Defect-induced magnetism in graphite through neutron irradiation
Yutian Wang, Pascal Pochet, Catherine A. Jenkins, Elke Arenholz, Gregor Bukalis, Sibylle Gemming, Manfred Helm, Shengqiang Zhou
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Revisiting defect-induced magnetism in graphite through neutron irradiation
Yutian Wang,
1, 2
Pascal Pochet,
3, 4
Catherine A. Jenkins, Elke Arenholz, GregorBukalis, Sibylle Gemming,
1, 7, 8
Manfred Helm,
1, 2, 8 and Shengqiang Zhou Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physicsand Materials Research, P.O. Box 510119, 01314 Dresden, Germany Technische Universit¨at Dresden, 01062 Dresden, Germany Univ. Grenoble Alpes, INAC-SP2M, L
Sim , F-38000 Grenoble, France CEA, INAC-SP2M, Atomistic Simulation Lab., F-38000 Grenoble, France Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Helmholtz-Zentrum Berlin f ¨ u r Materialien und Energie, Lise-Meitner-Campus, Hahn-Meitner-Platz 1, 14109 Berlin, Germany Faculty of Science, Technische Universit¨at Chemnitz, 09107 Chemnitz, Germany Center for Advancing Electronics Dresden, Technische Universit¨at Dresden, 01314 Dresden, Germany
We have investigated the variation in the magnetization of highly ordered pyrolytic graphite(HOPG) after neutron irradiation, which introduces defects in the bulk sample and consequentlygives rise to a large magnetic signal. We observe strong paramagnetism in HOPG, increasing withthe neutron fluence. The induced paramagnetism can be well correlated with structural defectsby comparison with density-functional theory calculations. In addition to the in-plane vacancies,the trans-planar defects also contribute to the magnetization. The lack of any magnetic orderbetween the local moments is possibly due to the absence of hydrogen/nitrogen chemisorption, orthe magnetic order cannot be established at all in the bulk form.
I. INTRODUCTION
Defect induced magnetism in carbon based materialsgives many attractive perspectives in the fundamentalunderstanding of magnetism as well as in future spin-tronic applications. As early as 2003 highly orderedpyrolytic graphite (HOPG) was reported to be ferro-magnetic after proton irradiation , which provides anapproach to control the defect-induced magnetism ingraphite both concerning strength and in lateral distri-bution. After that, successive investigations were per-formed for testing the reliability of the ferromagnetism ingraphite and for finding other carbon-based ferromag-netic materials . As a consequence, the investigationon defect induced magnetism in semiconductors has beengreatly stimulated . So far experiments and theoryshow the following common features:1. Paramagnetism can be greatly enhanced by intro-ducing defects in graphite or graphene . Someresearch groups conclude that these paramagneticcenters do not show any magnetic ordering downto 1.8 or 2 K .2. Ferromagnetism only appears under certain defectconcentrations, i.e., in a narrow ion fluence window,and the magnetization is weak .3. In a microscopic picture, it has been found boththeoretically and experimentally that defect-induced or disturbed electron states play an impor-tant role in generating local moments in graphite.4. Foreign (or impurity) atoms, particularly, hydrogenand nitrogen, are helpful in establishing the ferro-magnetic coupling between defects . However, as to our knowledge, the research has focusedmostly on thin-film like samples: ion implanted graphitewith nm– µ m affected thickness or graphene flakes. Theas-measured magnetization is always in the range of10 − –10 − emu per sample . The small mag-netization renders data interpretation controversial asshown in a recent intensive discussion on the potentialcontamination in graphite as well as on artificialeffects in magnetometry . Moreover, the implantedions, especially those that differ chemically from the sub-strate, will stay in the matrix as foreign atoms and an in-terface will naturally form between the implanted regionand the untouched substrate. Both the interface and theimplanted ions will make it difficult to unambiguouslyidentify the defect type and hamper the interpretationof the mechanism for the observed magnetization. Toavoid these problems we use neutron irradiation. Neu-trons have a much stronger penetrating capability thanions and will generate defects throughout the whole sam-ple. In this way, the foreign ion effect and