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FMR evidence of ferromagnetic correlations at zigzag edge states in single-layer graphene
Journal of Molecular Structure 1076 (2014) 31–34
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
FMR evidence of ferromagnetic correlations at zigzag edge states in single-layer graphene Krzysztof Tadyszak, Mariusz Mac´kowiak ⇑, Maria A. Augustyniak-Jabłokow, Roman Strzelczyk ´ , Poland Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowski Str 17, 60-179 Poznan
h i g h l i g h t s Magnetism of zigzag edges of single layer graphene can be studied by FMR/ESR method. Ferromagnetic spin correlation lengths were evidenced. Magnetic order in low-dimensional systems is sensitive to thermal fluctuations. ESR spectra of conduction electrons show Pauli type behavior.
a r t i c l e
i n f o
Article history: Received 16 April 2014 Received in revised form 17 July 2014 Accepted 17 July 2014 Available online 23 July 2014 Keywords: Graphene Ferromagnetism of graphene Ferromagnetic resonance Electron spin resonance
a b s t r a c t Magnetic properties of zigzag edges of single-layer graphene were investigated by ferromagnetic resonance (FMR)/electron spin resonance (ESR) technique. We observed the FMR lines in single-layer graphene, which provide the most direct experimental proof of the theoretical prediction of ferromagnetic correlations at zigzag edges. To explain the observed temperature dependence of the FMR lines we analyzed the magnetic spin correlation length, which is responsible for magnetic ordering in these quasi-1D ferromagnetic nanodomains formed by zigzag edges. ESR spectra of conduction electrons were also studied. Ó 2014 Elsevier B.V. All rights reserved.
Introduction Graphene, a two-dimensional form of carbon, has attracted considerable attention due to its unique physical properties and potential technological applications. Nanographene, whose shape is described in terms of a combination of armchair and zigzag edges, has spin-polarized nonbonding p-electron state (edge-state) localized in the zigzag-edge region in spite of the absence of such state in armchair edges, as suggested by theoretical predictions and scanning tunneling microscope/scanning tunneling spectroscopy (STS) experiments [1–4]. According to theoretical studies [5], the edge-state spins are strongly coupled in parallel with each other in a zigzag edge through strong intrazigzag-edge ferromagnetic interaction J0 having a strength of 103 K. In a nanographene sheet with zigzag-edge regions separated by the presence of armchair edges, the ferromagnetically coupled edge-state spins in a zigzag edge are interacting with those in other zigzag edge through interzigzag-edge ⇑ Corresponding author. Tel.: +48 61 8695 208. E-mail address: [email protected] (M. Mac´kowiak). http://dx.doi.org/10.1016/j.molstruc.2014.07.047 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
ferromagnetic/antiferromagnetic interaction J1 having a strength of (101–102) J0 and mediated by conduction p carriers. There have been a large number of theoretical efforts investigating edge state magnetism [6–8] in graphene nanostructures terminated by zigzag edges. However, we are not aware of any direct experimental observation of these phenomena in single-layer graphene. The intrinsic magnetic properties of graphene in finite sizes are far from being understood, because magnetic signal from one piece of graphene in finite sizes is too weak to be detected by macro-magnetic measurement. Therefore, a massive amount of high-purity graphene (at least in milligram-scale) is an essential prerequisite to unveil the intrinsic magnetism contributed from graphene edges or vacancy defects. Even the possibilities of such phenomena were questioned by the fact that no true long-range magnetic ordering in 1D systems is possible at finite temperatures [9]. Nevertheless, nanometer range spin correlation lengths in certain 1D systems have been achieved in practice [10]. Establishing the range of magnetic order at graphene edges as well as the underlying physical mechanisms is thus crucial for understanding and practical realization of the nanoelectronic and spintronic devices.
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K. Tadyszak et al. / Journal of Molecular Structure 1076 (2014) 31–34
In this work, we study the magnetic correlations at zigzag edges of single-layer graphene by investigating the FMR/ESR measurements. In particular, the use of ferromagnetic resonance (FMR) is noticeable. We found the FMR signal in the sample of a single layer graphene in a high vacuum. The ferromagnetically coupled edge spins gave a broad FMR signal, and as the edges are one-dimensional, the signal is shifted to the low magnetic field. One of the advantages of FMR over conventional magnetization measurements is that it yields information on the dynamics of the system. A mixture of microscopic phases containing a ferromagnetic contribution and a paramagnetic one is not easy to discriminate in a DC magnetization measurement, while it should be clearly distinguished in an FMR experiment. The zigzag edges exhibit ferromagnetic behavior when their size is sufficiently large, wherein the internal field undergoes ferromagnetic ordering revealing FMR lines. We observed the FMR lines in single-layer graphene, which provide the most direct experimental proof of the theoretical prediction of ferromagnetic correlations at zigzag edge states so far.
