Gabriela Bar-Nes

Ofra Klein-Bendavid

Laure Chomat

Nathalie Macé

Michal Arbel-Haddad

Stéphane Poyet

Sr immobilization in irradiated Portland cement paste exposed to carbonation


Anis Aloulou

Cédric Luduc

François Duforez

Julien Piscione

Jeremy Cheradame

François Bieuzen

Claire Thomas

Mounir Chennaoui

Pascal Van Beers

Mathieu Nedelec
email: mathieu.nedelec@insep.fr

Effect of an Innovative Mattress and Cryotherapy on Sleep after an Elite Rugby Match

Keywords: POLYSOMNOGRAPHY, CORE BODY TEMPERATURE, MUSCLE DAMAGE, RECOVERY

Introduction: This study aimed to explore the relationship between elite rugby union match and post-match sleep architecture and to investigate the effects of a high-heat capacity mattress (MAT) and a whole-body cryotherapy session (WBC) on post-match sleep architecture.

Methods:

Nineteen elite male U23 rugby union players performed in three official matches, followed by three experimental conditions, in a randomized order: MAT, WBC, and no intervention (CONT). Match load was evaluated using global positioning system (GPS) trackers and video analyses. Sleep architecture was assessed by polysomnography (PSG). Core body temperature (CBT) and mattress surface temperature were monitored during sleep. Linear mixedeffects models were conducted to assess the effects of each experimental condition on sleep, with match load variables as covariates. Results: A lower wake after sleep onset (β = -10.5 min, p < 0.01) and higher rapid-eye-movement sleep proportion (β = +2.8%, p < 0.05) were reported for MAT compared with CONT. Moreover, a lower mean CBT (β = -0.135°C, p < 0.001) and mean mattress surface temperature (β = -2.736°C, p < 0.001) during sleep were observed for MAT compared CONT. Whole-body cryotherapy did not affect nocturnal CBT nor interfere with sleep architecture. For every 100-m increase in high-speed running distance, a higher slow-wave sleep (SWS; β = +1.1%, p = 0.05) and lower light sleep proportion (β = -1.2%, p < 0.05) proportion were observed. Conversely, for every 10 supplementary collisions, a lower SWS (β = -1.9, p = 0.09) and higher light sleep (β = +2.9%, p < 0.001) proportion were observed. Conclusion: MAT use had a positive effect on sleep architecture after an elite rugby union match, potentially through a more efficient nocturnal heat transfer.

Introduction

Rugby union is a high-intensity, intermittent sport, played worldwide [START_REF] Duthie | Applied physiology and game analysis of rugby union[END_REF]. During match play, high-speed running and collision-based activities, such as tackling, static holds, scrums, rucks, and mauls, have been shown to induce high levels of fatigue and muscle damage [START_REF] Mclellan | Biochemical and endocrine responses to impact and collision during elite rugby league match play[END_REF][START_REF] Tavares | Fatigue and recovery in rugby: a review[END_REF].

Professional teams play weekly matches and train twice daily for two or more consecutive days [START_REF] Mclean | Neuromuscular, endocrine, and perceptual fatigue responses during different length between-match microcycles in professional rugby league players[END_REF], which can make player readiness for competitions challenging. Therefore, the optimal management of the recovery process is required to minimize training-and competition-induced fatigue [START_REF] Mujika | An Integrated, Multifactorial Approach to Periodization for Optimal Performance in Individual and Team Sports[END_REF]. Sleep is recognized by the scientific community and by players to be a major component of the recovery process [START_REF] Tavares | Fatigue and recovery in rugby: a review[END_REF][START_REF] Venter | Perceptions of team athletes on the importance of recovery modalities[END_REF]. A previous study examining rugby union players showed that the mean sleep time was reduced by approximately one hour and sleep efficiency was reduced by approximately 4.5% on nights following a match compared with nights following regular training days [START_REF] Shearer | Effects of competition on the sleep patterns of elite rugby union players[END_REF]. Reductions in sleep quantity have been shown to negatively impact physical performance [START_REF] Azboy | Effects of sleep deprivation on cardiorespiratory functions of the runners and volleyball players during rest and exercise[END_REF] and increase injury risk [START_REF] Rosen | Too little sleep and an unhealthy diet could increase the risk of sustaining a new injury in adolescent elite athletes[END_REF]. Previous studies have also reported reduced sleep quality and quantity among rugby players compared with non-athletes controls [START_REF] Shearer | Effects of competition on the sleep patterns of elite rugby union players[END_REF][START_REF] Caia | Intra-individual variability in the sleep of senior and junior rugby league athletes during the competitive season[END_REF]. Consequently, post-match sleep conditions should be optimized to ensure that players experience the maximum levels of physical and psychological recovery [START_REF] Dunican | Sleep is an important factor when considering rugby union player load[END_REF].

Sleep and thermoregulation are closely related [START_REF] Kräuchi | The interrelationship between sleep regulation and thermoregulation[END_REF][START_REF] Van Someren | Mechanisms and functions of coupling between sleep and temperature rhythms[END_REF]. Sleep initiation is associated with the maximal rate of decline in core body temperature (CBT), which occurs through an increase in cutaneous temperature and heat loss from the periphery [START_REF] Kräuchi | The interrelationship between sleep regulation and thermoregulation[END_REF]. Within the sleep period, lowering the minimum CBT has been suggested to increase slow-wave sleep (SWS) and to positively impact sleep quality [START_REF] Togo | Influence on human sleep patterns of lowering and delaying the minimum core body temperature by slow changes in the thermal environment[END_REF][START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF]. Krauchi et al. [START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF] reported a higher proportion of SWS (≈ 3.7%) when sleeping on a high-heat capacity mattress (MAT), which facilitates the continuous and

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slow removal of body heat via conductive heat transfer. However, this study was conducted on untrained subjects. To the best of our knowledge, MAT use on sleep quality and quantity after competitions has not been examined among elite athletes.

Whole-body cryotherapy (WBC: 3 min at -110°C) has been shown to decrease cutaneous temperature during the exposure, and to slightly reduce CBT (≈ 0.3°C) after the exposure [START_REF] Costello | Muscle, skin and core temperature after -110 degrees c cold air and 8 degrees c water treatment[END_REF][START_REF] Zalewski | Whole-body cryostimulation increases parasympathetic outflow and decreases core body temperature[END_REF]. Whole-body cryotherapy has also been shown to reduce actigraphic activity during sleep, which may potentially indicate a deeper sleep [START_REF] Douzi | 3-min whole body cryotherapy/cryostimulation after training in the evening improves sleep quality in physically active men[END_REF][START_REF] Douzi | Partial-body cryostimulation after training improves sleep quality in professional soccer players[END_REF]. However, CBT and sleep architecture were not assessed in these studies. Moreover, it is not clear whether the acute presleep WBC cooling effect persists throughout the night and interfere with sleep architecture.

Earlier research stated that sleep and autonomic modulation are linked as higher delta activity during non-rapid eye movement (NREM) sleep has been associated with reduced sympathetic modulation [START_REF] Bonnet | Heart rate variability: sleep stage, time of night, and arousal influences[END_REF]. Heart rate variability (HRV) indices are higher directly after WBC exposure [START_REF] Schaal | Effect of recovery mode on postexercise vagal reactivation in elite synchronized swimmers[END_REF] and during the first SWS sequence following a night-time exercise [START_REF] Douzi | 3-min whole body cryotherapy/cryostimulation after training in the evening improves sleep quality in physically active men[END_REF]. However, the relationship between WBC-induced parasympathetic hyperactivity during the early phase of NREM and the overall sleep architecture is still to be elucidated.

The aim of the present study was to investigate the effect of MAT -continuous cooling strategy during the night -and WBC -acute cooling intervention before the night -on sleep architecture and short-term recovery after an elite rugby union match. This study was designed to compare each intervention with a control condition. The secondary aim of this study was to investigate the potential effect of rugby match load variables on sleep architecture. We hypothesized that MAT

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use and WBC would enhance sleep compared with a control condition, and that a higher match load would negatively impact sleep architecture. Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

Methodology

Participants

A C C E P T E D

Experimental sessions

The study was conducted over three weekends within the same month (April 2018). The study was designed according to a within-subject crossover comparison that finally resulted in unbalanced experimental conditions order due to substitutions, injuries, and player unavailability. The design consisted of one familiarization night and three experimental conditions: 1) High heat capacity MATtress (MAT) condition, during which players slept on a specific mattress (described elsewhere); 2) Whole Body Cryotherapy (WBC) condition, during which players spent 3 min in a specific chamber, at -110°C, two hours before bedtime (≈ 21:30, i.e. ≈ 4 h post-match); and 3) control (CONT) condition, during which players received no intervention after the match. The players were blinded to the MAT condition, and they were informed that the aim of the study was solely to evaluate the effects of WBC on sleep. For each of the experimental weekends, the entire team arrived at the training centre on Friday, played an official match on Saturday afternoon (15:00), and left the centre on Sunday afternoon (Figure 1).