the interface ef-fect can be excluded in the present study. Therefore, theapplication of neutron irradiation could be a promisingmethod to clarify the long standing question regardingthe origin of the defect induced magnetism in graphite inthe following aspects. • To verify whether the defect induced paramag-netism or ferromagnetism is a bulk effect or onlya surface effect; • To make a correlation between magnetism and de-fects based on the strong magnetic signal and re-sults from various structural analysis techniques.Accordingly, our work has been performed in the fol-lowing way. HOPG specimens were subjected to neutronirradiation, whereby the irradiation fluence is varied toinduce defects in graphite from slight damage to nearamorphization. The magnetic and structural propertieshave been measured by various techniques. The resultswere complemented with a theoretical interpretation ofthe role of in-plane defects from literature and from newfirst-principles calculations of magnetic states of trans-planar divacancy configurations.The paper is organized as follows. In section II allexperimental methods employed will be described. Thenthe results will be presented in three sub-sections. In sec-tion III.A, we present the large paramagnetism inducedby irradiation and its dependence on the neutron fluence.In section III.B and C, the defect type and its concentra-tion evolution will be discussed based on Raman and X-ray absorption spectroscopy, respectively. In section IV,we attempt to correlate the induced paramagnetic cen-ters with in-plane vacancies and trans-planar defects byreviewing the literature data as well as by first-principlescalculations. In the end of the discussion section, we alsoexplain why the magnetic coupling between the inducedmoments is missing. The paper is finished with a shortconclusion.
II. EXPERIMENTAL METHODS
In the experiment, the used graphite samples werehighly oriented pyrolytic graphite (HOPG) with a gradeof ZYA, which are generally referred as graphite in thismanuscript. Neutron irradiation was performed at thereactor BER II (Position DBVK) at Helmholtz-ZentrumBerlin . During irradiation the temperature of the sam-ples was less than 50 ◦ C (see ref. 41). Four samples wereirradiated with the fluences of 6.24 × , 1.25 × ,6.24 × , and 3.12 × cm − , which are named as 3H,6H, 30H and 150H according to the irradiation time of3 hours, 6 hours, 30 hours, 150 hours, respectively. Themechanism to produce crystal lattice defects by neutronirradiation is the elastic or inelastic scattering betweenneutrons and target nuclei. If the target nucleus getsenough energy after scattering, it will irreversibly dis-place the lattice atom from its original site, resultingin vacancies and interstitials. The minimum energy re-quired to displace a carbon atom in graphite is around25 eV . Therefore, we only consider the epithermal (0.5eV – 100 keV) and fast neutrons (100 keV – 20 MeV) in calculating the fluence. The elastic scattering domi-nates when the energy is below 5.5 MeV in carbon andthe nuclear reaction (inelastic scattering) only becomesappreciable when the energy is above 9 MeV .Magnetometry was performed using a SQUID-VSM(Quantum Design). The magnetic properties were mea-sured regarding their dependences on magnetic field andon temperature. The structure change is characterizedby Raman spectroscopy which is sensitive to defects inthe aromatic ring, the edge state, the hybridization type,the interstitial ions, and also to the stacking orders, etc .The µ -Raman system is equipped with a 532 nm wave- -40000 -20000 0 20000 40000-0.6-0.4-0.20.00.20.40.6-2000 -1000 0 1000 2000-202 (b) Magnetization at 1.8 K M agne t i z a t i on ( e m u / g ) Field (Oe)
Virgin 6H150H30H3H
Virgin M agne t i z a t i on ( - e m u / g ) Field (Oe)(a) Magnetization at 300 K
FIG. 1. Magnetization vs. field (a) the low field range at 300K and (b) the large field range at 1.8 K. length laser and a liquid nitrogen cooled CCD detectorworking in backscattering geometry. X-ray absorptionspectroscopy (XAS) will further detect the bonding statechange resulting from neutron irradiation. The variationsof the magnetization, the Raman scattering and the X-ray absorption at the carbon K-edge depending on theirradiation fluence allow us to clearly correlate the den-sity of vacancies interstitials with the magnetism in theneutron irradiated graphite.
