Hints of granular superconductivity in natural graphite verified by trapped flux transport measurements

This study describes electrical transport measurements as a function of magnetic field and temperature that provide hints of the existence of superconductivity with a critical temperature of Tc∼350 K in a natural graphite sample. The measurements were done in a restricted temperature 300 K ⩽T⩽450 K and magnetic field B⩽400 mT range. Electrical resistance measurements at remanence (zero field), after the application of a magnetic field, indicate the existence of trapped flux, which remains nearly unchanged within ∼30 min but it vanishes at a temperature of ∼330 K. The apparent transition is accompanied by a clear enhancement of the magnetoresistance at T<Tc . Raman measurements on the bulk sample reveal the existence of the rhombohedral stacking order, which interfaces with the usual Bernal phase were predicted to lead to high temperature superconductivity due to the formation of robust flat bands in the electron dispersion relation.


Introduction
The phenomenology of granular superconductors is an important issue especially when new superconductors are discovered, which structure and stoichiometry are not well known or their homogeneity is not clarified. Surprisingly, this phenomenology was not always taken into account in the very first publications of new superconductors as, e.g. the recently discovered hydrides under pressure [1] or in twisted bilayer graphene superconductors [2]. Several reports with clear descriptions on the phenomenology of granular superconductors were published in the past, for example see [3][4][5] and References therein. One of the main examples of a granular superconductor is the very first report on the high-temperature superconducting oxides, where no zero resistance was achieved added to very broad transitions in temperature [6]. However, even in the case of sharp transitions in the temperature dependence of the resistance, the phenomenology of granular superconductors should be always considered, as the recently discussion on the interpretation of the available experimental data on the apparent superconductivity in some hydrides under pressure demonstrates [7][8][9][10][11].
A granular superconductor is a material with superconducting nano-or micro-grains coupled through Josephson junctions, sometimes known as 'weak links' in the literature [4]. In this case, the main characteristics of bulk superconductors, as the total flux expulsion or Meissner state, should not be expected to be measurable through, e.g. magnetization measurements. Although a partial field expulsion in granular superconductors is possible, its amount depends on the size of the grains in comparison with the London effective penetration depth and the strength of the Josephson coupling between the grains. Moreover, a demagnetization factor near one due to the sample geometry as is the case of two dimensional (2D) superconducting states, like in twisted bilayer graphene [2] or at certain 2D stacking faults (SFs) in the graphite structure [12,13], may prevent the observation of a full Meissner state. In the case of very thin superconductors, the effective penetration depth, the so-called Pearl penetration depth [14] inversely proportional to the sample thickness, could be larger than any sample size making even more difficult the measurement of any flux expulsion due to Meissner currents. In such cases, the measurement of a remanent state at zero field as well as hysteresis in the magnetization [3] and magnetoresistance [5,15] can provide further hints for the existence of a superconducting state, as proposed recently by J. E. Hirsch for the case of the hydrides under high pressure [9].
In contrast to magnetization measurements with high resolution, which requires nowadays relatively expensive SQUID magnetometers, electrical transport measurements can be a simple and cheap alternative to check for the existence of granular superconductivity. The Josephson coupling between superconducting grains may establish a percolative path throughout-or in parts of-the sample, upon the amount or density of superconducting grains in it. Therefore, the existence of a superconducting material in a non-superconduc ting matrix cannot be simply ruled out when no zero resistance is measured. Strictly speaking, a zero resistance state (a zero with infinite number of zeros after the comma) cannot be measured.
Experimentalists have the possibility to check for the existence of superconducting grains in granular samples by performing current-voltage (I − V) measurements, which could reveal a Josephson-like behavior [2,16,17]. Otherwise, the measurement of a hysteresis in the magnetoresistance due to trapped magnetic flux can be a clear hint for the existence of superconductivity, if a ferro-or ferrimagnetic origin for the hysteresis can be ruled out.
A hysteresis in the magnetoresistance, as well as in the magnetization, can be caused by pinning of vortices within the superconducting grains or by permanent currents through Josephson-coupled regions after removing a large enough applied field in the superconducting state of the sample. The existence of trapped flux through permanent currents was proposed by Hirsch and Marsiglio as a way to check for the existence of superconductivity in the hydrides [8]. In this study we follow this proposal to confirm the existence of a remanent magnetic state below a temperature of ∼350 K in a bulk natural graphite sample that contains a mixture of Bernal and rhombohedral stacking orders, confirming recent reports of room temperature superconductivity in different graphite samples with similar characteristics [18][19][20][21].