Material and methods We investigated graphene produced by the substrate-free gasphase synthesis with an average flake size of 550 nm, supplied by Graphene Supermarket in the form of graphene suspension in pure ethanol and declared to be monolayer. This material was reported to be free of functional groups and to have low defect concentration [11]. However, we established [12] the presence of quite a significant amount of paramagnetic defects in the sample prepared by deposition of about 0.02 mg of the graphene flakes on amorphous SiO2 of highly developed surface. It should be noted, that conventional magnetization measurements require much larger sample. Graphene deposition and the sample transfer to the measuring tube were performed in the chamber filled with the protective argon atmosphere prepared by repeated filling of chamber by pure argon followed by its removal. This procedure was applied to minimize pollution with traces of paramagnetic oxygen and water molecules. As argon is heavier than air, the fast transfer of the measuring tube from the chamber with protective atmosphere to the vacuum pump should not cause contact of the sample (graphene deposited on SiO2) with the atmospheric oxygen or moisture. The spectra recorded before switching on the pump and during first hours of pumping did not show any traces of the ESR signal. A weak signal appeared only 60 h after attaining high dynamic vacuum (105 Pa). Several days of sample storage under static vacuum in the closed ampoule resulted in a significant increase in signal intensity and in its narrowing. Such delay in signal appearance can be understand under assumption that the potentially paramagnetic defects were blocked by some kind of functional groups or adatoms attached to graphene surface and edges. Storage in vacuum caused gradual detachment of the adatoms and/or functional groups resulting in release of paramagnetic defects and the appearance of ESR signal. The spin content was established by the use of K3NbO8:Cr5+ standard. After several day storage in vacuum the spin concentration reached the value of 3 1013 spin/cm2 (4 1020 spin/g) then a gradual decrease in the signal intensity was observed. If the observed ESR signal is assigned to the magnetic moments localized on carbon vacancies, a decrease in the signal intensity should be related to the reconstruction of these vacancies resulting in a decrease in the magnetic moment. After several months and additional annealing at 400 °C for 12 h the ESR signal associated with localized states disappeared completely. The sample exposed to such a long conservation in high vacuum and annealing reveals ESR spectrum of conduction electrons and low-frequency FMR lines.
Decrease in the localized states concentration to the amount below the detection level weakens the exchange coupling and the conduction electrons can be observed separately. ESR measurements were performed with the RADIOPAN SX spectrometer with Oxford CF935 cryostat allowing the measurements in the temperature range of 4.2–300 K.
Results and discussion FMR lines Temperature variation of the FMR/ESR spectra in single-layer graphene is shown in Fig. 1. The presence of a distinct FMR lines situated at ca. 210 mT with a peak-to-peak width of ca. 20 mT is evident up to T = 50 K. The FMR lines are typical to ferromagnetic quasi-1D nanodomains formed by zigzag edges. Between 50 K and 65 K the FMR line disappears. Above 125 K the wide FMR lines characterized by low values of widely distributed effective local fields are visible. To understand this behavior we have to analyze the magnetic spin correlation length, which is responsible for magnetic ordering in ferromagnetic nanodomains formed by zigzag edges. The spectrum in Fig. 1 in the vicinity of g 2 is overmodulated and the measurements for these regions were repeated in proper conditions. The resonant microwave absorption in ferromagnetic materials for a given frequency is controlled by an effective field Beff, which is a vector sum of an external applied field and various contributions of internal magnetization. The localized edge-state spins in nanographene contribute to the formation of an unconventional carbon-based magnetic system, as the edge state is strongly spin polarized. The resonance center field (Bcenter) for the ferromagnetic resonance signals shifts to a lower value (about 210 mT). It can be understood from the condition for resonance in the presence of local magnetic field (BA): hf/lBg = Bcenter + BA, where h is the Planck’s constant, g 2 for a free electron, f (8.970 GHz) is the fixed frequency of the applied microwave magnetic field, and lB is the Bohr magneton, respectively. Magnetic order in low-dimensional systems is exceptionally sensitive to thermal fluctuations. In particular, the Mermin–Wagner theorem excludes long range order
Fig. 1. Temperature variation of the FMR/ESR spectra in single-layer graphene.