III. RESULTS AND DISCUSSIONA. Magnetic properties
Figure 1 shows the magnetization measurements at 300K and 1.8 K for the virgin and irradiated graphite with-out any background correction. For the virgin graphite,the diamagnetic background dominates the magneticproperties. A weak ferromagnetic hysteresis is observedalready in the virgin graphite. It is probably caused by M agne t i z a t i on ( e m u / g ) Field (Oe)
FIG. 2. The magnetic moments of all irradiated sample mea-sured at 1.8 K as a function of the applied external field. intrinsic defects or by Fe contamination . More-over, the ferromagnetic contribution is not changed sig-nificantly upon neutron irradiation. Therefore, this weakferromagnetism is not the topic of our study in thismanuscript. Besides the marginal change in the ferro-magnetic component, there is a huge increment of themagnetization at low temperature. Figure 1(b) showsthe comparison of the magnetization measurement at 1.8K for the virgin graphite and sample 150H. Sample 150Hshows a large paramagnetic component which will be dis-cussed in detail later. Note that the change in the slopeof the MH curves in Fig. 1(a) is due to the large increaseof the paramagnetism upon irradiation as shown. At lowtemperature, the weak ferromagnetism in the irradiatedsamples is dominated by the paramagnetism and not re-solvable.The field dependence of the magnetization at 1.8 Kfor all samples is shown in Fig. 2. Neutron irra-diation leads to strong paramagnetism. The graphitesample is changed completely from diamagnetic-like toparamagnetic-like with increasing neutron fluence. How-ever, even for the sample with the highest neutron flu-ence, the magnetization is not saturated at 1.8 K up to afield of 50000 Oe. In our experiment, the measured ab-solute magnetic moment for a graphite sample of around4 × is in the range of 0.001-0.01 emu at 1.8 or5 K. This value is much larger than the previously re-ported ion implanted samples with a magnetic momentof around 10 − –10 − emu and is far above thesensitivity of SQUID-VSM. As shown in Fig. 3(a), theinduced paramagnetism can be precisely described by thestandard Brillouin function after removing the residualdiamagnetic background and the intrinsic paramagneticcontribution from the virgin graphite: M ( α ) = N Jµ B g [ 2 J + 12 J coth ( 2 J + 12 J α ) − J coth ( 12
J α )](1)where the g factor is about 2 obtained from electron spin resonance measurement (not shown), µ B is Bohrmagneton, α = gJµ B H/k B T , k B is the the Boltzmannconstant and N is the density of spins. The Brillouinfunction provides excellent fits for J = 0.5, which cor-responds to single electrons as charge carries and N =8 × µ B /mg for sample 150H. The fits using larger J unequivocally deviate from the shape of the measuredM-H curves, as they give significantly different, sharperchanges with faster saturation.The Curie law χ = MH = N J ( J + 1)( gµ B ) k B T (2)with J = 0.5 and N = 8 × µ B /mg inferred from Fig.3(a) also gives a good fit to the temperature dependentmagnetization as shown in Fig. 3(b). The inset of Fig.3(b) shows the inverse susceptibility versus temperature,revealing a linear, purely paramagnetic behavior with noindication of magnetic ordering.Figure 6 (shown later in the paper) shows the density ofparamagnetic centers obtained by fitting the magnetiza-tion measured at 1.8 K for different samples as a functionof neutron fluence in double logarithmic scale. With in-creasing neutron fluence, i.e. the amount of defects, moreand more paramagnetic centers are generated. This in-dicates that even the most strongly irradiated sample isstill not totally amorphous.We also noted the work by Ramos et al. Using ionimplantation to introduce defects into graphite, they re-ported an anomalous paramagnetic contribution. Thiscontribution remains independent of temperature up to100 K, whereas the field dependent magnetization showsneither saturation nor any nonlinearity . Meanwhiletheoretical calculations also pointed out that if sufficientcarbon adatoms were available, they could weakly ag-glomerate in graphene and superparamagnetism can befinally observed . However, in our experiment the mag-netic properties for all samples can be well described byspin 1/2 paramagnetism