High-temperature superconductivity is expected in systems where the electronic dispersion relation is relatively flat, as in topological flat-band systems [22], e.g. at the surface of rhombohedral (3R) graphite [23][24][25] or at the SFs or interfaces between Bernal (2H) and rhombohedral (3R) stacking orders [24,26,27]. Therefore, besides the study of the intrinsic properties of graphite with only the 2H phase, several recent studies try to confirm the existence of the 3R stacking order in usual bulk and thin, exfoliated graphite samples, e.g. [28], and to correlate any anomalous behavior in some transport or magnetic properties with this minority phase; or to the existence of SFs between the 3R and 2H orders. Previous studies suggest that natural graphite samples with this kind of SFs show a possible superconducting transition at T c ∼ 350 K [18]. A recent study supports the existence of a superconducting transition in graphite samples at similar [20] or even higher temperatures [21]. Those new works provided, however, no knowledge on the existence of the 3R stacking order in their samples.
The aim of our study is rather modest, namely: Can we measure trapped magnetic flux by transport measurements in a sample that has the 3R and 2H phases and simultaneously obtain a hint for a superconducting transition at the reported temperature(s)? To fulfill these purposes, from several available bulk natural graphite samples we selected one that showed the existence of the two stacking orders according to detailed Raman studies we present in this report. With the help of a high-temperature oven system that allowed us the measurement of the resistance between 300 K and 450 K in an applied field B ≲ 0.4 T, we were able to measure a finite shift in the electrical resistance compatible with trapped magnetic flux in the remanent state of the sample, i.e. at B = 0 T after applying a magnetic field. The observed behavior is compatible with the expected one for granular superconductors. Moreover, the measured resistance shift (due to trapped flux) decreases to negligible values at temperatures T ≳ 340 K, in agreement with previous [18,19] and recent studies [20]. Our overall results support the existence of a superconducting state above room temperature in graphite samples with 2H and 3R stacking orders.

Sample characteristics and experimental methods
The selected flakes of natural graphite were extracted in an artisanal way from the company Nacional do Grafite (MG, Brazil), which is the third largest graphite miner in the world. From its mines one can obtain graphite samples of highest structural and purity quality. The flakes were cleaned with isopropyl alcohol to eliminate organic residues, dried at room temperature and cut using a diamond thread. A piece of them (NGS02) was carefully selected taking into account its overall shape, which should be appropriate to contact the sample for transport measurements without the need of any lithography. Four electrodes were prepared on the macroscopic sample using Ag-paste, see figure 1(a). The length, width and thickness of the sample were 3 mm × 0.5 mm × 0.5 mm. These dimensions assure the existence of a large number of SFs, especially those between Bernal and rhombohedral stacking orders, see, e.g. the transmission electron microscopy (TEM) picture in figure 1 of [18].
The sample was fixed with varnish on a Si substrate with a SiN layer at one side, and this fixed on a chip carrier, see figure 1(a), in such a way that the c-axis of the sample could be oriented parallel to the applied field. The magnetic field B ⩽ 0.4 T was produced by a water-cooled solenoid, which is sufficient for our purposes. The chip carrier was fixed in an especially made holder, which allows us to increase the temperature of the sample to 450 K in vacuum. Two field independent thermometers were used. One just on the back part of the substrate where the sample was placed and a second one fixed on the main column of the chip holder. The whole arrangement was included in a especially made oven, which diameter at the position of the sample holder fits between the poles of the electromagnet, see figure 1(b). The whole sample holder was kept in vacuum with a pressure <10 −6 mbar. Independent measurements (performed in other laboratory) of the magnetic properties of the used substrate as well as of the bottom material of the chip carrier (a part was cut from it) show that no significant remanent magnetic moment remains after applying 30 mT at room temperature. Moreover, there is no sudden change of the magnetic moment of those materials in the temperature region of our measurements, which can provide the observed change in the remanence of the resistance at ∼320 K, as shown below.
The sample resistance was measured with a Lakeshore 370 AC resistance bridge with an effective maximum current of 10 mA. The sample voltage-current response was linear in the used current region within experimental error. The temperature control was achieved using a Lakeshore 335 temperature controller.