Sleep was only assessed on Saturday nights, following match play. However, one night of familiarization was conducted on the very first Friday of the experimental period [START_REF] Agnew | The First Night Effect: An Eeg Studyof Sleep[END_REF]. On Saturday morning, baseline tests (BASELINE) were conducted at 09:00, before the first warmup protocol; they were used to assess test-retest reliability. One hour after the match (around 18:00), the same testing battery (POST) was conducted as BASELINE. Dinner was served around 21:00. The meal was prepared by a nutritionist and included a variety of breads, cereals, milk/yogurts, meats, pasta/rice, fruit, and vegetables, to ensure the adequate intake of macro-and micronutrients. The same meal was replicated for each of the three conditions. The PSG equipment was assembled by a team of qualified practitioners (≈20 to 30 min for each player), and bedtime was set at 23:30. The following morning, wake-up was planned at 08:00. At 10:00, Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

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after breakfast, the same testing battery was conducted (D+1) to assess recovery status. During the PSG nights, room temperature and humidity were assessed continuously, using an iButton (DS 1922L, iButtonLink, Whitewater, USA; resolution 0.0625 °C; sampling rate: 1 value per minute), which was placed on the bedroom wall. No significant differences were noted in ambient temperatures (CONT = 21.6 ± 1.6°C; WBC = 20.8 ± 1.3°C; MAT = 21.7 ± 1.0°C) or humidity (CONT = 52.9 ± 11.2%; WBC = 52.4 ± 8.2%; MAT = 53.1 ± 6.2%) between conditions. ***Figure 1***

Mattress properties

The mattress used for all conditions was composed of the following layers: i) an upper quilted panel, composed primarily of foam (thickness of 2.5 cm and density of 23 kg/m 3 ); ii) a core comprised of a specific foam type (nano, Bultex, France), with a thickness of 16 cm and a density of 33 kg/m 3 ; and iii) a lower quilted panel, composed primarily of foam (thickness of 1.8 cm and density of 23 kg/m 3 ). For the MAT condition, we added a 6-cm polyurethane, high-heat capacity layer (see Figure, Supplemental Digital Content 1, which illustrates the bedding conditions, http://links.lww.com/MSS/C2), with a density of 1.006 kg/m 3 which allows the slow removal of body heat via conductive heat transfer [START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF]. All mattresses used in the study were identical in size (100  200  23 cm). The same cover types (non-quilted textile, with a weight of 400 g/m 2 ) and pillows were used throughout the study to avoid potential bias. Participants were required to sleep in the same clothes for all three conditions. The mattress surface temperature

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was continuously assessed with the same iButtons used to assess ambient temperatures, which were placed in the middle of the mattress, 60 cm from the top.

Match analysis

Global positioning systems (GPS) and video analyses were used to monitor the external workloads of each player during the three matches. Each player wore the same 16-Hz unit (Sensoreverywhere V2, Digital Simulation, Paris, France), in a Lycra vest that positioned the unit on the upper thoracic spine, between the scapulae. Data were downloaded after the game, and playing times were fixed for each player, to ensure that only game data were used for analysis. In this study, we focused on three GPS-derived locomotor variables: i) total covered distance (TD); ii) distance covered at high speeds (HS; > 5 m.s -1 ); and iii) distance covered at low-speeds (LS; < 5 m.s -1 ) [START_REF] Lacome | Fluctuations in running and skill-related performance in elite rugby union match-play[END_REF]. The GPS measures previously showed high levels of validity and between-device reliability for maximal sprinting and acceleration [START_REF] Lacome | Can we use GPS for assessing sprinting performance in rugby sevens? A concurrent validity and between-device reliability study[END_REF]. In addition, video analyses were conducted via the Hudl system (Sportstec, NE), to assess the total number of collisions during the match, which was calculated as the sum of offensive and defensive tackles, rucks, and contact hits [START_REF] Jones | Match play performance characteristics that predict post-match creatine kinase responses in professional rugby union players[END_REF].

Sleep analysis

Polysomnography (PSG) recordings were obtained the night after each match using two types of portable devices (Nox A1, Resmed, United States [n=11] and Actiwave©, CamNtech Ltd., Cambridge, UK [n=8]). Each participant used the same device for all conditions. Both systems provided continuous monitoring of four electroencephalograms (F3-M2, F4-M1, C4-M1, O2-

M1), two electrocardiograms (ECG), two electrooculograms (outer canthus of each eye), and two

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electromyograms (chin). Contralateral mastoid leads served as references for all unipolar measurements (electroencephalograms and electrooculograms). Polysomnography data were scored by two trained technicians who were assigned all the nights from one PSG model, and were blinded to the experimental conditions. The American Academy of Sleep Medicine (AASM) criteria were employed [START_REF] Berry | AASM scoring manual updates for 2017 (Version 2.4)[END_REF]. Analyses were conducted using Noxturnal software version 5.1 (Resmed, United States) and Somnologica (TM; Medcare©, Reykjavik, Iceland). The sleep variables were measured as follows: sleep onset latency (SOL) was defined as the time between lights off and sleep onset; wake after sleep onset (WASO) was defined as the total wake time during the sleep period; total sleep time (TST) was defined as the time spent asleep, as determined from sleep start to sleep end, minus WASO; sleep efficiency (SE) was defined as the TST divided by the time in bed (expressed as a percentage); and finally, light, SWS, rapid eye movement (REM) and non-rapid eye movement (NREM) were defined as the proportion of time spent in each of these sleep stages expressed as a percentage of TST.

Core body temperature (CBT)

During the afternoon, players ingested a radio telemetric pill (BodyCap, e-Celsius® Performance, France), to continuously record their nocturnal CBTs. This method has been shown to be reliable and valid [START_REF] Bongers | Validity, Reliability, and Inertia of Four Different Temperature Capsule Systems[END_REF], with an accuracy of 0.23°C, an intra-class correlation coefficient of 1.00, and a standard error of measurement of 0.03.

Nocturnal heart rate (HR) and heart rate variability (HRV)

The ECG signal was derived from positions at the right midclavicular and approximately 6 cm under the left armpit. The electrodes were connected to the polysomnographic systems (Nox A1,

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Resmed, United States or Actiwave©, CamNtech Ltd, Cambridge, UK), and ECG data were continuously recorded at 200 Hz. Data were then converted into a European data format and imported into Somnologica Studio (version 2.0.1 Medcare-Embla®, Reykjavik, Iceland) for further analysis. This software has been used in previous sleep studies [START_REF] Song | The effect of aging and severity of sleep apnea on heart rate variability indices in obstructive sleep apnea syndrome[END_REF]. Nocturnal HRV and HR indexes were determined using the first 5-min stationary segment (free from arousals) in the first SWS sequence that lasted for longer than 15 min. Slow wave sleep has been shown to be better for discriminating sympathovagal balance states than waking periods [START_REF] Brandenberger | Is slow wave sleep an appropriate recording condition for heart rate variability analysis?[END_REF]. All data acquisition and analyses were performed in accordance with established standards [START_REF] Force | the European Society of Cardiology and the North American Society of Pacing and Electrophysiology[END_REF].

Markers of fatigue and subjective assessments

Markers of peripheral fatigue and exercise-induced muscle damage included countermovement jump performance (CMJ), blood creatine kinase concentration ([CK]), and perceived delayedonset muscle soreness (DOMS). These indicators were obtained at BASELINE and at D+1 (Figure 1).

Countermovement jump (CMJ) performance was assessed to evaluate neuromuscular fatigue.

Prior to testing, players performed a 10-minute dynamic warm-up, consisting of active mobility

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and progressive lower-body loading using lunges, step-ups, and squats. Jump assessments required each participant to perform unloaded CMJs, with a wooden stick placed on their shoulders. The CMJ mean force (CMJ-F) was assessed using a portable linear encoder device (GymAware Power Tool, Kinetic Performance Technologies, Canberra, Australia) [START_REF] Mathieu | Usefulness of typical tests of short-duration maximal effort used to assess players readiness to perform[END_REF]. Each participant performed four repetitions, pausing for approximately 3-5 s between each jump. The mean of the trials (excluding the best and the worst trial) was calculated and used as a marker of neuromuscular performance. A typical error of the mean (TEM) of 177.4 N, an intraclass correlation coefficient (ICCc) of 0.87, and a coefficient of variation (CV) of 8.6% were obtained.

Blood creatine kinase concentration ([CK]

) was assessed by collecting 500 l of blood from fingertip capillary punctures, which were stored in a microtube containing lithium heparinase (BD Microtainer, BD, New Jersey, US). Within one hour after the blood collection, 32 l of each sample was taken from the tube, using a specific pipette, and placed on a measurement strip.

Analyses were performed using a Reflotron Sprint (Roche Diagnostics, Grenzacherstrasse, Switzerland). The Reflotron was calibrated according to the manufacturer's recommendations. A TEM of 65.7 IU•L -1 , an ICCc of 0.99, and a CV of 10.6% were obtained for [CK] measurements.

Subjective assessments

The well-being Hooper Index is a rating of general fatigue, DOMS, stress, and sleep perception.

Players were asked to subjectively evaluate, twice for each condition (PRE and D+1), the four items, using a 1-7 scale, with 1 representing the most positive rating and 7 representing the most negative rating, for each variable. The Hooper index was calculated as the sum of all four scores. Each variable was presented separately [START_REF] Hooper | Monitoring overtraining in athletes[END_REF].

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Rating of perceived exertion of the session (sRPE) was assessed for each player at the end of each match. Players answered the question "How was your workout?" using a scale from 0 (rest) to 10 (maximal). The obtained score was then multiplied by the playing duration for each player [START_REF] Quarrie | Managing player load in professional rugby union: a review of current knowledge and practices[END_REF] and recorded as arbitrary units (AU).

Perceived thermal comfort (on a scale from -2 "very uncomfortable" to +2 "very comfortable") and sensation (on a scale from -3 "cold" to +3 "hot") (34) was recorded for each player the morning after each post-match night.

The total quality of recovery (TQR) scale was reported by the players in the morning, after each post-match night. Scores varied from 6, "very, very poor recovery," to 20, "very, very good recovery" [START_REF] Kenttä | Overtraining and recovery. A conceptual model[END_REF].

