Abstract
Muon spin resonance (μSR) is a powerful technique for investigating the local magnetic fields in materials through implanted muons. Here we report a μSR study of chemically produced thermally exfoliated graphene. Our results provide an experimental answer to the many theoretical investigations of magnetic properties of graphene. The observed muon spin precession is attributed to a localized muon–hydrogen nuclear dipolar interaction rather than to a hyperfine interaction with magnetic electrons. This proves the absence of magnetism in chemically produced thermally exfoliated graphene.
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1. Introduction
Graphene is the mono-atomic layer of sp2 carbon atoms. Besides its unique electronic structure and transport properties, this system is nowadays considered as one of the most promising nano-materials [1, 2] for a wide range of applications due to its high optical transmittance, low resistance, high chemical stability and high mechanical strength. Just after the graphene discovery, chemical methods, like the thermal exfoliation of graphite oxide (GO), were developed in order to extend its availability to gram-scale amounts [3]. Chemically produced graphene, also called reduced graphite oxide (RGO), is a highly porous material, composed of flakes of single and multiple layers of graphene, suitable for bulk applications and studies.
One of the most debated subjects in graphene research is the possible presence of bulk magnetism, which is a feature typically observed in d and f elements. Magnetic properties were theoretically predicted on carbon layered materials [4, 5] and room temperature ferromagnetism in proton irradiated graphite was experimentally observed [6]. The most common interpretation of carbon magnetism is related to the sp2 hybrid bipartite hexagonal lattice into which carbon atoms are organized. If a disproportion occurs between the two sublattices of the honeycomb structure of graphene, the Lieb theorem states that the system achieves a total spin proportional to the difference of sublattices populations [7]. Magnetism in graphene may therefore emerge as a consequence of either the presence of adatoms covalently chemisorbed on the graphene layer (e.g. hydrogen) or to the presence of vacancies originating from the removal of single carbon atoms from the graphene layer [8], or extended defects such as graphene edges [9, 10]. Both cases result in a net spin population on graphene sublattices [11].
Structural defects in thermally exfoliated graphene are naturally present as a consequence of the production method: the oxidation of graphite [12] causes the different chemical functional groups in addition to sp2 carbon. The high temperature exfoliation treatment promotes the functional groups detachment which generates a propellant for graphite planes separation and usually produces defects such as carbon vacancies in graphene layers [13]. Different oxidation treatments or the addition of partial reduction steps allows for controlling the amount of 'in plane' defects created during the exfoliation process. RGO therefore turns out to be the ideal system for testing the above mentioned theoretical predictions of the defect-induced magnetism in carbon-based materials. However, the question is whether a given sample of defective graphene is magnetically ordered, and if yes, whether the magnetic ordering is of ferromagnetic or antiferromagnetic (AF) type. To probe magnetism in defective graphene, the common magnetometric techniques are therefore less suitable (as insensitive to AF) and a local probe like μSR, which allows the measurement of the local hyperfine field, is required. For instance, the absence of Bernal stacking present in graphite, which breaks the equivalence of the two sublattices, here prevents the occurrence of the sublattice disproportion, proved to be essential for the onset of ferromagnetism. A random distribution of the defects on the lattice would instead yield an AF type of order [8, 14].
A further advantage of this technique is that in covalent materials with a low density of free electrons like graphene, the implanted muons bind to an electron and form muonium, a light isotope of hydrogen. Muonium, as atomic hydrogen, is expected to be chemisorbed on the surface of graphene, similarly to what is observed in graphite [15], or to react with possible unsaturated defects. In both cases it acts as an 'in plane' defect and is expected to bear a magnetic moment, capable of acting as a spin probe sensitive to a small local hyperfine field (expected in the case of long-range magnetic order onset in graphene) [8]. This makes μSR a precious technique for probing both magnetism and hydrogen interactions in graphene.
In the present paper we report a μSR study of chemically produced graphene. The observation of a clear muon spin precession signal could be ascribed to the formation of long-range magnetic order. However, we prove that in all the investigated samples, this precession originates from a localized muon–hydrogen nuclear dipolar interaction arising from the formation of a CH-Mu group at a graphene defect. This observation demonstrates the absence of magnetism on graphene in highly disordered graphene chemically produced by means of thermal exfoliation.
2. Sample preparation
Samples were obtained from highly pure graphite powder produced either by SGL carbon, RW-A grade, average size 66 μm, or Aldrich, 99% purity, average size 1.5 μm, following this three step treatment.