The reason for selecting a natural graphite sample to search for superconductivity at or above room temperature is that the 3R stacking order is found in those samples in a larger percentage than in other commercial graphite samples (pyrolytic of high grade or Kish graphite obtained from molten steel). Because the detection of the 3R phase through XRD requires a very high sensitive equipment to measure its secondary XRD Bragg peaks that do not coincide with the Bernal (2H) phase [18], we decided to use Raman spectroscopy.
Raman spectroscopic characterization was performed at room temperature (293 K) using a WITec alpha 300R system equipped to acquire spectra with a green laser (λ = 532 nm). The Raman spectra was obtained along the sample as well as confocal hyperspectral Raman imaging by means of a piezoelectric stage accessory of the system. A sample mapping was done between the internal voltage electrodes in an area of ∼1 × 0.5 mm 2 . More than 2000 Raman spectra were obtained in this mapping continuously, showing both the usual 2H and the 3R phases in the selected sample (MC02) for transport measurements. All acquisitions were performed using a grating of 1800 grooves mm −1 , 100 × objectives (NA 0.9) and with an incident laser power of 2 mW. The main difference is the width of the 2D band. A detailed explanation and the quantitative fits can be seen in [29]. (b) 2D Raman mapping of the region between the voltage electrodes of the measured sample. The color scale is related to the two stacking orders, where the lightest, yellow color is related to the 3R phase and the rest the 2H phase.

Raman results
Raman spectroscopy has proven to be a useful tool to study graphite-based materials and provides different valuable informations [30,31]. The so-called D, G and 2D bands are the designations of Raman peaks found in graphene and graphite materials widely reported in the literature. The presence of disorder and defects manifests itself by the appearance of the Raman D band, which can also be used to distinguish between zigzag and armchair edges [32,33]. In the case of a graphene single layer, only one zone-center mode is allowed in the Raman spectra giving rise to the G band at 1580 cm −1 . On the other hand, the stacking order can also be distinguished from the shape of the 2D band (at 2700 cm −1 ) in the few and multilayers graphene. Particularly, the shape and width of the 2D band is associated with the two stacking orders of graphite. The 2H phase is the most stable and abundant in nature. The 2H graphite unit cell has four inequivalent carbon atoms (z = 4). On the other hand, graphite samples can have up to a 30% of the 3R stacking sequence, known as rhombohedral.
The primitive 3R unit cell of graphite has only two inequivalent carbon atoms (z = 2) [34,35]. Particularly, the 2D band of the 3R has a peak width larger than the one of the 2H phase, which can be interpreted as the existence of more double resonance channels in comparison to the 2H phase. This is because the volume Brillouin zone (BZ) of the 3R phase is twice that of the 2H, which allows further resonance conditions involving different states within the BZ [29]. Figure 2(a) shows the Raman spectra performed on the entire graphite sample in an area of 1 mm × 0.5 mm. From this mapping we can mainly recognize two regions with different stacking orders, the 2H and the 3R phases. These regions were characterized through the shape and width of the 2D bands (FHDM 2D ), which are clearly different as can be seen in figure 2(a). For the 2H regions we observed a FHDM 2D ≃ 27 cm −1 and for the 3R regions ≃70 cm −1 , a clear difference of the 2D Raman band that can be used to identify them.
In figure 2(b) we show a Raman mapping image of part of the sample, in which a systematic study was made to identify the 3R and 2H phases. As an attempt to show these two phases and their distribution in the graphite sample, a color mapping was performed using FHDM 2D , where the yellow regions represent those with the 3R phase, the rest correspond to regions with the 2H phase. The 2D mapping was taken with the laser beam pointing parallel to the c-axis of the graphite sample and in the sample region between the voltage electrodes. The Raman mapping in figure 2(b) shows signals produced to a sample depth of ∼1 µm. Figure 3(a) shows the temperature dependence of the electrical resistance (R) of the selected sample at zero applied field. The measurements were done by heating with a heating rate of 2 K min −1 . When a temperature of 450 K was reached, the measurement continued by cooling stabilizing the temperature for 15 min before the next point at lower temperature was obtained. The small irreversibility (hysteresis in temperature), clearly observed at the highest temperature, has its origin in the difference between the actual sample temperature and the one measured by the thermometer. Note that at the heating curve, the temperature of the sample followed the thermometer temperature with a lag because of the relatively large heating rate chosen. Because the resistance of the sample increases with temperature, it is obvious that the cooling curve in equilibrium should be above the heating curve, as observed.