K. Tadyszak et al. / Journal of Molecular Structure 1076 (2014) 31–34
in one-dimensional magnetic systems (such as the magnetic graphene edges) at any finite temperature [9]. Nevertheless, a recent theoretical report using quantum Monte Carlo supports the existence of such a long spin–spin correlation length along the zigzag edge and justifies the picture obtained from the oneelectron theories [13]. Despite these spectacular theoretical predictions, the experimental demonstration of this long-range spin order in graphene is still missing. One of the most appealing experimental examples of 1D magnetism is monoatomic Co chains on Pt substrate characterized by a ferromagnetic order range of 4 nm at 45 K [10]. The range of magnetic order is limited by the temperaturedependent spin correlation lengths na (a = x, y, z) which define the decay law of the spin correlation:
a a a a ^si ^siþl ¼ ^si ^si expðl=na Þ;
ð1Þ
where ^sai are the components of magnetic moment unit vector ^si at site i. In principle, the spin correlation length imposes the limitations on the spintronic device dimensions. In order to establish this parameter one has to determine the energetics of the spin fluctuations contributing to the breakdown of the ordered ground-state configuration. The energetics of the transverse and longitudinal spin excitations have been explored using DFT calculations [8]. The magnetic correlation parameters in the presence of spin-wave fluctuations, the dominant type of spin disorder in this case, were obtained with the help of one-dimensional Heisenberg model Hamiltonian:
H ¼ J 0
X X X ^si ^siþ1 d ^szi^sziþ1 mH ^si ; i
i
ð2Þ
i
where ^si is the magnetic moment unit vector at site i, H is the external magnetic field vector, and m is the total magnetic moment per unit cell of zigzag edge. At a zigzag edge of graphene, the total magnetic moment of the outermost edge atoms was estimated as m = 0.30 lB per unit cell [8]. The estimated small anisotropy parameter d/J0 104 originates from the weak spin–orbit interaction in carbon. This simple model Hamiltonian has known analytic solutions and determines the spin correlation lengths calculated for our particular case. As shown in [8], above the crossover temperature Tx 10 K, weak magnetic anisotropy does not play any role and the spin correlation length n / T1. However, below Tx the spin correlation length grows exponentially with decreasing temperature. At T = 300 K the spin correlation length n 1 nm. From a practical point of view, this means that the dimensions of spintronic devices based on the magnetic zigzag edges of graphene and operating at normal temperature conditions are limited to several nanometers. Nevertheless, one has to keep in mind that there is room for improvement. Achieving control over the magnetic anisotropy d/J0 could possibly raise the crossover temperature Tx above 300 K and thus significantly extend n [8]. Possible approaches for reaching this goal include chemical functionalization of the edges with heavy-element functional groups or coupling graphene to a substrate. For the Heisenberg model, the enhancement factor for the susceptibility in comparison with one of noninteracting spins reads [14]:
v 1 þ u 2J0 ¼ ¼ ; v0 1 u T
ð3Þ
where u = coth(J0/T) T/J0 and the approximation being valid at J0 T. At temperature 125 K the susceptibility enhancement factor vv0 12. This yields a ferromagnetic coupling J0 750 K, which is close to the theoretical predictions [5]. Recently, the intrinsic magnetism of graphene edge states based on unidirectional aligned graphene sheets derived from completely carbonized SiC crystals
33
was studied [15]. The value of ferromagnetic coupling 820 ± 80 K was found, which is close to our result. As shown in Fig. 1, the local field determining the FMR frequency is practically constant up to T = 50 K. The local field is created mainly by the nearest neighbor spins in the quasi-1D ferromagnetic nanodomains formed by zigzag chains. As far as the rapidly decreasing with temperature magnetic correlation lengths are longer than ferromagnetic nanodomains, the local effective spin is constant. Above 50 K (between 50 K and 65 K) magnetic correlations become too short to produce stable local field and fast magnetic spin fluctuations lead to averaging of the effective field. The presence of wide FMR lines at temperatures above 125 K, characterized by low values of widely distributed effective local fields, is a consequence of the development of spin glass state [4]. In general, a spin glass state develops when the strengths of exchange interaction vary randomly in space. At this temperature region the magnetic correlation lengths are very short and rapid fluctuations of a frustrated spin system take place. Bhowmick and Shanoy [6] calculated that the zigzag edges of single layer graphene nanostructures that are longer than three to four repeat units are always magnetic, irrespective of other regular or irregular edges. Therefore, the edge irregularities and defects of the bounding edges do not destroy the edge state magnetism. We should admit that after another year of storage in vacuum, the signal from the coupled edge states