without superparamagnetic con-tributions. As expected if the whole volume contributes,in our experiment the as-measured magnetization signalis as large as 0.001–0.01 emu per sample. The large mag-netization signal allows us to draw reliable conclusionsand to exclude any spurious and anomalous paramag-netic contribution.To further exclude a possible ferromagnetic order-ing in our sample we measured the magnetization vs.field at different temperature to perform an Arrott plotanalysis . This method is usually used to accuratelydetermine the Curie temperature T C and to verify theparamagnetic to ferromagnetic phase transition. Suchan analysis is based on the relationship derived byWohlfarth [ M ( H, T )] = [ M (0 , [1 − ( T /T C ) + 2 χ H/M ( H, T )](3)Note that this relationship results in parallel lines of theisothermal M which cross zero ( H/M = 0) in the vicin- M agne t i z a t i on ( e m u / g ) Field (Oe) at 1.8 K Experiment J=0.5 J=1 J=1.5 (a)(b) M agne t i z a t i on ( e m u / g ) Temperature (K) -1 ) FIG. 3. (a) The measured magnetization at 1.8 K for sample150H and the fitting using Brillouin function with J = 0.5,1, 1.5. (b) Temperature dependent susceptibility measuredunder a field of 10000 Oe. The black symbols are experimentaldata and the red solid curve is is the fitting result by theequation (2). Inset: Inverse susceptibility versus temperaturedemonstrating a linear, purely paramagnetic behavior withno indication of magnetic ordering. ity of T = T C ± δ . Figure 4 shows the isothermal magne-tization Arrott plot for sample 150H (irradiated up to thehighest fluence). The measurement temperatures rangefrom 1.8 K to 20 K. With increasing temperature, themagnetization decreases, but none of the lines crossesthe zero point ( H/M = 0). It confirms that down to 1.8K no magnetic order appears in this sample. It is purelyparamagnetic.
B. Raman spectroscopy
Figure 5 shows the Raman spectra of graphite samplesafter neutron irradiation. From top to bottom are thevirgin sample and samples 3H...150H, respectively. Alinear background has been removed.
20 K M (( e m u / g ) ) H/M (10 Oe/(emu/g))
FIG. 4. Isothermal magnetization an Arrott plot: M versus H/M . The lines with different color correspond to themeasurements in the temperature range 1.8 to 20 K.
The reference sample shows the peaks typical for thehigh-quality HOPG . The G peak located at around1590 cm − corresponds to the inherent E g mode of thearomatic ring. The D peak around 1360 cm − representsan elastic scattering at defects in crystal .Upon neutron irradiation, the most pronouncedchanges occur in the D peak and in its overtone G’ peak(2D peak): the D peak rises with irradiation fluenceand becomes as strong as the G peak. Two pronouncedchanges will be described in the following.
1. In-plane vacancies
The increase of peak D is generally attributed to thein-plane vacancies in graphite . By independentmethods such as X-ray diffraction and transmission elec-tron microscopy, the intensity ratio between D and G peaks has been confirmed as a measure of the in-planegrain size. Neutron irradiation induces a large numberof interstitial and vacancy pairs ( I-V ). Most of
I-V de-fects will recombine simultaneously and the remainingspecies can form various defects. Since a high energybarrier blocks the diffusion of vacancies, most vacanciesbecome in-plane vacancies or form vacancy clusters. Theinterstitial atoms prefer staying in the region betweenthe layers owing to the energetically highly unfavorableinterstitial in-plane position . In Figure 6, we plot thefluence dependent I D /I G (the intensity ratio between D and G peaks). In our samples, the strength of the D peak increases with the neutron fluence when the irra-diation time is less than 30 hours. Further increasingthe neutron fluence, I D /I G reaches a saturation value. Itindicates that with increasing the irradiation time from D1 G’ D G GD Raman shift (cm -1 ) R a m an i n t en s i t y ( a r b . un i t ) G’1
Virgin
G’2
FIG. 5. Raman spectra of graphite after neutron irradiation.From the top to bottom shown are data for virgin graphiteand 3 hours to 150 hours irradiated samples, respectively. Thepeaks were deconvoluted to reveal the detailed variation afterneutron irradiation. .