Temperature dependence of the resistance at zero field
At a first glance one cannot clearly recognize in figure 3(a) any transition in R(T). In the right y-axis of the same figure we show the first derivative of R(T) (without any subtraction) where a clear maximum is observed between 401 K and 412 K, upon temperature sweep direction. This maximum in the first derivative of R(T) provides a hint of a possible transition. Figure 3(b) shows the same data as figure 3(a) but after subtraction of a linear in temperature background. This difference suggests the existence of a transition that levels off below a temperature T ≃ 340 K. The subtracted linear temperature background is actually arbitrary but helps to realize the change in the temperature dependence of the resistance in a restricted temperature range. We would like to emphasize that in this temperature range one expects a smooth temperature dependence in the resistance [36]. The temperature dependence of graphite bulk samples from different origins reported in the literature, can be very well explained in a broad temperature range taking into account the semiconducting contributions of both stacking orders and the one from the SFs in parallel, see [37] for more details.
The hint of a transition from the behaviour of R(T), though small (see figure 3), is similar to the observed change in R(T) at similar temperatures in other graphite bulk samples, see figure 6 in [18]. Moreover, a finite difference between the magnetic moment in the field cooled (FC) and zero-field cooled (ZFC) states vs. temperature starts at a similar temperature (see figure 6(c) in [18]). Magnetic force microscopy measurements of the magnetic field gradient produced by a permanent current path in remanent state (zero field) of a graphite sample after applying a magnetic field, indicate that the current path amplitude vanishes between 350 K and 380 K, in agreement with the transition temperature obtained from R(T) or even its remanence on the same graphite sample (see figure 7(g) in [19]). Recently published magnetization measurement vs. temperature in the ZFC and FC states of bulk graphite samples indicate the existence of a superconducting transition at ∼350 K (see figure 4(d) in [20]).
One interesting property of granular superconductors is the negative magnetoresistance they show above a certain applied field and at low enough temperatures. Normalized magnetoresistance results of graphite samples show a behavior in the magnetoresistance comparable to that of conventional granular superconducting materials, see figure 7 in [38]. Measurements of the temperature dependence of this negative magnetoresistance part reveal that it tends to vanish at T ≃ 350 K, see figure 5 in [39].
One may speculate that the tiny change in the slope of R(T), see figure 3, as well as the vanishing of the remanence in the magnetoresistance at a similar temperature (see figure 5 discussed below) could be related to a hidden magnetic order transition of unknown origin. However, in the literature there is no report on any magnetic transition in pure graphite at the temperatures of our measurements. If we speculate that ferromagnetic cementite Fe 3 C exists in our sample, its Curie temperature ranges from 446 K to 460 K upon Fe concentration. We could further speculate that part of the graphite structure of the sample can show a magnetic transition because of the structural defects, the phenomenon known as defect-induced magnetism [40]. However, magnetically ordered graphite samples show a negative [41] not a positive magnetoresistance as our sample shows, see figure 4.

Temperature dependence of the resistance at different applied fields
Before we discuss below the obtained results, it is necessary to emphasize some concepts on the real nature of the electronic system of ideal graphite samples, i.e. without the contribution of the SFs. Old as well as relatively new publications on graphite assume that ideal graphite is a semimetal. The main origin of this assumption is the metalliclike temperature dependence of the resistance and the Shubnikov-de Haas quantum oscillations measured at low temperatures. However, these two main characteristics are not observed in thin enough ≲50 nm graphite samples, where the number or density of SFs is negligible [42][43][44][45]. Ideal graphite is a narrow-gap semiconductor with an energy gap of the order of 30 meV for the Bernal and 100 meV for the rhombohedral stacking order [37,46]. Optical pump-probe spectroscopy experiments on 20-30 nm thick graphite flakes indicate a semiconductorlike carrier dynamic with a non-zero band gap of about 30 meV [47]. Temperature dependent resistance measurements of graphite samples of different thickness reveal the contribution of the SFs and the semiconducting nature of the ideal graphite regions [37,45,46]. Recent scanning tunneling spectroscopy measurements revealed also the semiconducting nature of the ideal graphite structure with Bernal stacking order, with an energy gap of the order of that obtained by transport measurements [48].