Statistical analysis

Three types of linear mixed-effects models were fitted with regards to the dependent variables (DVs) tested and the research question. Table 1 provides an overview of the models' designs.

For the second type of model, the variations between each experimental condition and the CONT condition for each DV were adjusted according to the number of collisions and the HS distance recorded for each player. These two variables represented the most important components associated with rugby union match-related metabolic and neuromuscular fatigue [START_REF] Jones | Match play performance characteristics that predict post-match creatine kinase responses in professional rugby union players[END_REF]. All models were fitted using the "lme" function of the nlme package in the R program (version 1.1.456).

Data are presented as the estimate (β), the standard error (SE), the 95% confidence interval (CI),

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and the P-value. For the interpretation of the models, the intercept represented the mean CONT value of the DV when the fixed effects were null. The effects of MAT and WBC on mattress surface temperature kinetics (8 time points, with 1-h intervals) compared with the CONT condition were assessed using a two-way (condition  time) repeated-measures analysis of variance (ANOVA). Multiple Student's paired t-tests, with Bonferroni correction, were then used for post hoc pairwise comparisons when a significant interaction between time and condition was observed. The level of significance was set at p < 0.05.

***Table 1***

Results

Match load, sleep schedules and baseline fatigue between conditions

Match load. Global match load variables are presented as the intercept of the mixed-effect model (see Table, Supplemental Digital Content 2, which illustrates the internal and external match load, http://links.lww.com/MSS/C3). Independently from the experimental conditions, total distance covered was 3643.0 ± 468.9m, including 3416.8 ± 455.0m of LS running distance and 226.4 ± 54.5m of HS running distance. The number of collisions was 16.2 ± 2.9 and sRPE was 434.1 ± 65.4 AU.

A significantly higher total distance (β = +980.2 m, p < 0.05), LS running distance (β = +899.0 m, p < 0.05) and number of collisions (β = +4.4, p = 0.05) were reported for the WBC condition compared with the CONT condition. No significant differences were observed for HS distance (β = +81.5 m, p = 0.17 Baseline fatigue markers. No significant differences between conditions were reported at BASELINE for any marker of fatigue.

Effects of MAT on sleep, temperature and fatigue markers

Polysomnography. Tables 2 and3 provide an overview of the effects of the MAT condition on sleep architecture compared with the CONT condition. A significantly lower WASO (β = -10.5 min, p < 0.01) and a trend towards higher sleep efficiency (β = +2.9%, p = 0.11) for the MAT condition compared with the CONT condition were observed (Table 2). A higher REM sleep proportion (β = +2.8%, p < 0.05) was noted for MAT condition compared with the CONT condition (Table 3).

***Table 2 and 3***

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Temperature, HR and HRV. A significant reduction in mean nocturnal CBT (β = -0.135°C, p < 0.001) and mattress surface temperature (β = -2.736°C, p < 0.001) were observed for the MAT condition compared with the CONT condition (Table 4). The two-way ANOVA revealed main effects for time and condition and for the interaction between time and condition (p < 0.001).

Significant differences between the two conditions were observed at all-time points (p < 0.05), except at bedtime and 4 to 5 hours after bedtime (Figure 2). A higher nocturnal thermal comfort was perceived for the MAT (β = +0.6, 95% CI: 0.1 to 1.2, p < 0.05) condition compared with the CONT condition. The MAT use did not affect HR and HRV, compared with the CONT condition. ***Table 4 andFigure

Effects of WBC on sleep, temperature and fatigue markers

Polysomnography. Whole-body cryotherapy did not affect any of the sleep variables compared with the CONT condition (Table 2 and3).

Temperature, HR and HRV. No significant differences between the WBC and CONT conditions were observed for mean CBT (Table 4). However, WBC showed a higher nocturnal thermal comfort (β = +0.7, 95% CI: 0.2 to 1.3, p < 0.05) and a colder sensation during the night (β = -0.8,

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95% CI: -1.6 to -0.0, p = 0.05) than the CONT condition. Frequency domain analyses of HRV during the SWS sequences showed a higher normalized HF power for the WBC condition (β = +9.3%, 95% CI: -0.1 to 18.7%, p = 0.05) suggesting an increased parasympathetic activity compared with the CONT condition.

Fatigue markers. No significant differences between WBC and the CONT condition for TQR scores, and the variations between BASELINE and D+1 of [CK] levels, CMJ-F, and DOMS were reported.

Effects of match load covariates on sleep architecture and fatigue markers

Table 3 provides an overview of the potential relationships between match load covariates (HS and the number of collisions) and sleep architecture DVs. We observed a higher SWS proportion (β = +1.1%, p = 0.05) and a lower light sleep proportion (β = -1.2%, p < 0.05) for every 100-m increase in HS during the match. For every 10 supplementary collisions during the match, the SWS proportion decreased (β = -1.9%, p = 0.09) and the light sleep proportion increased (β = +2.9%, p < 0.001) (Table 3).

Relationships between the match load covariates (HS and number of collisions) and ∆ [CK] and

∆ DOMS were observed: for every 100-m increase in HS running distance, significantly higher ∆ Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

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Discussion

The aim of the present study was to investigate the effects of a high-heat capacity mattress (MAT) and whole-body cryotherapy (WBC) intervention on sleep architecture and short-term recovery after an elite rugby union match. Main results showed: i) MAT use reduced mean nocturnal CBT, and had a positive impact on sleep architecture compared with the CONT condition; ii) WBC did not affect nocturnal CBT nor interfere with sleep architecture. Highspeed running and the number of collisions experienced during the match had positive and negative influences on sleep architecture, respectively.

Effects of MAT on sleep, temperature and fatigue markers

The efficacy of MAT use on sleep after participation in a rugby union match was investigated.

The upper layer of the MAT tested in the present study contained a high-heat capacity material, which remained cooler than the CONT mattress during the major part of the night (Figure 2).

Decreasing CBT during sleep may enhance sleep quality [START_REF] Togo | Influence on human sleep patterns of lowering and delaying the minimum core body temperature by slow changes in the thermal environment[END_REF][START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF]. Our results showed significantly lower mean CBT (-0.135 °C) and mattress surface (-2.736 °C) temperatures during the MAT than the CONT condition. These findings are in agreement with studies using a similar high-heat capacity mattress [START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF]36), and suggest an enhanced conductive body heat loss with MAT. Moreover, a significant improvement in subjective thermal comfort was reported when sleeping on the MAT. Sleeping on MAT significantly reduced WASO (-10.5 min) and increased REM sleep proportion (+2.8%) compared with the CONT condition. Krauchi et al. (15) used a similar cooling strategy and showed a higher SWS proportion (3.7%). These results suggest potential distinct positive effects for MAT use on sleep architecture, which could be explained by differences in the population studied and/or the experimental protocol. Moreover, the mean Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

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SWS proportion in our study during the CONT condition was higher (27.7 % vs 23.1%) and the REM sleep proportion was lower (19.4 % vs 22.1%) compared with Krauchi et al. [START_REF] Krauchi | Sleep on a high heat capacity mattress increases conductive body heat loss and slow wave sleep[END_REF], which may reveal a ceiling or "maximum level of SWS in a single night" (37), beyond which even MAT use cannot induce further increases in SWS. Wake after sleep onset is an indicator of sleep quality and is usually higher for elite athletes than for non-athletic individuals (38,39). Our results showed significantly lower WASO for the MAT condition compared with the CONT condition (-10.5 min), suggesting better sleep continuity for MAT. The observed increase in REM sleep during MAT use may be related to the relatively low post-match REM proportion, coupled with increased sleep continuity. Despite positive effects on sleep architecture, MAT use did not affect the short-term neuromuscular and perceptual recovery compared with the CONT condition. Futures studies are required to assess the interest of chronic use of MAT on sleep and recovery.

Effects of WBC on sleep, temperature and fatigue markers

The present study showed no difference for nocturnal CBT between WBC and CONT, which suggests that the slight decrease of CBT previously reported at 30 and 60min after the exposure [START_REF] Costello | Muscle, skin and core temperature after -110 degrees c cold air and 8 degrees c water treatment[END_REF][START_REF] Zalewski | Whole-body cryostimulation increases parasympathetic outflow and decreases core body temperature[END_REF] does not persist during the night. A previous study by Douzi et al. [START_REF] Douzi | 3-min whole body cryotherapy/cryostimulation after training in the evening improves sleep quality in physically active men[END_REF] reported lower actigraphic nocturnal activity after WBC preceded by night-time running exercise.

Discrepancies between studies may be explained by the different pre-intervention exercise type and timing, and the methodology of sleep assessment. One of the rationale for using WBC after exercise is to reduce sympathetic activity and increase vagal tone after the exposure (21,40) and during subsequent sleep [START_REF] Douzi | 3-min whole body cryotherapy/cryostimulation after training in the evening improves sleep quality in physically active men[END_REF]. In the present study, we examined the sympathovagal balance during the first sequence of SWS [START_REF] Brandenberger | Is slow wave sleep an appropriate recording condition for heart rate variability analysis?[END_REF] for WBC and CONT conditions. Our results showed

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increased parasympathetic activity during this period of SWS, as inferred by higher normalized HF power. This finding is consistent with previous studies that have assessed the effects of WBC on autonomic modulation [START_REF] Douzi | 3-min whole body cryotherapy/cryostimulation after training in the evening improves sleep quality in physically active men[END_REF][START_REF] Schaal | Effect of recovery mode on postexercise vagal reactivation in elite synchronized swimmers[END_REF]. Nevertheless, as sleep architecture and short-term recovery were not affected after an acute WBC exposure, future studies should focus on its chronic effect on recovery, e.g. during an intensified training cycle.