2. Out-of-plane defects
The G’ peak around 2720 cm − is the overtone of the D peak. It is often referred as the 2D peak and is very sen-sitive to the c -axis stacking order of graphite. The lineshape and intensity of G’ are signatures of the stack-ing of graphene layers. For bulk graphite consisting of N ( B / c m ) Fluence (/cm ) M at 1.8 K 0.00.51.01.5 I D /I G I D1 /I G I D /I G ( o r I D /I G ) FIG. 6. The intensity ratio between D and G peaks (I D /I G )and the fitted paramagnetic center density ( N , at 1.8 K) vs.neutron irradiation fluence. The grey bar indicates the satu-ration value of I D /I G for ion implanted graphite . an ... ABAB ...stacking, the G’ peak is composed of twopeaks. When the stacking is absent, the interaction be-tween the planes is very weak and they behave as two-dimensional crystals. For a single graphene layer, the G’ peak is composed of a single peak . For our experiment,in the virgin sample the interaction between the layers in3 D graphite makes the G’ peak to be split into G’1 and
G’2 . When the irradiation time is less than 6 hours,two peaks can fit the spectra, but their strength becomesweak with increasing irradiation fluence. This indicatesa slight crystalline damage in the graphene sheet stack-ing. The influence of shear moments caused by the in-terstitial atoms between the two sheets is less notable forirradiation times of less than 6 hours. When the irra-diation time is over 30 hours,
G’1 and
G’2 peaks de-cease strongly and mix into a single weak peak. Thisis attributed to the out-of-plane defects in graphite .With increasing neutron fluence, more interstitial atomsare assumed to diffuse into regions between the graphenesheets so that the distance between the sheets increasesstrongly enough, such that the graphene sheets behavelike an isolated single graphene sheet. The appearanceof the D1 peak at around 1500 cm − for sample 150His another indication for the interstitial atoms betweengraphene sheets . At low fluence range, the D1 peakis too weak to be fitted even for samples 30H. The D1 peak was also observed in ion implanted graphite whenthe implantation fluence is large enough .This Raman analysis allows us to define two regimesfor the four reported fluences. In the first regime (3H, 6Hand 30H) defects are created in plane without interactionbetween neighboring planes. In the second regime (30Hand 150H), the latter interaction becomes a dominant ef-fect and trans-planar defects (interstitial or vacancy) areexpected to play a major role: due to the high defect con-centration, newly created defects are expected to com-bine with pre-existing defects in the neighboring planesas revealed by the rather saturated value of I D /I G in thesecond fluence regime. Interestingly, these transplanardefects seem also contribute to the total magnetization. C. X-ray absorption spectroscopy
To further probe the change in the electronic statein graphite after neutron irradiation from a microscopicpoint of view, we performed near-edge X-ray absorptionfine structure spectroscopy (NEXAFS, Beamline 6.3.1 atthe Advanced Light Source in Berkeley). The descriptionof the experimental set up can be found in reference 30.In our experiment, the incident light was inclined by 45 ◦ to the sample surface. The signals were collected in thetotal electron yield mode at room temperature. All thespectra are normalized by the input flux for comparison.As shown in Fig. 7, there are two resonances around285 eV and 292 eV, respectively. They correspond tothe transitions from core-level electrons to π ∗ and σ ∗ empty states, respectively. For samples 3H and 6H witha small neutron fluence, there is no significant changeeither in the peak intensity or in the peak shape com-pared with the virgin sample. After the irradiation over30 hours, the intensity of the π ∗ peak decreases, which in-dicates that the aromatic π system is severely perturbed.At the same time, the π ∗ and σ ∗ features are becomingbroader. In previous literature, it has been shown thatthe π ∗ and σ ∗ resonances of carbon are much more broad-ened in proton implanted graphite than our case .The inset of Fig. 7 shows a zoom into the energyrange 280–284 eV. Compared with previous results onion implanted graphite , the fundamental difference ofour sample is the missing of a pre-edge peak at around282 eV. In ref. 26, a new small, but sizeable peak inthe pre-edge region (281.5 eV to 284.5 eV), has been re-ported in ion implanted ferromagnetic graphite. Thisnew peak was attributed to be closely related with de-fect states near the Fermi energy level, and it was tem-porarily assigned to rehybridized C-H bonds. The lack ofrehybridized C-H bonds in our samples may explain theabsence of ferromagnetism, which will be discussed later. IV. DISCUSSION