Having clarified this important point, the next one we need to discuss is on the nature of the field-driven metal insulator transition (MIT) observed in thick enough graphite samples [49]. It is obvious that this MIT is not intrinsic of ideal graphite because it does not occur in thin enough samples without SFs (they show a semiconducting behavior in the resistance at zero applied field [37,44,46]). The MIT is related to the physics of the electronic system at certain 2D SFs embedded in thick enough and well-ordered graphite samples.
One may speculate that the semiconducting behaviour of the electrical resistance of thin enough graphite samples is due to some lattice disorder within the graphene layers in those samples. However, this does not seem the case as confocal micro-Raman spectroscopy reveals [37,45]. Moreover, experimental results on micro-fabricated constrictions in micrometer small graphite flakes of a few tens of nanometers thickness, i.e. without SFs [50], indicate that the carriers behave ballistically at 300 K with micrometers-large mean free path. Similar results were obtained in a 20 nm thick graphite sample without constrictions [51]. The mobility of the carriers in thin graphite samples of high quality clearly overwhelms the one obtained in suspended graphene [50]. All these results indicate that it is not the lattice disorder the reason for the absence of (semi)metallicity and of the MIT in thin samples but the absence of SFs.
Field-driven MITs were also reported in single [52][53][54] and bilayer graphene [55] samples, which details depend on the sample disorder and on the carrier density. Whether the origin of the MIT in those samples is related to localized superconductivity or not, is not yet clarified. The superconducting behavior found in twisted bilayer graphene samples [2], themselves a SF, is similar to that measured at certain SFs found in thick enough graphite TEM lamellae, which provided the possibility to contact the edges of the SFs [16] and allowing therefore a direct comparison between them [17]. Taking into account that the metalliclike behavior of the resistance of graphite samples is directly related to the existence of certain 2D SFs, it is not surprising to find some similarities and differences between the MITs. In particular, beyond the field at which the MIT occurs, i.e. at fields B ≳ 1T and at low enough temperatures, bulk graphite samples show a clear and systematic reentrance to a metalliclike state [49] as well as a negative magnetoresistance above ∼20 T, which appears to be related to granular superconductivity hidden at certain SFs as shown in [38,39].
Therefore and taking into account this new knowledge, the magnetoresistance of graphite samples has been recently revised and its similarities to granular superconductors was revealed [38]. From the study of the magnetoresistance of a graphite TEM lamella sample at very high magnetic fields and temperatures, the magnetoresistance of the SFs themselves has been obtained [39]. It reveals a granular superconducting behavior with a T c ∼ 350 K [39]. Several results of this work overwhelm previous interpretations of the magnetoresistance of graphite published in the literature, like, e.g. the magnetic catalysis scenario [56][57][58]. Some of the reported anomalous features in the magnetoresistance of graphite at high fields, like the temperature dependence of the maximum in the resistance at a field B max (T), turned out to be artifacts due to the in-parallel, competitive contributions of the magnetoresistance of the semiconducting graphite matrix and the one from the SFs [39]. Figure 4(a) shows the temperature dependence of R(T) at different fields applied normal to the graphene planes and the SFs. The observed behavior clearly indicates that there is a qualitative change in the magnetoresistance between the high and low temperature regions. This difference is better recognized when we plot R(T) normalized by its value at 450 K, see figure 4(b). Note that were the magnetoresistance independent of temperature in the applied field range (which increases only a few percent the R(T, 0) in this temperature range), we should obtain a single normalized R(T)-curve, independent of the applied field.