Relationship between match load covariates and sleep architecture

Match loads in the present study were similar to those previously reported among elite U23 players (41). To our knowledge, this is the first study to evaluate sleep architecture for a full night with PSG following a rugby match. Our results indicated that the number of collisions experienced by players during the match impaired subsequent sleep architecture. This result may be explained by the accumulation of metabolic waste in the brain, including beta-amyloid, following recurrent head impacts; such accumulation may then disrupt the inhibition of the noradrenergic signaling in the locus coeruleus and negatively impact sleep architecture (42).

Conversely, increased HS running distance during the match improved SWS proportion during the following night, which is in agreement with the hypothesis that higher diurnal activity is associated with increased SWS (43).

Practical applications

The present study highlighted the importance of sleep environment and the optimization of nocturnal heat transfer via MAT for improved post-match sleep among elite athletes. Moreover, WBC did not interfere with post-match sleep. High-speed running and the number of collisions experienced during the match had positive and negative influences on sleep architecture, Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

A C C E P T E D

respectively. Consequently, practitioners should be aware of the importance of monitoring these activities and sleep after rugby union match to ensure adequate recovery.

Limitations

Due to the real-world sports setting examined in this study, controlling the match load for each player was not feasible, and the match load was found to be slightly higher for the WBC condition compared with the CONT condition. Linear mixed-effects models were, therefore, used to assess the difference between conditions with match load variables as covariates. Due to practical issues, fatigue states were monitored only the morning after the match. Future studies are required to assess the effects of the recovery strategies on the overall post-match recovery kinetics (e.g. up to 3 days after the game).

Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

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Copyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited. The player and the slope (15 time points with 30min intervals) CONT: control condition, MAT: high heat capacity mattress condition, WBC: whole body cryotherapy condition, sRPE: Rating of perceived exertion of the session, TD: total distance, HS: high speed running distance, LS: low speed running distance, WASO: wake after sleep onset, SWS: slow wave sleep proportion, REM: rapid eye movement sleep proportion, RMSSD: Root Mean Square Standard deviation of R-R interval, HF: high frequency band, LF: low frequency band, LF/HF : the ratio of low by high frequency, ∆ [CK]: the variation from PRE to D+1 of blood creatine kinase levels, ∆ DOMS: the variation from PRE to D+1 of delayed onset muscle soreness levels, ∆ CMJ-F: the variation from PRE to D+1 of the force developed during a counter movement jump test, CBT: core body temperature.

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A C C E P T E D a b

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  Twenty-three elite male under-23 rugby union players, competing at the highest national French level, were initially recruited. Due to substitutions related to tactical choices, injuries, and player unavailability, nineteen players who participated in at least two conditions (CONT+WBC+MAT: n=10, CONT+WBC: n=2, CONT+MAT: n=2 and WBC+MAT: n=3), or only in the CONT condition (n=2), were included in the final analysis. Ten backs (mean ± SD; age: 20.8 ± 1.0 yrs; body mass = 91.4 ± 7.4 kg; height = 183.5 ± 8.5 cm) and nine forwards (mean ± SD; age: 20.6 ± 1.3 yrs; body mass = 111.7 ± 8.7 kg; height = 189.4 ± 8.8 cm) were included. The study was conducted according to the Helsinki Declaration (1964: revised in 2001), and the protocol was approved by the local ethics committee (East III, France. Ref. 170605). All players provided a detailed medical history and underwent a medical examination, including an electrocardiogram at rest. The players also provided their written informed consent before the initiation of experiments. The inclusion criteria were as follows: i) an intermediate or moderately evening type, according to the Horne and Ostberg questionnaire (i.e. < 58 and > 31); ii) free from PSGconfirmed sleep disorders, such as sleep apnea (apnea-hypopnea index > 10), periodic limb movement syndrome, hypersomnia, or narcolepsy; and iii) free from diabetes, severe hypertension, heart disease, anorexia, and bulimia.

  Electrocardiogram waveforms were analyzed to obtain temporal and frequency domain components. Time-domain variables, including mean R-R interval (RRI) and the root mean square standard deviation (RMSSD) of RRI, were assessed. Frequency domains were assessed for low-(LF; 0.04-0.15 Hz) and high-frequency (HF; 0.15-0.40 Hz) bands and the ratio of LF/HF during each 5-min spectrum. Mean HR was calculated using the following formula: HR (bpm) = 1 / R-R (sec) * 60.

  ) and sRPE (β = +78.6 AU, p = 0.20) between the WBC and CONTCopyright © 2020 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited. significant differences were observed for any match load variables between the MAT and CONT conditions (see Table, Supplemental Digital Content 2, http://links.lww.com/MSS/C3).Sleep schedules. No significant differences were reported for bedtimes (intercept: 23:35 ± 00:33; ∆ WBC -CONT = 00:11 min, p = 0.38; ∆ MAT -CONT = 00:17 min, p = 0.17) or get up times (intercept: 08:02 ± 00:16; ∆ WBC -CONT = -00:04 min, p = 0.52; ∆ MAT -CONT = -00:08 min, p = 0.16) between the conditions.

  2*** Fatigue markers. No significant differences between MAT condition and the CONT condition for TQR scores, and the variations between BASELINE and D+1 of [CK] levels, CMJ-F, and DOMS were reported.

[

  CK] levels (β = +78.0 IU•L -1 , 95% CI: 35.6 to 120.3 IU•L -1 , p < 0.001) and ∆ DOMS (β = +0.3 AU, 95% CI: 0.1 to 0.4 AU, p < 0.001) were observed. Additionally, for every 10 supplementary collisions during the match, a significantly higher ∆ [CK] (β = +112.6 IU•L -1 , 95% CI: 33.7 to 191.5 IU•L -1 , p < 0.05) was noted.

Figure 1 .Figure 2 .

 12 Figure 1. Experimental design

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Table 1 :

 1 Outline of models' details (the random and fixed effects) used for each dependent variable depending on the research question.

		Objective		Dependent variables	Fixed effect(s)	Random
							effect(s)
	Assess the difference in match	-Match load : sRPE, TD, HS, LS and	The experimental condition	The player
	load and sleep time between	number of collisions	(categorical predictor with
	CONT and the two experimental		CONT as reference)
	conditions				-Sleep: bed time, wake up time and time
					in bed
	To evaluate the effect of MAT	-Sleep : total sleep time, sleep onset	The experimental condition	The player
	and WBC on sleep, HRV and	latency, WASO, sleep efficiency, light	(categorical predictor with
	fatigue	markers	with	a	sleep, SWS, REM and NREM	CONT as reference) + the
	comparable match load between	-HRV: RMSSD, HF, LF and LF/HF	number of collisions + the HS
	conditions				-Fatigue markers: ∆ [CK], ∆ DOMS and	distance
					∆ CMJ-F
	To compare nocturnal CBT and	-CBT	The experimental condition
	mattress surface temperature	-Mattress surface temperature	(categorical predictor with
	between	the	experimental		CONT as reference)
	conditions and CONT

Table 2 .

 2 Linear mixed-effects models evaluating the effect whole body cryotherapy (WBC) and high heat capacity mattress (MAT) on sleep quality, assessed using polysomnography, compared with CONT condition (reference).

		Total sleep time (min)	Sleep onset latency (SOL)	Wake after sleep onset	Sleep Efficiency (SE) (%)
						(min)			(WASO) (min)
		Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p
	Fixed effects
	(Intercept)	438.9	403.2 -474.5 <0.00	27.8	5.6 -50.0	0.02	37.9	24.9 -50.8 <0.00	86.6	80.8 -92.3 <0.00
		(17.0)		1	(10.6)			(6.2)		1	(2.8)		1
	CONT	Reference		Reference		Reference		Reference
	WBC	-17.9	-46.0 -10.3	0.20	-4.8	-23.2 -13.6 0.59	-5.0	-13.1 -3.2	0.22	-1.6	-5.6 -2.5	0.43
		(13.4)			(8.8)			(3.9)			(1.9)
	MAT	-8.8	-34.5 -16.9	0.48	-3.2	-20.1 -13.8 0.70	-10.5	-17.8 --3.3 0.01	2.9	-0.7 -6.5	0.11
		(12.3)			(8.1)			(3.5)			(1.7)
	HS (km)	-4.5	-74.7 -65.8	0.90	-6.4	-50.6 -37.7 0.76	21.5	-1.8 -44.8	0.07	-0.2	-11.1 -10.8 0.98
		(33.6)			(21.1)			(11.1)			(5.2)
	Collisions (n)	0.3	-1.1 -1.7	0.67	0.1	-0.8 -0.9	0.85	-0.6	-1.1 --0.1	0.03	0.0	-0.2 -0.3	0.69
		(0.7)			(0.4)			(0.2)			(0.1)
	Random part
	N		18			18			18			18
	Observations		41			41			41			41

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Table 3 .

 3 Linear mixed-effects models evaluating the effect of whole body cryotherapy (WBC) and high heat capacity mattress (MAT) on sleep architecture compared with a CONT condition (reference)

			Light sleep (%)	Slow wave sleep (%)		REM sleep (%)	NREM sleep (%)
		Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p
	Fixed effects
	(Intercept)	50.8	45.3 -	<0.00	27.7	22.0 -	<0.00	19.4	15.4 -	<0.00	80.6	76.6 -	<0.00
		(2.6)	56.3	1	(2.7)	33.3	1	(1.9)	23.3	1	(1.9)	84.6	1
	CONT	Reference		Reference		Reference		Reference
	WBC	-4.1	-9.6 -1.4 0.13	2.2	-2.5 -6.8 0.34	0.8	-1.9 -3.4 0.56	-0.7	-3.4 -1.9 0.56
		(2.6)			(2.2)			(1.3)			(1.3)
	MAT	-2.3	-7.4 -2.9 0.37	-0.1	-4.4 -4.1 0.95	2.8	0.4 -5.2	0.02	-2.8
		(2.5)			(2.0)			(1.1)			(1.1)

Table 4 .