2.1. Production of GO
Graphite powder was oxidized following the Staudenmaier method [16, 17]. The powder was added to a mixture of concentrated sulfuric acid and nitric acid in a fume hood while cooling it by immersion in an ice bath. The mixture was kept under continuous stirring and potassium chlorate was slowly added. The suspension was then stirred in a fume hood for 5 days under nitrogen flow, in order to avoid the potentially explosive concentration of chlorine dioxide gas. The suspension was then diluted in water and filtered through coarse filter paper. The product was suspended in hydrochloric acid acqueus solution and again filtered, then carefully washed on the filter with water. Finally the product was dried at 333 K overnight. Laboratory x-ray diffraction analysis showed that the inter-planar distance changed from 0.335 nm graphite interplanar distance to 0.690 nm, due to the presence of intercalated water molecules and functional groups attached on the graphene planes. When the product undergoes thermal annealing at 373 K for 3 h in dynamic vacuum water molecules are removed and the interplanar distance decreases to 0.622 nm [18, 19].
2.2. Production of partially reduced graphene oxide (PRGO)
This step consists in a partial reduction of the GO [20], obtained by suspending it in sodium borohydride water solution. This was slowly added to the GO suspension under continuous stirring. The pH was adjusted to 10 with the addition of Na-carbonate solution. Sonication was applied on the mixture at 353 K and aggregation of the PRGO was observed at the end of the treatment. The product was then filtered and dried at 333 K overnight.
2.3. Production of thermally reduced graphene oxide
The complete reduction of the graphene oxide is reached by controlled thermal annealing. PRGO is annealed at 673 K for several minutes under dynamic vacuum, while the pressure was continuously monitored. An expansion of the powder was observed, due to the exfoliation promoted by the release of the remained functional groups.
This method, which consists of a two-step reduction of the oxide (chemical and thermal), was chosen for the preparation of several samples. In order to increase the number of in-plane vacancies, some samples were obtained without the intermediate step of partial reduction, therefore by a direct exposure of GO under vacuum at 1323 K, thus obtaining the reduction and exfoliation of graphite planes, clearly visible as a sudden growth of sample volume up to 1000 time of the initial GO volume (thermally expanded graphite oxide—TEGO) [3]. After high temperature exfoliation, every sample was handled in pure argon atmosphere in oxygen and moisture free conditions (below 1 ppm).
Hydrogen and deuterium treated graphene samples were obtained after heat treatment of TEGO under hydrogen or deuterium flux. Samples, placed in a evacuated quartz vial, were heated up to a temperature in the range 873–1273 K and then treated for 1 h under H2/D2 flux.
3. Experimental details
Superconducting quantum interference device (SQUID) measurements were performed on a quantum design MPMS5 XL magnetometer. Samples were sealed under 10 mbar He atmosphere in pre-calibrated quartz vials, whose contribution was subtracted using the automatic background subtraction mode of the instrument.
Zero field (ZF) μSR experiments were performed on the EMU spectrometer at the ISIS-Rutherford Appleton laboratory in both an He flux cryostat and a furnace environments. Samples were sealed in titanium cells having thin Ti foil windows.
4. Estimate of the density of defects
In order to provide a quantitative analysis of the magnetic behavior of magnetism dependent on defect concentration, the concentration of defects has to be estimated. In particular the amount of in-plane vacancies on graphene surfaces can be estimated by SQUID magnetometry, which shows that all the samples display a Curie T dependence of magnetization (apart from a sample dependent ferromagnetic contribution consistent with the amount of metal impurities in the precursors). Since the ideal graphene has a diamagnetic behavior [21], the paramagnetic contribution observed in the temperature dependence of magnetization provide a quantitative estimation of defects concentration [22]. A qualitative estimation can also be obtained by Raman spectroscopy, since the ratio of the D and G band intensities (Id/Ig) provides an indication of the concentration of defects present in graphene [23]. By comparing the two measurements, we found a qualitative agreement between the two techniques for all tested samples, and the one for which the muon spin resonance (μSR) histogram is reported in figure 2 showed 1300(150) ppm paramagnetic defects concentration.