We have investigated the magnetic and structuralproperties of graphite after neutron irradiation. Differentfrom ion implantation, neutron irradiation can introducedefects in the whole graphite sample. The resulting mag-netization is very large and allows one to draw a reliableconclusion free of the influence of contamination. Our ex-perimental results lead to two conclusions: (1) only spin1/2 paramagnetism is induced in graphite by neutron
280 285 290 295 300
280 281 282 283 284
Photon energy (eV)
Virgin 3H 6H 30H 150H I n t en s i t y ( a r b . un i t s ) FIG. 7. The NEXAFS spectra of the graphite samples afterneutron irradiation for different time. Inset: zoom into theenergy range 280–284 eV. irradiation; and (2) both in-plane vacancies and out-of-plane defects appear after irradiation. In this discussion,we attempt to correlate the magnetization and defectsand to understand why the magnetic ordering is lacking.
A. The origin of the paramagnetism
Defect induced magnetism in both graphite andgraphene has been intensively investigated theoretically.Structural defects, in general, can give rise to localizedelectronic states. It is well accepted that the in-plane va-cancies are the origin of local magnetic moments . Uponremoval of one atom, each of the three neighboring atomshas one sp dangling bond. Two of the C atoms canform a pentagon, leaving one bond unsaturated. Thisremaining dangling bond is responsible for the magneticmoment. Moreover, the flat bands associated with de-fects lead to an increase in the density of states at theFermi level. Lehtinen et al., used spin-polarized DFT anddemonstrated that vacancies in graphite are magnetic .They also found that hydrogen will strongly adsorb atvacancies in graphite, maintaining the magnetic momentof the defect. Zhang et al. have confirmed that the lo-cal moments appear near the vacancies and with increas-ing vacancy accumulation the magnetization decreasesnon-monotonically. Using a combination of a mean-fieldHubbard model and first principles calculations, Yazyevalso confirmed that vacancies in graphite and graphenecan result in net magnetic moments , while the pre-served stacking order of graphene layers is shown to be anecessary condition for achieving a finite net magneticmoment of irradiated graphite. In most calculations,the moment per vacancy is sizeable up to 1–2 µ B .Indeed, by scanning tunneling microscopy experiments,Ugeda et al . have observed a sharp electronic resonanceat the Fermi energy around a single vacancy in graphite,which can be associated with the formation of local mag-netic moments .In our neutron irradiated graphite, we observed astrong correlation between the magnetization and vacan-cies. Figure 6 shows the irradiation-fluence dependentmagnetization and the values of I D / I G of the Ramanspectra. At the low fluence regime, the density of mag-netic moments shows an excellent correlation with I D / I G (the density of in-plane vacancies): both increase mono-tonically with the fluence. This indicates an agreementwith the theoretical calculation: the vacancy in graphiteresults in local magnetic moment. In the next subsection,we discuss the role of out-of-plane defects. B. The role of trans-planar defects