 4 Linear mixed-effects models evaluating the effect of whole body cryotherapy (WBC) and high heat capacity mattress (MAT) on mean core body temperature (CBT) and mattress temperature compared with CONT condition (reference).

		Core body temperature (°C)	Mattress surface temperature
						(°C)
		Est. (SE)	95% CI	p	Est. (SE)	95% CI	p
	Fixed effects
	(Intercept)	36.378	36.294 -	<0.001	34.857	34.427 -	<0.001
		(0.043)	36.462		(0.226)	35.286
	CONT	Reference			Reference
	WBC	0.041	-0.019 -0.101	0.18	-0.030	-0.627 -0.567 0.92
		(0.031)			(0.306)
	MAT	-0.135	-0.211 --0.060 <0.001	-2.736	-3.315 --2.156 <0.001
		(0.038)			(0.298)
	Random part
	N		14			18
	Observations		330			583

  Supplemental Digital Content 2. Table that illustrates the internal and external match load variation from CONT (reference) for WBC and MAT

		Total distance (m)	LS running distance (m)	HS running distance (m)		Collisions (n)		sRPE (U.A)
		Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p	Est. (SE)	95% CI	p
	Fixed effects
	(Intercept)	3643.0	2633.5 -	<0.001	3416.8	2479.8 -	<0.001	226.4	114.3 -	<0.001	16.2	10.2 -	<0.001	434.1	299.3 -	<0.001
		(490.2)	4652.5		(455.0)	4353.9		(54.5)	338.5		(2.9)	22.2		(65.4)	568.8
	CONT	Reference			Reference			Reference		Reference		Reference
	WBC	980.2	14.4 -	0.05	899.0	21.1 -	0.05	81.5	-37.4 -	0.17	4.4	-0.0 -	0.05	78.6	-43.9 -	0.20
		(468.9)	1946.1		(426.3)	1776.9		(57.8)	200.5		(2.1)	8.8		(59.4)	201.0
	MAT	304.4	-661.5 -	0.52	279.2	-598.7 -	0.52	25.0	-93.9 -	0.67	-0.6	-5.0 -	0.78	9.5	-112.9 -	0.87
		(468.9)	1270.2		(426.3)	1157.1		(57.8)	144.0		(2.1)	3.8		(59.4)	131.9
	Random part
	Ngrp		19			19			19			19			19
	Observation		46			46			46			46			46

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Acknowledgments

Anis Aloulou was supported by a scholarship from Bultex, a company specialized in bedding.

The authors are very grateful to the players and the managers of the "Stade Français" rugby team for their efforts and involvement in this study. Special thanks to Alexis Peeters, Florent Carton, Jean-Robert Filliard and Alexandre Dubois for their support conducting these experiments.

Conflict of interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.

The results of the present study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation and do not constitute any endorsement by the American College of Sports Medicine.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest. The results of the present study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation and do not constitute any endorsement by the American College of Sports Medicine.

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Diana Pchelina
email: di.pchelina@physics.msu.ru

Vera Sedykh

Nataliya Chistyakova

Vyacheslav Rusakov

Yulia Alekhina

Alexey Tselebrovskiy

Bernard Fraisse

Lorenzo Stievano
email: lorenzo.stievano@umontpellier.fr

Moulay Tahar Sougrati

Alkaline-earth metal-doped perovskites La 0.95 A 0.05 MnO 3+δ (A = Ca, Sr): new structural and magnetic features revealed by 57 Fe Mössbauer spectroscopy and magnetic measurements

Keywords: perovskites, doped lanthanum manganites, Mössbauer spectroscopy, phase separation, magnetic properties, superparamagnetism

published or not. The documents may come

Alkaline-earth metal-doped perovskites La0.

Introduction

Doped lanthanum manganites of the La 1-x A x MnO 3 -type (LAM), where A is a divalent alkali-earth metal ion Ca 2+ , Sr 2+ or Ba 2+ , are widely applied as cathode elements for fuel cells, in information recording and solid-state storage devices, and in the production of hydrogen with solar energy [START_REF] Parkin | Giant Magnetoresistance in Magnetic Nanostructures[END_REF][START_REF] Kharton | Oxygen permeability of LaFe1-xNixO3-δ solid solutions[END_REF][START_REF] Huang | Oxide-ion conducting ceramics for solid oxide fuel cells[END_REF][START_REF] Gokon | Thermochemical twostep water splitting cycle using perovskite oxides based on LaSrMnO3 redox system for solar H2 production[END_REF][START_REF] Jiang | Development of lanthanum strontium manganite perovskite cathode materials of solid oxide fuel cells: a review[END_REF]. These compounds, largely investigated from both the fundamental and the applied point of view, derive from the parent compound LaMnO 3 and usually exist in the non-stoichiometric form La 1-x А x MnO 3+δ . In nonstoichiometric LaMnO 3+δ , manganese is contained both as Mn +3 and Mn +4 . In the stoichiometric composition, however, manganese is only in the trivalent state, which undergoes Jahn-Teller distortion and leads to severe distortions of the crystal lattice, and eventually to the phase transition from the highly symmetric phase PnmaI to low-symmetry PnmaII [START_REF] Sedykh | Reversibility of structure phase transitions in LaMnO3+δ manganite under heat treatment[END_REF]. Below the temperature of magnetic ordering, the paramagnetic phase PnmaI and PnmaII become ferromagnetic and antiferromagnetic, respectively [START_REF] Huang | Structure and magnetic order in undoped lanthanum manganite[END_REF].

The stoichiometric composition (δ = 0) can be obtained in two ways: (i) by introducing increasing amounts of a divalent doping element, which by charge compensation stabilises increasing contents of non-Jahn-Teller Mn +4 ions, or (ii) by removing interstitial oxygen. Up to now, stoichiometric LAM with low contents (x ≤ 0.2) of the doping element have been only rarely studied.

Previous investigations of stoichiometric LAM containing low amounts of dopants, carried out at room temperature, revealed structural phase separation correlated with the Jahn-Teller effect [START_REF] Sedykh | Reversibility of structure phase transitions in LaMnO3+δ manganite under heat treatment[END_REF][START_REF] Huang | Structure and magnetic order in undoped lanthanum manganite[END_REF][START_REF] Dubinin | Phase separation in a manganite La0.95Ba0.05MnO 3 crystal[END_REF]. The strongest differences was observed for a dopant concentration of 5 %, corresponding to a low content of Mn 4+ , which was attributed to the occurrence of competing processes [START_REF] Dubinin | Phase separation in a manganite La0.95Ba0.05MnO 3 crystal[END_REF][START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0[END_REF]. For Ca-doped LAM, this problem was preliminary investigated by Mössbauer spectroscopy at 5 K, 80 K and by magnetization measurements [START_REF] Sedykh | Mössbauer and X-ray studies of the structural phase transformations and suppression of polymorphism in La1 -x Sr x Mn0.98Fe0.02O3 + δ (x = 0.05-0.30[END_REF]. In this work a special model for processing Mössbauer spectra was proposed, allowing us to better understand the nature of the magnetic clusters as well as the magnetic properties of a new PnmaII* phase. However, these properties have not yet sufficiently understood and need further investigations, which may eventually reveal new properties of these manganite phases.

In this work, we studied stoichiometric (S) and non-stoichiometric (NS) LAM (A = Ca, Sr) containing low contents of doping element (5 %) in a wide temperature range (including low temperature), and in particular investigated the effect of doping on the physical properties. The two systems La 1-x А x MnO 3+δ (A = Ca, Sr) were compared in order to understand the influence of the nature of the doping element on the structural, electronic and magnetic properties, as well as on cluster formation. For instance, the different ionic radii of Ca and La produces a more intense Jahn-Teller distortion in Ca-than in Sr-doped LMA, which is expected to have a strong impact on structural and magnetic properties.

Compared to previous studies, this one was carried out using a novel approach including the temperaturedependent measurements of the magnetic susceptibility, of the magnetization in ZFC-FC mode as well as of the 57 Fe Mössbauer spectra, the latter made possible by the inclusion of small amounts of isotopically enriched 57 Fe iron in the materials. This comprehensive study allowed a qualitative and quantitative determination of the magnetic state and the transition temperature of the studied phases, as well as their dependence upon the particle size distribution in the different materials.

Material and methods

Polycrystalline La 0.95 A 0.05 Mn 0.98 Fe 0.02 O 3+δ (A = Ca, Sr) samples were prepared by the sol-gel method from lanthanum, isotopically enriched 57 Fe, calcium/strontium nitrates and manganese acetate. The synthesis procedure as well as the (no)-stoichiometry of the synthesised materials were described in detail in previous works [START_REF] Sedykh | Mössbauer and X-ray studies of the structural phase transformations and suppression of polymorphism in La1 -x Sr x Mn0.98Fe0.02O3 + δ (x = 0.05-0.30[END_REF][START_REF] Sedykh | Specific features of the structural transformations in La1 -x Ca x Mn0.98 57Fe0.02O3 + δ (x = 0.05-0.50[END_REF]. Stoichiometric compositions were obtained by annealing the (no)-stoichiometric samples at Т = 650 0 C in vacuo (10 -3 Torr) for 10 -15 hours. 57 Fe Mössbauer spectra were measured using a 57 Co (Rh) source on an MS-1104Em spectrometer at 300 and 80 K, and a WissEl spectrometer equipped with a Janis SHI-850 cryostat for low-temperature analyses below 80 K. The spectra were processed using the SpectrRelax computer program [START_REF] Matsnev | SpectrRelax An application for Mössbauer spectra modeling and fitting[END_REF] using the many-state superparamagnetic relaxation model. Within this model, the parameter α is the ratio of the magnetic-anisotropy energy to the thermal-oscillation energy:

(K eff is effective magnetic anisotropy constant, Vthe particle volume, k Bthe Boltzmann constant, Tthe absolute temperature).