5. Estimate of the local field due to magnetic ordering
Similarly to hydrogen, muonium covalently binds to one of the carbon atoms in graphene planes [15]. Its spin does not couple directly to the magnetic moments in the π-electron system of graphene. Due to its indirect nature such hyperfine coupling is very local, and hence reflects the local electron spin densities on the three carbon atoms which are the nearest neighbors to the binding carbon atom [24]. The hyperfine interaction is isotropic (Fermi contact) with very small hyperfine anisotropy (dipolar) contribution. According to the relation established on the basis of first-principles calculations [24], each Gauss of the local field felt by muon spins is equivalent to an average local magnetic moment of 8.38 × 10−4 μB localized on the carbon which are the nearest neighbors to the atom binding muon. In order to provide an estimate of the hyperfine coupling assuming the presence of long-range magnetic order, we perform first-principles calculations on a model system with muonium bound to carbon atoms in one sublattice of pristine graphene. Such a distribution of chemisorption sites results in ferromagnetic correlation [8, 25]. Electronic states introduced by the covalently bound species in graphene are quasi-localized in nature, that is, their degree of localization shows a logarithmic dependence on the total concentration of defects contributing to the zero-energy band [26]. This peculiar property relates the magnitude of local field to the absolute number of electron spins in graphene planes induced by disorder. We establish this relation by carrying out calculations on a series of models with different concentrations of chemisorption defects. Due to the computational cost of first-principles calculations, only the models with defect concentration of ∼ 1% or above have been considered. The results have been extrapolated to experimentally relevant lower defect concentrations. The calculated hyperfine couplings (see figure 1) show a pronounced logarithmic dependence which can be accurately fitted with Hhf = 1/ln(a + b/x) (G) (a = 1.0078; b = 4.75 × 10−5), where x is the defect concentrations or, equivalently, the average absolute magnetic moment per carbon atom induced by defects. This estimate shows that local fields of the order of 100 G can be expected for systems with large (x > 0.01) concentration of defects, giving rise to magnetic order. Defect concentrations x = 10−5 − 10−4 correspond to local fields of the order of 1 G. These results allow us to conclude that long-range magnetic order in disordered graphene samples can be reliably measured by means of the μSR technique.
Figure 1. Dependence of the muon-probed local field on the concentration x of single-atoms defects calculated from first principles (x = 0.01–0.04 per sublattice). The dashed curve shows a logarithmic fit of the calculated values. The atomic structure of the muonium chemisorbed on graphene is shown in the inset.
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Standard image High-resolution image6. μSR results
ZF μSR displayed in figure 2 shows two main contributions which are present independently of sample preparation:
- 1.A Lorentzian relaxation of polarization, which is assigned to the influence of isolated paramagnetic electrons located at unsaturated defects sites, and to the local fluctuating magnetic moment induced by the muonium itself when chemisorbed on the graphene plane [14]. This signal is similar to the one already observed in other graphitic materials [22].
- 2.A damped oscillation, corresponding to the muon spin precession around a local magnetic field of the order of a few Gauss (Hhf = 7.5(1) G, see figure 2).
Figure 2. Fit of ZF μSR decay asymmetry at 300 K for a hydrogenated sample in the two proposed models: blue line represents the fitting according to the magnetic hypothesis (single frequency), the green one shows the fitting under the dipolar interaction model. Insets show the isolated precessing asymmetry after the subtraction of both background and the Lorentzian decaying component. Best fit parameters according to equations (1) and (2) (magnetic hypothesis): χ2 = 1.08, Aosc = 0.029(1), Hhf = 7.5(1) G, σ = 0.19(1) μs−1, Arel = 0.158, λ = 0.07 μs−1; fit results according to equations (1) and (3) (Mu–H hypothesis): χ2 = 1.06, Aosc = 0.064(2), Bdip = 5.74(4) G, λosc = 0.073(5) μs−1, Arel = 0.123(2), λ = 0.043(1) μs−1.
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Standard image High-resolution imageThe general model function for such a polarization can then be written as
where Abg is the contribution from non-decaying muons implanted outside the sample (hitting the sample cell), the second component is the Lorentzian relaxing part and the last term represents the oscillating contribution. In most cases an oscillatory μSR signal indicates the existence of an ordered magnetic phase. In this case the precession is induced by the local hyperfine field Hhf and can be described by a single damped harmonic wave
where ω = γμ Hhf is the precession frequency and γμ = 13.55 kHz G −1 the muon magnetogyric ratio.
As observed in figure 2 where the fit of this model is applied to a very high statistic experiment performed on hydrogenated graphene, the single precession frequency expected for the magnetic case fails to reproduce the observed behavior in the longer time scale region. In order to get a more detailed view and a clearer explanation of the observed muon precession, a substitution of hydrogen with deuterium was carried out. ZF-μSR histograms obtained in the three different cases: pristine, hydrogen and deuterium treated graphene are reported in figure 3.
Figure 3. ZF muon spin evolution in pristine graphene (middle plot, green), after hydrogen treatment at 1073 K (bottom plot, red) and after deuterium treatment at 1073 K (top plot, blue).