The results in figure 4 indicate that there should be a transition in (part of) the electronic system within the sample region picked up by the voltage electrodes. Furthermore, note that R(T) changes from a metallic-like behavior to a semiconducting one by the application of a field of B > 0.2 T. This is remarkable and provides a further hint of the existence of a transition in a granular superconducting system embedded at certain SFs of the sample. Were the graphite sample as well as the superconducting system homogeneous, we would then expect a (small) broadening of the transition accompanied by a (small) shift of the transition to lower temperatures, keeping its metalliclike character in the field and temperature range of our measurements. This is clear not the case in our sample. The results shown in figure 4 are similar to those published in [18] 3.4. Remanence in the resistance after application of 30 mT As mentioned in the introduction, one key experiment that provides a hint of the existence of superconductivity, homogeneous or granular, is to check for the existence of permanent currents at remanence, i.e. at zero field after the application of a magnetic field. This remanence can be observed in magnetization field loops, in the electrical resistance as well as in magnetic force microscopy measurements. In this section we describe the finite remanence measurements at zero field after applying a fixed field of 30 mT at constant temperatures. We have used the following sequence to measure the change in the remanence of the resistance at different fixed temperatures: (1) We cooled down the sample from the highest reachable temperature of our oven (450 K) to the selected temperature at zero applied field. After reaching the selected temperature we wait approximately 2 h. to assure thermal equilibrium and to check that the resistance labeled R 1 does not depend on time within the total time of the field cycle measurement. (2) We applied the selected field and measured the resistance point R 2 during ∼30 min (the points shown at fixed field in figure 5(a)). (3) We turned off the field and measured again the resistance at zero field R 3 during ∼30 min, see figure 5(a). Afterwards, we repeated the same sequence at a different fixed temperature.
We note that the whole measuring sequence at fixed temperature starting from the data point R 1 , i.e. from zero field to 30 mT and again to zero field, i.e. at remanence, took about 60 min (the time necessary to change the magnetic field is ≲1/2 min). This time is short but comparable with the times needed to see changes in the resistance due to the logarithmic in time flux creep effects in the resistance of graphite samples, see the results taken at 1 T field in figure 21 of [18], as example. Note, however, that flux creep effects produce a decrease in the resistance with time, reassuring that the increment of the resistance at remanence, relative to its value at zero field in the virgin state, cannot be due to flux creep effects. Certainly, flux creep effects can play a role when the temperature reaches the critical one at T c . In this case the flux trapped at remanence vanishes at or near T c . Flux creep results at remanence, after applying a field comparable to the one of this work, were also obtained by magnetic force microscopy measurements following the shift with time of the position of the current path [59] as well as its vanishing at a T c ≃ 350 K [19]. The fact that the remanent value of the resistance at zero field R 3 remains after ∼30 min clearly indicates that permanent currents exist in this state of the sample, in agreement with the results obtained from magnetic force microscopy measurements of remanent current paths [19,59].
Time dependent effects due to desorption of foreign atoms or molecules measured mainly at temperatures T > 350 K in bulk graphite samples with SFs, see for example [60], indicate that the resistance decreases with time at a fixed temperature. Upon the used temperature cycle, an increase of the resistance can be also observed after cooling down [60]. Note, however, that these time dependent effects do not play any role in our experiment because of the way we performed our resistance measurement at remanence, before and after applying the magnetic field, all at a fixed temperature and within a rather restricted time range. Figure 5(b) shows the difference ∆R = R 3 − R 1 , see figure 5(a), as a function of the selected temperature. The results clearly show that the observed remanence in the resistance shows a transition from a low temperature value of ∼7 µΩ to a much smaller value of ∼0.5 µΩ at T ≳ 340 K. This last temperature coincides, within experimental error, with the temperature at which we would expect a percolation of the granular superconducting system according to the transition in resistance shown in figure 3(b). These results support the existence of a superconducting transition at a temperature of ∼350 K in agreement with the critical temperature measured by magnetization [18,20], electrical resistance [18,20,39] and magnetic force microscopy [19] measurements in similar samples, but do not rule out the existence of further superconducting systems with lower or higher critical temperatures as recently reported [16,20,21].

Conclusion
In conclusion, with a relatively simple electrical resistance measuring system and an electromagnet we could show the existence of finite remanence after the application of a magnetic field on a natural graphite sample. The temperature dependence of the resistance at zero field, as well as of the finite trapped flux, the origin of the remanent resistant, indicate the existence of a granular superconducting system at T ≲ 350 K, in agreement with recent reports. Taking into account earlier reports, graphite samples without SFs show a semiconducting behavior in the temperature dependence of the resistance and accordingly no field-driven metal-insulator transition. Therefore, the key for a successful experiment of this kind is the selection of graphite samples with SFs. In particular the existence of the rhombohedral phase together with the Bernal one in the sample appears to be of importance to get high temperature superconductivity, in agreement with theoretical reports. Future studies should also try to measure the Hall effect of the graphite sample at remanence, a difficult task because this might be very small due to the smallness of the expected frozen magnetic field.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.