As shown in Fig. 6, I D / I G reaches its saturation valueof around 1.2–1.4 when the neutron fluence is higher. I D / I G of 1.2–1.4 is also a threshold of amorphisation inion irradiated graphite . Despite the saturation in thedensity of in-plane vacancies, the density of local mo-ments still increases with neutron fluence as shown inFig. 6. What is the contribution for these additionallocal magnetic moments? We consider the role of thetrans-planar defects. As shown in Fig. 5, for the largestirradiation fluence, D . In order to as-sess the experimental findings described in the above sec-tions, we have investigated the possible magnetic state fortrans-planar defects.We start our analysis from the seminal work of Tellinget al. who firstly propose the trans-planar divacancyconfigurations (see Figure 8) that breaks the symmetryrules in graphite. Interestingly, the spin-polarized statesfor these defects was discussed in the paper but neverassessed. In order to answer this question without anyartifacts we have decided to run additional spin-polarizedcalculations in a super-cell which is large enough toavoid elastic effects between neighboring defect images(in-plane). Systems containing 448 atoms per graphenesheets have proven to be reliable to study triangular va-cancy clusters in hexagonal boron nitride sheets andare also used in the present study. Here, two of thesesheets with Bernal stacking were considered. The dis-tance between the two sheets was fixed to 6.45 Bohrradii ( a ) for simplifying the treatment of the interlayer.This is achieved by the freezing of the perpendicular dis-placements in a band close to the edges of the super-cell(pink area in Fig. 8). This treatment allows for a fullrelaxation both in-plane and out-of-plane of the centralpart of the super-cell where the defect sits. The PBEexchange and correlation function was chosen as it wasfound to well reproduce the in-plane relaxations . The TABLE I. Formation energy (E f ) and energy difference(E spin ) between the singlet and triplet states for the threeconsidered divacancies. The values in bracket are correspond-ing results in ref. 57.Samples E f (eV) E spin (meV)V in-plane 7.55 (8.7) 2V trans-planar 13.85 (14.6) 560V trans-planar 12.77 (13.0) 1 BigDFT code was used to perform DFT calculationswithin surface boundary conditions .The two trans-planar divacancies V and V are con-sidered together with the in-plane divacancy V as a ref-erence. The formation energy of the defect is calculatedusing the chemical potential of carbon in the pristine bi-layer system. Singlet and triplet states are obtained byrunning spin averaged and spin polarized calculations,respectively. The results are summarized in table I. Theformation energy of the three defects increases in-linewith the initial report of Telling et al. . However, impor-tant differences arise, underlying the role of the in-planerelaxations that were blocked in the previously used 64atoms box . Indeed, while the estimated error of about0.4 eV holds for the trans-planar vacancies, the differ-ence is much more bigger for V . As a consequence, theenergy difference between the two trans-planar divacan-cies remains in the order of 1.5 eV.In Table I we also report the singlet to triplet forma-tion energy for each defect. In line with the report of adouble bond for the inter-planar C-C bond (see bondlength scale in figure 8), the V divacancy is in a singletstate. This situation is different for the V divacancy:the inter-planar C-C bond is longer and more twisted,thus preventing further hybridization between the twocarbon atoms. As a consequence, the triplet state is sta-bilized by more than 500 meV with respect to the singletstate. According to Telling et al., the existence of tripletstates gives a solid explanation for the observed spin 1/2paramagnetism. C. Why is the magnetic interaction missing?
As shown in Fig. 2 and Fig. 6, the paramagnetism ingraphite can be strongly enhanced by irradiation induceddefects. After irradiation even to the largest fluence, thesamples are not fully amorphous and I D / I G of around1.2 corresponds to a planar grain size of 3.5 nm . Whyis the magnetic interaction between the generated para-magnetic centers then missing? To answer this question,we first need to estimate the density of defects, i.e. theaverage distance between adjacent local moments.Assuming the defects are homogeneously distributed inthe sample matrix, we estimate the average distances ( r ) FIG. 8. The top (left) and side (right) view of the two considered trans-planar divacancies: V (a, c) and V (b, d). Blackballs are carbon atoms. Bonds between two neighboring atoms are colored as a function of length: black stands for standarddistances [2 . ± .