Magnetization measurements were carried out on a LakeShore 7404 vibrating sample magnetometer in the temperature range 100-300 K in fields up to 1280 kA/m. Investigations of the temperature dependence of the magnetization in ZFC-FC mode (heating in a nonzero field after cooling in a zero magnetic field (ZFC -Zero-Field Cooled) and cooling in a non-zero field (FC -Field Cooling)) in an external magnetic field of 2.4 kA/m (30 Oe) were carried out in the temperature range 100-300 K. Magnetic ZFC-FC measurements in the range 2-300 K with the magnetic field up to 5 Tesla (in an external magnetic field of 8 kA/m or 100 Oe) were collected with a Quantum Design MPMS-7XL SQUID magnetometer.

The temperature dependence of the magnetic susceptibility was measured on an AGICO Kappabridges MFK1-A instrument in the temperature range 70-275 K. The sensitivity of the device is 1 * 10 -7 SI. The Néel temperature T N was estimated from the temperature dependence of the magnetic susceptibility. The Curie-Weiss temperature  CW was determined by linear extrapolation from the 1/χ vs. temperature experimental plot.

In order to calculate the size of the magnetic clusters from the magnetic measurements, the magnetization curve was approximated by a linear function in the saturation region, In this way, the reference parameters of the saturation magnetization and the paramagnetic contribution coefficient A were determined. Then, a section of the magnetization curve where the magnetization is not less than 90% of the obtained saturation magnetization was selected. This section was approximated by the magnetization function M(H), approximated for all the studied samples by the function . Here M S is saturation magnetization, a is symmetry parameter, describing the special distribution of easy magnetization axes, K eff is the effective anisotropy constant, H is magnetic field. The effective anisotropy constant at a temperature below the blocking temperature was estimated using the Akulov's law [START_REF] Akulov | Uber den Verlauf der Magnetisierungskurve in starken Feldern[END_REF]. To subtract the paramagnetic contribution, the linear field term was added. Thus, the function was used in the form ., with A and B as fitting parameters. The effective anisotropy constant was determined from parameter B. The symmetry parameter a was taken equal to 0.5, which corresponds to systems with a random distribution of the axes of easy magnetization. Then the values of K eff , reported in Table 4, are determined as .

Results and discussion

Crystal structure of the studied materials

The crystal structure of all samples was determined by X-ray diffraction (XRD) in previous works [START_REF] Sedykh | Mössbauer and X-ray studies of the structural phase transformations and suppression of polymorphism in La1 -x Sr x Mn0.98Fe0.02O3 + δ (x = 0.05-0.30[END_REF][START_REF] Sedykh | Specific features of the structural transformations in La1 -x Ca x Mn0.98 57Fe0.02O3 + δ (x = 0.05-0.50[END_REF][START_REF] Sedykh | The features of structural transformations in lanthanum manganites La1-xAxMnO3+δ (A = Ca, Sr, Ba)[END_REF]. The LCM-NS and LSM-NS samples studied in this work are rhombohedral (space group R-3c). The LCM-S and LSM-S samples obtained by annealing in vacuo the respective LAM-NS precursors have an orthorhombic PnmaII* structure (space group Pnma). The lattice parameters for all samples are listed in Table 1 and compared to those of the parent compound LaMnO 3+δ . These data clearly show that 5 % doping is sufficient to produce significant structural changes in systems of stoichiometric composition. The emergence of Mn 4+ leads to a structural change: the PnmaII phase begins to transform into the high symmetry PnmaI phase via the PnmaII* intermediate. One should note that it is difficult to discriminate the three orthorhombic phases by XRD in a mixture of stoichiometric low-doping LAM since their patterns are very close to each other [START_REF] Sedykh | The features of structural transformations in lanthanum manganites La1-xAxMnO3+δ (A = Ca, Sr, Ba)[END_REF].

57 Fe Mössbauer spectroscopy analysis

The small amount of isotopically-enriched 57 Fe added to perform the Mössbauer spectroscopy analysis is known to replace Mn 3+ in the crystal structure as Fe 3+ [START_REF] Sedykh | Reversibility of structure phase transitions in LaMnO3+δ manganite under heat treatment[END_REF]. Since the ionic radii of Fe 3+ and Mn 3+ are very similar, Fe-doping practically does not introduce any distortion in the lattice, and, according to XRD, the lattice parameters are not modified with such low Fe loadings [START_REF] Sedykh | Reversibility of structure phase transitions in LaMnO3+δ manganite under heat treatment[END_REF][START_REF] Sedykh | Mössbauer and X-Ray studies of the dynamics of phase transformations and suppression of polymorphism in the LaMn1 -x Fe x O3 + δ compound (x = 0.015-0.500[END_REF]. However, as previously shown in refs. [START_REF] Sedykh | Reversibility of structure phase transitions in LaMnO3+δ manganite under heat treatment[END_REF][START_REF] Sedykh | Mössbauer and X-ray studies of the structural phase transformations and suppression of polymorphism in La1 -x Sr x Mn0.98Fe0.02O3 + δ (x = 0.05-0.30[END_REF][START_REF] Sedykh | Specific features of the structural transformations in La1 -x Ca x Mn0.98 57Fe0.02O3 + δ (x = 0.05-0.50[END_REF][START_REF] Sedykh | Mössbauer and X-Ray studies of the dynamics of phase transformations and suppression of polymorphism in the LaMn1 -x Fe x O3 + δ compound (x = 0.015-0.500[END_REF], even a small iron loading in undoped stoichiometric lanthanum manganite leads to phase separation: in addition to the main contribution of the PnmaII phase in the XRD pattern, small amounts of two other orthorhombic phases PnmaII* and PnmaI can be identified. This means that, similarly to Mn 4 + , also Fe 3 + destroys the Jahn-Teller distortion as expected given its d 5 electron configuration.

The Mössbauer spectra at 300 and 80 K of samples LCM-NS, already studied in refs. [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF][START_REF] Sedykh | Mössbauer and Magnetic Study of Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF], and LSM-NS are shown in Fig. 1, and the corresponding hyperfine parameters are presented in Table 2. The spectra at room temperature consist of an asymmetric quadrupole contribution, indicating the (super)paramagnetic nature of the pristine samples. The spectra were processed using distributions of quadrupole splitting. The local environments of iron nuclei with the parameters of the Mössbauer spectra shown in Table 2 correspond to the R-3c phase. The maximum isomer shift values δ max are almost identical for all spectra and are characteristic of high spin trivalent iron located in octahedral oxide environments. The maximum quadrupole splitting (Δ) of the R-3c phase is larger in the spectrum of the LCM-NS sample than in LSM-NS. This result reflects a lower distortion of the local environment of the Fe centres in LSM-NS compared to LCM-NS, which can be attributed to a smaller amount of interstitial oxygen. This probably derives from the smaller ionic radius of Ca 2+ compared to Sr 2+ and La 3+ , which leads to a smaller unit cell volume for LCM-NS [START_REF] Sedykh | Specific features of the structural transformations in La1 -x Ca x Mn0.98 57Fe0.02O3 + δ (x = 0.05-0.50[END_REF].

The LSM-NS sample spectrum at 80 K (Figure 1d) is a broadened sextet with a typical shape of relaxation spectra; for the LCM-NS sample, it is a combination of a broadened sextet and a quadrupole doublet, the later representing approximately 25% of the total absorption [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF]. The spectrum of the LSM-NS sample was fitted using a distribution of hyperfine magnetic fields as implemented in the model of many-state superparamagnetic relaxation [START_REF] Jones | Many-state relaxation model for the Mössbauer spectra of superparamagnets[END_REF]. The shape of the spectra is characteristic of small magnetic particles heterogeneous in size undergoing superparamagnetic relaxation, leading to a distribution of hyperfine magnetic fields, as previously shown in for LCM-NS [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF]. For LSM-NS, T b lies above 80 K.

An additional quadrupole doublet in LCM-NS is due to the presence of tiny magnetic clusters having a blocking temperature below 80 K. This was previously confirmed for LCM-NS, which Mössbauer spectrum at 5 K shows only a magnetic contribution [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF].

The Mössbauer spectra of the stoichiometric (δ = 0) samples LCM-S and LSM-S obtained by vacuum annealing, measured at 300 K, are shown in Fig. 2. The spectra were first processed using distributions of quadrupole splittings, which permitted us to determine the number of spectral components in the samples as well as their respective contributions. The spectra of LCM-S and LSM-S were then fitted by a combination of three and two quadrupole doublets, respectively (Table 3).

