensity at 3 µm as a function of temperature.

Figure 4 :

 4 Figure4: From top to bottom : Evolution of the wavenumbers of the A g (1), A g (2) and A g (3) phonons as a function of temperature, for the three films and a bulk VO 2 single-crystal (SC). Full and dashed lines are guides for the eyes. The M2 phase is evidenced in the case of the B13 sample at ∼ 65°C, through an upshift of the A g (1) and A g (2) phonon wavenumbers.

Figure 5 :

 5 Figure 5: Specular θ /2θ scans of the three samples at room temperature. Multiple scattering peaks from the substrate are indicated (MS). Insets are zooms on the films reflections.

Figure 6 :

 6 Figure 6: (040) M reflection recorded as a function of temperature during a heating step: (a) pure VO 2 (B0), (b) 0.5 at. % B-doped sample (B05), (c) 1.3 at. % B-doped sample (B13). The inset for B13 highlights the two components used for fitting the data.

  angle comp.) B13 (high angle comp.)

Figure 7 :

 7 Figure 7: d spacings calculated from the 2θ positions of the (040) M reflections (heating step). The temperature-dependent curves of the B13 sample were fitted with two components, therefore leading to two distinct d spacing values.

(

[21 30 ]

 30 Al 2 O 3 (diagonal) or on the [10 10] Al 2 O 3 (on-axis) crystallographic directions of the Al 2 O 3 (0001) substrate. This leads to the following epitaxial relationships (in the rutile cell coordinates): • for the diagonal model: [011] R [21 30] Al 2 O 3 , • for the on-axis model: [010] R [10 10] Al 2 O 3 and [001] R [12 30] Al 2 O 3 .

Figure 8 :

 8 Figure 8: (top) In-plane RSMs of the B0 (left) and B13 (right) samples recorded below 50°C (in the insulating phase), close to the (1120) Al2O3 substrate reflection . The hkl reflections of VO 2 are indexed in the monoclinic system. (bottom) Cross-sectional scans of the monoclinic reflections at room temperature. The data, centered on φ = 0°, have been shifted for clarity by 20°and 40°for B05 and B13, respectively.

Table 1 :

 1 Potential reflections between 85.5°and 86.5°and corresponding bulk values for 2θ B and d hkl .

		400) R (040) M1 (004) M1 (800) M2 (004) M2
	2θ (°)	85.15	85.53	85.66	85.47	85.69
	d hkl (Å) 1.1385 1.1344	1.1330	1.1351	1.1328

Acknowledgments

The LANEF framework (ANR-10-LABX-51-01) is acknowledged for its support with mutualised infrastructure, as well as the Agence Nationale de la Recherche through the ANR-15-CE08-0035 Smart_VOx project. We also thank Frédéric Gay (I. Néel) for his assistance in performing the in situ electrical measurements using the Linkam sample stage. Dr Julie Cornette and Pr Corinne Champeaux (CNRS, IRCER, Limoges) are gratefully acknowledged for their help with the FT-IR experiments.