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Muon spin evolution in pristine and hydrogen treated graphene has qualitatively the same behavior but a clear difference in the signal amplitude is observed, which increases from 12 to 40% of the implanted muons after the hydrogenation process.
The magnetism hypothesis still seems in agreement with these results, as chemisorbed hydrogen is known to produce local magnetic moments on graphene, which are expected to order in a ferromagnetic or AF fashion [14], therefore the muon would probe the hyperfine field produced by this ordering.
It is useful to now recall that the model predicting the existence of long-range magnetic order on graphene relies on the presence of moment bearing defects. The addition of adatoms realized by the hydrogen treatment enhances the number of surface magnetic moments giving rise to the amplitude of the precessing component, but the local hyperfine interaction (i.e. proportional to the observed frequency) is also expected to increase, and this is not observed.
The deuterium treatment instead does not show any precession and only the second decaying component of the signal is retained. The binding of either hydrogen or deuterium atoms to graphene creates two equivalent systems where adatoms give rise to localized magnetic moments. For this reason no difference is expected, from the magnetic point of view, between D2 or H2 treatments. In the perspective of a dipolar interaction, which is the other possible source of a constant local field, muon asymmetry is instead changed according to a different nuclear moments of the two isotopes. The disappearance of the precession between the hydrogenated and the deuterated samples ZF-μSR provide a clear demonstration that the signal has a dipolar origin.
7. Discussion
As shown in the previous paragraph the precession originates from the nuclear dipolar field on the muon, produced by a nearby H atom. It is known that, while a multi-spin interaction induces a Gaussian (or in some cases a Kubo–Toyabe) decay of the muon polarization, the interaction with a single nuclear moment gives rise to a coherent precession of the muon spin involving more than one frequency which follows function [27]:
The dipolar field Bdip produced by the hydrogen nucleus on the muon site is related to the muon–hydrogen distance r by the relation:
where γH is the proton magnetogyric ratio. The comparison of the ZF fitting of an hydrogenated sample according to these two different models is shown in figure 2.
The study of the temperature dependence of the observed frequency further weakens the magnetic interpretation. The precession signal persists up to 1250 K, such a high critical temperature far exceeds the highest transition temperature ever reported in carbon materials and is hardly conceivable [22]. The formation of a Mu–H entangled state and the fitting of the local field allows, through equation (4), the evaluation of the dipolar distance of 1.70(2) Å, which matches the typical inter-hydrogen separation in CH2 groups involving an sp3 hybridized carbon (tetrahedral coordination sphere). The precession signal is therefore generated by isolated CH–Mu groups localized either on vacancies or edges, the presence of which in chemically produced graphene is easily explainable. The oxidation of graphite creates numerous chemical groups attached to the graphene sheets. During the thermal exfoliation, the groups desorption eventually leads to the removal of the carbon atom belonging to graphene involved in the bonding, as confirmed by the presence of CO and CO2 in the produced gases, hence to the production of in-plane vacancies [18]. Single-atom vacancies in graphene undergo Jahn–Teller distortion resulting in the fusion of two σ dangling bonds [28] and the reactive, unsaturated carbon gets easily bonded to a hydrogen (present during the thermal or chemical reduction). The muonium atoms produced during the thermalization of incoming surface muons, explore the graphene surface and show a strong tendency to get trapped on graphene defects promoting the formation of the CH–Mu entangled state and the complete saturation of the vacancies. The temperature evolution of the precession signal witnesses an exceptional stability of the CH–Mu (and more generally CH2 fragments) which survives on graphene layers up to 1400 K.
8. Conclusions
We have found that ZF-μSR shows a muon coherent precession whenever graphite is exfoliated into single layers. The muon precession was shown to originate from the nuclear dipolar interaction of a single proton located near the muon at a distance of 1.7 Å. The hypothesis of magnetism has been explored but (i) the inadequacy of the muon spin evolution fit (especially in the higher times region), (ii) the suppression of the precession after a deuterium treatment and (iii) the persistence of the precession signal at very high temperatures, rule out the presence of magnetic ordering in the chemically synthesized defective graphene. Nevertheless μSR provided a fundamental understanding of the interaction of hydrogen atoms with chemically produced graphene.
Acknowledgments
We thank the ISIS Laboratory beam time provision, S Giblin and I McKenzie for support during the μSR experiments. The authors affiliated to the University of Parma acknowledge financial support from the EC FP6-NEST Ferrocarbon project and from the Swiss National Science Foundation HyCarbo project (grant no. CRSII2-130509). OVY acknowledges financial support from the Swiss National Science Foundation (grant no. PP00P2_133552). Computations have been performed at the Swiss National Supercomputing Centre (CSCS) under project s443.