According to previous investigations [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0[END_REF], each subspectrum should correspond to a specific orthorhombic phase: on going from the smallest to the largest quadrupole splitting, subspectra 1, 2 and 3 should then represent the increasingly distorted phases PnmaI, PnmaII* and PnmaII. In this hypothesis, LCM-S contains the three phases, whereas in LSM-S no trace of the PnmaI phase is found. In these samples, the evolution of the different phases can be related to the oxidation state of the manganese centres: the PnmaII phase, containing in only Jahn-Teller Mn 3+ ions, has a strongly distorted lattice. Doping with a divalent impurity induces the partial replacement of the Mn 3+ ions by non-Jahn-Teller Mn 4+ , leading to the transformation of the PnmaII phase transforms in the more symmetric PnmaI one. The relative intensity of each subspectrum, which can be considered as a measure of the relative concentration of each phase if their Lamb-Mossbauer factors are assumed to be equal, are different for LCM-S and LSM-S (cf.

Table 3). The prevailing contribution of the PnmaII phase in LCM-S can be related to the difference in ionic radii of the doping elements and lanthanum, as already described in refs. [START_REF] Dubinin | Phase separation in a manganite La0.95Ba0.05MnO 3 crystal[END_REF][START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0[END_REF].

The Mössbauer spectra of LCM-S and LSM-S at 80 K (cf. Fig. 2) show only a relatively broad magnetic contribution, which can be fitted with 3 and 2 components (cf. Table 3), respectively, in line with the fits of the room temperature spectra: a distribution of magnetic fields and two relaxation subspectra in manystate superparamagnetic relaxation model [START_REF] Jones | Many-state relaxation model for the Mössbauer spectra of superparamagnets[END_REF] were used for LCM-S, whereas a distribution of the magnetic fields and one relaxation sextet were used for LSM-S. As for the nonstoichiometric samples, the relaxation components are connected with the presence of superparamagnetic particles [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0[END_REF][START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF][START_REF] Sedykh | Mössbauer and Magnetic Study of Lanthanum Manganite La1 -xCaxMn0.98Fe0.02O3 + δ (x = 0.05[END_REF]. By the analogy with previous work [START_REF] Pchelina | Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 -xCaxMn0.98Fe0[END_REF], we can assume that at low temperature the magnetic hyperfine field decreases in the series PnmaI > PnmaII* > PnmaII.

In conclusion, Mössbauer spectroscopy shows the formation of a phase-separated system composed of coexisting orthorhombic phases in the stoichiomertric lanthanum manganites after removing interstitial oxygen by vacuum annealing. Different amounts of the different phases are found in LSM-S compared to LCM-S due to the different ionic radii of the dopant ions. The undergoing of superparamagnetic relaxation is proved by the temperature dependence of the Mössbauer spectra, and is attributed to the presence of magnetic nanoparticles. The lower relaxation rate of the PnmaI phase can be related to the presence of particles of larger sizes than for the other phases.

3.3. Magnetic measurements

Magnetostatic measurements

Magnetic measurements were carried out to better understand the effect of doping and stoichiometry on the physical properties. In agreement with Mössbauer spectroscopy, both stoichiometric and nonstoichiometric samples exhibit paramagnetic behaviour at 300 K (Fig. 3), while magnetic order is reached at 100 K for all samples (Fig. 4). As expected, stoichiometric samples showed much lower magnetization values in the maximum field compared to non-stoichiometric ones. An increase in the coercive field for stoichiometric samples (more than 5 times that of non-stoichiometric samples) indicates the appearance of magnetic anisotropy. Anisotropy can be caused by the appearance of a higher coercive phase or by an increase in cluster size after the temperature treatment of the samples. Moreover, the shape of the hysteresis loops (lack of saturation and the loop shift) of the annealed samples indicates the presence of an antiferromagnetic phase in their composition (Fig. 4). Saturation is not achieved for the LCM-S sample in a maximum field of 1280 kA/m; whereas an offset from zero magnetic field is observed indicating the presence of interacting antiferromagnetic and ferromagnetic phases (exchange bias) [START_REF] Meiklejohn | New Magnetic Anisotropy[END_REF]. The arising of a highly anisotropic antiferromagnetic phase interacting with ferromagnetic clusters leads to the appearance of a wider hysteresis loop. Since the ferromagnetic phase is responsible for the hysteresis, the interaction of ferromagnetic clusters with the antiferromagnetic phase leads to the induction of a kind of anisotropya preferred direction of magnetization appears. The consequence of this is an increase in the coercive force and exchange displacement.

Calculation and analysis of the magnetic cluster size from Mössbauer and magnetic measurements

The values of the effective anisotropy constant K eff at 100 K reported in Table 4 is very similar for all samples (from 5.5 to 23*10 4 J/m 3 ), suggesting that the cluster sizes depend on the type of doping element (there is no saturation for the LCM-S; therefore, it was not possible to determine the magnetic anisotropy constant for this sample).

The cluster sizes of LCM and LSM samples of both stoichiometric and non-stoichiometric composition was estimated using a variable parameter α obtained from Mössbauer spectrum fitting in many-state superparamagnetic relaxation model at 80 K. It follows that cluster sizes in the LCM-NS sample are approximately 1.5 times smaller than in LSM-NS. According to LSM-S we can see that PnmaII* phase is characterized by a much larger size of the magnetic clusters region. It can be assumed from an analysis of the data obtained that there is a spontaneous formation of localized magnetic clusters ~ 2.5-4.6 nm above T c for all samples. The existence of analogous clusters ~ 1.2 nm in size in doped lanthanum-manganite systems was detected using small-angle neutron scattering measurements in [20].

Temperature dependence of the magnetic properties

The temperature dependence of the magnetization in samples LCM-NS and LSM-NS (Fig. 5a) in the temperature range 80-300 K was measured in a field of 2.4 kA/m, which is expected to be less than the coercive field so that the difference between the blocked and unblocked state is visible. In the case of samples LCM-S and LSM-S (Fig. 5b), the measurements were carried out in an external magnetic field of 8 kA/m in the temperature range 0-300 K. These measurements demonstrate the presence of superparamagnetic clusters in the LSM and LCM systems, in agreement Mössbauer spectroscopy.

Moreover, for sample LCM-NS, the blocking temperature is outside the measurement range, i.e., below the temperature of liquid nitrogen, also in agreement with the Mössbauer results indicating a large contribution of the disordered phase at 80 K. Such a significant difference in blocking temperatures for the non-stoichiometric samples can also be related to the different size of the ferromagnetic clusters. For samples LCM-S and LSM-S, on the other hand, practically identical blocking temperatures of 120 and 122 K were measured, respectively. Some blurring of the ZFC peak for sample LCM-S indicates a relatively large particle size distribution.

Magnetic susceptibility

For all samples, the evolution of the magnetic susceptibility with the temperature was measured, the direct and inverse dependences of which are shown in Fig. 6. The measurements were carried between 70 and 275 K. At room temperature, the LCM-NS and LSM-NS samples behave as single-phase paramagnets, while a phase transition to the ferromagnetic state is observed as temperature decreases. The Curie temperatures Tc corresponding to the initial state of the samples, determined at the intersection of the straight line approximating the linear portion of the reciprocal susceptibility with the abscissa, is higher for LCM-NS than for LSM-NS. It should be noted that, unlike LCM-NS, the LSM-NS sample has a rather sharp drop in susceptibility in the range T = 170-185 K. (Fig. 6) This form of the χ(T) dependence is typical for characteristic of polycrystalline LaMnO 3+δ containing interstitial oxygen [START_REF] Arbuzova | Magnetic susceptibility of nanostructural manganite LaMnO3 + δ produced by mechanochemistry method[END_REF]. In turn, χ(T)

for LCM-NS has a more complex form with a singularity in the range 170-230 K. Such behaviour of LCM-NS sample might depend on the presence of small-size magnetic clusters with a transition temperature below 80 K, as confirmed by both Mössbauer and magnetisation results.

Other factors influence the shape of the temperature dependence of the magnetic susceptibility, such as the ionic radius of the dopant. In fact, doping with calcium decreases the volume of the crystal lattice and the amount of interstitial oxygen compared to Sr, which has almost the same size of La. The higher amount of interstitial oxygen in LSM-NS than in LCM-NS induces an increase in number and inhomogeneous distribution of lattice defects, resulting in an inhomogeneous magnetic state. Similarly, the large size distribution of the ferromagnetic nanoparticles in LCM-NS leads to a noticeable increase in T C and to a broader phase transition range. Finally, according to iodometric titration, the amount of Mn 4+ ions in LCM-NS is lower than in LSM-NS. Considering the higher magnetic moments of Mn 3+ (2 µ В ) compared to Mn 4+ (1.5 µ В ), a higher effective magnetic moment per cell is expected for LCM-NS. In doped lanthanum manganites, the magnetic order is determined by the sum of contributions from the double exchange Mn 3+ -O-Mn 4+ (DE model) and super-exchange (SE mechanism). The DE model leads to the ferromagnetic ordering of the magnetic moments of Mn ions, and the SE mechanism leads to antiferromagnetic ordering of the magnetic moments of the Fe and Mn ions [START_REF] Dagotto | Nanoscale Phase Separation and Colossal Magnetoresistance[END_REF]. Since the Fe content in the two systems is the same and amounts to 2%, it can be assumed that the formation of a Fe-O-Fe bond at such a concentration is unlikely [START_REF] Song | Magnetic and electronic properties of transition-metalsubstituted perovskite manganites-La0.7Ca0.3Mn0.95X0.05O3[END_REF], and the only possible metal-oxygen Fe-O-Mn bond occurs via SE mechanism. Also, it can be proposed that the greatest effect will be exerted by double exchange interaction (ferromagnetic ordering always creates a greater magnetic moment than antiferromagnetic ordering). Thus, it can be supposed that the broadening of the transition range to the magnetically ordered state of the LCM-NS sample over the temperature region (Fig. 6 -χ(T) slope for (b) is less than for (a)) is associated precisely with a smaller amount of Mn 4+ ions than in LSM-NS.