05 Bohr radius ( a )], blue and red stand for short (2 . ± . a ) and long (2 . ± . a ) distances,respectively. between local moments in our irradiated graphite sam-ples. This value amounts to 2.2 nm for the sample withthe largest neutron fluence. The nearest average distancebetween two spins is around 16 a ( a = 0.14 nm is the C-Cbond length). Therefore, the direct coupling between thelocalized spins at the vacancies is nearly negligible. Alter-natively, the Ruderman-Kittel-Kasuya-Yosida (RKKY)coupling is suggested to appear in defective graphite andgraphene . This coupling might be ferromagnetic at afinite temperature when k F r ≪
1. If assuming a Fermienergy of 20 meV in graphite , the inverse of the Fermiwave vector 1 /k F ∼
30 nm. To have ferromagnetic order-ing, the distance between two spins r should be ≪
30 nmwhich corresponds to a spin density of 3.7 × cm − .In principle, all samples fulfill this criteria. All these mo-ments may tend to be ferromagnetically coupled via theRKKY coupling, although the Curie temperature can bevery low . However, we do not observe any magneticordering down to 1.8 K even for sample 150H. It is notpractical to further increase the defect density, since thestacking order of graphenes plane must be preserved .Our sample with the highest neutron fluence is already atthe verge of amorphization. A larger irradiation fluencewill perturb the graphene lattice too much and destroythe necessary band structure and carrier density.Both published theory and experimental results sug-gest a crucial role of hydrogen or nitrogen chemisorp-tion in enhancing the spin density and in establishing themagnetic coupling . All these moments fromchemisorption will tend to be ferromagnetically coupled,enhancing the Curie temperature by the RKKY coupling.Recently, by careful angular dependent NEXAFS, He etal. observed a new small peak in the pre-edge region(281.5 eV to 284.5 eV) . This new peak has been inter-preted to be closely related with the defect states nearthe Fermi energy level and it is assigned to the formationof C-H bonds . Ohldag et al. also observed an X-raymagnetic circular dichroism (XMCD) signal in the pre-edge region of the C K-edge. However, as shown in Fig. 7, our present findings do not exhibit any new peak inthe pre-edge of the C K-edge. This may explain why theferromagnetic coupling is missing. V. CONCLUSION
Neutron irradiation in graphite can induce a largeamount of defects throughout the bulk specimens, con-sequently leading to a large measurable magnetization.This approach allows for a revisiting of defect inducedmagnetism in graphite by eliminating the influence ofcontamination or artificial effects. We conclude that onlyspin 1/2 paramagnetism is induced in neutron irradiatedgraphite. The creation of trans-planar vacancies (with-out dangling bonds) reduces the concentration of singlein-plane vacancies. Complementing our study by first-principles calculations, we propose that both in-plane va-cancies and trans-planar defects can form local magneticmoments, which are responsible for the observed 1/2paramagnetism. The paramagnetism scales up with in-creasing the amount of defects, however, magnetic orderunlikely can occur in a bulk form in defective graphite.
VI. ACKNOWLEDGEMENT
The work was financially supported by the Helmholtz-Gemeinschaft Deutscher Forschungszentren (VH-NG-713and VH-VI-442). Y. Wang thanks the China ScholarshipCouncil (File No. 2010675001) for supporting his stay atHZDR. The authors also acknowledge the support by theInternational Science and Technology Cooperation Pro-gram of China (2012DFA51430). The Advanced LightSource is supported by the U.S. Department of Energyunder Contract No. DE-AC02-05CH11231. Calculationswere performed using French HPC ressources from theGENCI-CCRT (grant 6194). P. Esquinazi, D. Spemann, R. H¨ohne, A. Setzer, K.-H.Han, and T. Butz, Phys. Rev. Lett. , 227201 (2003). S. Talapatra, P. G. Ganesan, T. Kim, R. Vajtai, M. Huang,M. Shima, G. Ramanath, D. Srivastava, S. C. Deevi, andP. M. Ajayan, Phys. Rev. Lett. , 097201 (2005). K. W. Lee and C. E. Lee, Phys. Rev. Lett. , 137206(2006). H. Xia, W. Li, Y. Song, X. Yang, X. Liu, M. Zhao, Y. Xia,C. Song, T.-W. Wang, D. Zhu, J. Gong, and Z. Zhu,Adv. Mater. , 4679 (2008). 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