To clarify the nature of magnetic transitions in stoichiometric samples after annealing in vacuum (i.e., in the absence of interstitial oxygen), the dependence of the magnetic susceptibility of LCM-S and LSM-S was measured in similar conditions. Supposing that LCM-S consist of three phases (PnmaI, PnmaII*, PnmaII) and LSM-S of two phases (PnmaII*, PnmaII), with decreasing temperature, PnmaI would transform into a ferromagnetic state, and PnmaII into an antiferromagnetic state. For the two samples, therefore, both Néel and the Curie temperatures (T N and T c , respectively) were determined (cf. Table 5).

The first difference between the systems in the form of the χ(T) dependence is the different peak widths.

The broad peak for sample LCM-S can be explained by the presence of two phases with mismatched Néel temperatures: T N1 =121 K, T N2 =130 K. In the LSM-S sample, the peak is rather narrow, and it can be at best attributed to two peaks with close Néel temperatures. The second difference is the presence of a detectable ferromagnetic phase for LCM-S with a Curie temperature of about 136 K.

Summarizing the data obtained, we can conclude that the type of alloying element, the amount of interstitial oxygen, and, the number of Mn 4+ atoms in samples of nonstoichiometric composition are significant factors affecting the magnetic properties of doped lanthanum manganites. Samples of stoichiometric composition are characterized by the presence of several phases for each of the samples.

The results of magnetic studies demonstrate the antiferromagnetic behaviour of LSM-S, which allows us to conclude that the magnetic order in PnmaII* is antiferromagnetic. Magnetic measurements confirm the coexistence of several phases characterized by different magnetic ordering.

Conclusion

Attractive structural and magnetic properties are manifested precisely in low-doped lanthanum manganites by virtue of presence of different interactions: Jahn-Teller effect, double and super-exchange, coexistence of antiferromagnetic and ferromagnetic order.

Here, via the complementary information obtained by Mössbauer spectroscopy, magnetization and magnetic susceptibility measurements, it is shown that the type of doping element, i.e., Ca or Sr, the amount of interstitial oxygen, as well as the change in the Mn 3+ /Mn 4+ ratio lead to intrinsic inhomogeneities and the coexistence of varying amounts of different structural and magnetic phases.

Different orthorhombic structures, which were practically impossible to distinguish by X-ray diffraction methods, could thus be evidenced. In addition, it is shown for the first time that the PnmaII* phase is characterized by antiferromagnetic ordering.

The presence of superparamagnetic clusters with more or less wide distribution of sizes depending on the composition could be demonstrated by the temperature dependence of the Mossbauer spectra and the magnetization curves measured with an external field. The PnmaII* phase, in particular, is characterized by a much larger sizes. The presence of such clusters can be considered as a proof of the high stability of ferromagnetic ordering.

Figure Captions

Fig. 1 .

 1 Fig. 1. 57 Fe Mössbauer spectra of LCM-NS and LSM-NS measured at room temperature and 80 K (a,b and c,d, respectively).

Fig. 2 .

 2 Fig. 2. 57 Fe Mössbauer spectra of LCM-S and LSM-S measured at room temperature and 80K (a,b and c,d, respectively).

Fig. 3 .Fig. 4 .

 34 Fig. 3. Hysteresis loops obtained at 300 K for all samples: 1 -LSM-S, 2 -LSM-NS, 3 -LCM-S, 4 -LCM-NS.Fig. 4. Hysteresis loops obtained at 100 K for all samples: 1 -LSM-S, 2 -LSM-NS, 3 -LCM-S, 4 -LCM-NS.

Fig. 5 .

 5 Fig. 5. The temperature dependence of the magnetization (ZFC/FC measurements) in the field of 2.4 kA/m for 2-LSM-NS and 4-LCM-NS samples (a) and in tne field of 8 kA/m for 1-LSM-S and 3-LCM-S samples (b).

Fig. 6 .

 6 Fig. 6. Temperature dependence of the direct and inverse magnetic susceptibility of the investigated samples: a) LCM-NS, b) LSM-NS, c) LCM-S, d) LSM-S.

FiguresFig. 1

 1 Figures

  Fig.1.

Fig. 2 .

 2 Fig.2.

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig.3.

Fig. 6 .

 6 Fig.6.

Table 1 .

 1 The lattice parameters for the R-3c and PnmaII* phases of La 0.95 A 0.05 Mn 0.98 Fe 0.02 O 3+δ (A = Sr, Ca) of non-stoichiometric and stoichiometric compositions[START_REF] Sedykh | The features of structural transformations in lanthanum manganites La1-xAxMnO3+δ (A = Ca, Sr, Ba)[END_REF]. For comparison, the data for R-3c and PnmaII phases of the parent LaMnO 3+δ with 1.5 at% 57 Fe Mossbauer isotope are listed as well.

	Tables
	Sample	Phase	a, Å	b, Å	c, Å	V, Å 3
	LaMnO 3+δ	R-3c	5.523(2)	-	13.326(4)	352.1(3)
	LCM-NS	R-3c	5.519(2)	-	13.322(4)	351.4(3)
	LSM-NS	R-3c	5.522(2)	-	13.343(4)	352.4(3)
	LaMnO 3	PnmaII	5.725(2)	7.703(3)	5.537(2)	244.5(3)
	LCM-S	PnmaII*	5.681(2)	7.718(3)	5.534(2)	242.9(3)
	LSM-S	PnmaII*	5.638(2)	7.729(3)	5.542(2)	241.8(3)

Table 2 .

 2 Parameters of the 57 Fe Mössbauer spectra of nonstoichiometric La 0.95 A 0.05 Mn 0.98 Fe 0.02 O

		Sample	LCM-NS	LSM-NS
		T, K	300	80	300	80
		δ, mm/s	0.365±0.001	0.415±0.003	0.366±0.002	-
	Doublet	, mm/s	0.290±0.006	0.375±0.005	0.276±0.006	-
		Г, mm/s	0.291±0.018	0.407±0.011	0.250-fix
		δ, mm/s	-	0.496±0.011	-	0.504±0.021
		ε, mm/s	-	0.043±0.011	-	0.017±0.019
	Sextet	Г, mm/s	-	0.328±0.030	-	0.250-fix
		H n , kOe	-	441±3	-	480±6
		α	-	1.5±0.1	-	8.1±1.6

3+ (A = Ca, Sr) samples measured at room temperature (300 K) and at 80 K. δis the isomer shift relative to -Fe at room temperature, Δis the quadrupole splitting, Гis the width of the Mössbauer line, εis the quadrupole shift, H n -is the hyperfine magnetic field, αis the parameter of the relaxation model. The maximum spectral parameters are given for LCM-NS (at RT), LSM-NS.

Table 3 .

 3 Parameters of the 57 Fe Mössbauer spectra of stoichiometric La 0.95 A 0.05 Mn 0.98 Fe 0.02 O 3 (A = Ca, Sr) samples measured at room temperature (300 K) and at 80 K. δis the shift relative to -Fe, Δis the quadrupole splitting, Гis the width of the Mössbauer line, Iis the relative intensity of the subspectrum (contribution of each phase), H nis the hyperfine magnetic field, αis the parameter of the relaxation model. The maximum spectral parameters are given in the Hamilton model.

		Sample		LCM-S		LSM-S
		№ subspectrum	1-(PnmaI)	2-(PnmaII*)	3-(PnmaII)	2-(PnmaII*)	3-(PnmaII)
		δ, mm/s	0.379±0.002 0.379±0.002 0.377±0.001 0.378±0.001 0.377±0.001
	Doublet	Δ, mm/s	0.338±0.007 0.782±0.003 1.170±0.001 0.542±0.002 0.857±0.002
	T=300 К	Г, mm/s	0.290±0.002 0.290±0.002 0.290±0.002 0.290±0.010 0.290±0.010
		I,%	9.0±0.4	34.5±0.5	56.5±0.5	54.3±1.1	45.7±1.1%
		δ, mm/s	0.519±0.060 0.609±0.060 0.475±0.010 0.525±0.018 0.491±0.100
		Г, mm/s	0.500 -fix	0.350 -fix	0.250 -fix	0.350 -fix	0.250 -fix
	Sextet
		H n , kOe	452±7	373 -fix	356.4±0.4	406±2	346±4
	T=80 K
		α	4±0.1	1±0.1	-	4±0.6	-
		I, %	6.9±1.1	26.0±0.2	67.1±0.1	64.5±8.0	35.5±8.0

Table 4 .

 4 The parameter α, calculated in the model of many-state superparamagnetic relaxation for different phases in the samples under study, K eff is the calculated magnetic anisotropy constant, Vthe particle volume, lapproximate clusters size.

			LCM-NS	LSM-NS	LCM-S	LSM-S
		R-3c	1.5	10
	α	PnmaI			4
		PnmaII *			1	4
	K eff , J/m 3		1.8*10 5	2.3*10 5	-	5.5*10 4
		R-3c	2.5	3.9
	l= , nm	PnmaI
		PnmaII*				4.6

Table 5 .

 5 Blocking temperatures T b , the Curie temperatures T C and the Néel temperatures T N for LSM and LCM samples.

Acknowledgments

The authors thank C. Reibel (PAC-ICGM, Univ. Montpellier), for magnetic measurements and N.S.

Perov (Lomonosov Moscow State University) for discussing the results of magnetic measurements.

The reported study was funded by RFBR, project number 19-32-90222.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.