disappears. The fundamental question for future application in spintronics and nanoelectronics is the stability in time and tuning of required magnetic and electric properties of graphene. This problem has been considered in many papers. In [17] the stability of edge states and edge magnetism in zigzag edge graphene nanoribbons is critically discussed. It was pointed out that magnetic edge states might not exist in real systems and showed that there are at least three very natural mechanisms—edge reconstruction, edge passivation, and edge closure—which dramatically reduce the effect of edge states or even totally eliminate them. Charge doping and the presence of edge defects further destabilize the intrinsic magnetism of such systems. Edge states may be passivated by functional groups or adatoms like oxygen, O–H groups, and other groups used in sonification process in the production of graphene. The existence of residual gas in vacuum may be also responsible for the observed decrease of magnetization. Time evolution of magnetization in single-layer graphene flakes was described in our previous paper [12]. We have shown that paramagnetic centers in graphene are sensitive to the atmospheric oxygen – samples must be tested in vacuum or in some inert environment. Quality of graphene flakes is important – even small contamination with nanographite can strongly influence ESR spectra. The signal disappears presumably due to coupling between graphene flakes (aggregation). This instability of the signal is, paradoxically, the proof that the observed signal is related to the graphene and not due to the presence of ferromagnetic impurities. However, suitable chemical modification of the graphene edges can result in the stable magnetic properties. Currently we are successfully working in this field. Graphene obtained by us from graphite by exfoliation/sonification in paraffin has very stable magnetic properties and strong FMR spectrum. Ferromagnetic resonance lines were also observed at about 200 mT and related to the presence of ferromagnetically correlated edge spins on the edges of the MoS2 nanosheets [18]. ESR lines The annealing induced disappearance of the narrow signal associated with localized electrons of carbon vacancies revealed a much broader and very weak signal shown in Fig. 2. This signal, corresponding to a spin concentration of about 4 1011 spin/ cm2, can be attributed to the conduction electrons in graphene.
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coupling between the ferromagnetic edge states and conduction electrons, which show Pauli type behavior. Conclusions
Fig. 2. Temperature dependence of the normalized ESR susceptibility vESR measured for the weak signal assigned to the conducting electrons. The solid line corresponds to the Curie law. The spectrum shown in the inset was recorded at 100 K with 64 accumulations.
We have assigned the signal shown in Fig. 2 to itinerant spins on basis of the Pauli type of temperature dependence of the ESR susceptibility. The observed signal is very weak, and as for now, we did not try to induce the spin echo. Moreover, the estimated short relaxation time of order of 30 ns indicates that the pulse methods do not allow observation of neither the echo nor the FID signal. We noted that the spin concentration determined by ESR was the same as that of conduction electrons determined from capacity measurements [16]. The observed weak temperature dependence can be a consequence of the interactions with the localized states on the zigzag edges. This supposition concerning the origin of the signal is confirmed by the signal shape, which can be fitted as the perpendicular component of the anisotropic powder spectrum with g|| > g\, as observed for the conduction electrons in graphite and expected for graphene. Because of a low spin concentration and a small amount of graphene in the sample, the signal is too weak to record its parallel component. For the fitting procedure we used the room temperature g-values typical of graphite (g\ = 2.0023, g|| = 2.051). In this procedure the linewidth in the perpendicular direction (in the graphene plane), in the temperature range 4.2– 300 K, varied between 0.39 mT and 0.45 mT. Yazyev and Katsnelson [8] have calculated spin density of states for the collinear domain wall excitation at a zigzag edge of graphene. They found that for the ferromagnetically coupled outermost edge atoms the spin energy is different than that for single zigzag edge or conduction electrons. That is why we do not observe a
In this study we provided the direct experimental evidence of ferromagnetic ordering in the zigzag edges of graphene. On the basis of our investigations we can conclude about the existence of the magnetic edges in graphene and presence of the ferromagnetic correlations between edge spins. The FMR technique requires much smaller sample comparing to conventional magnetometric measurements. Magnetic ordering is determined by the spin correlation length. Magnetic order in low-dimensional systems is exceptionally sensitive to thermal fluctuations. Several approaches have been proposed for extending the range of magnetic order by increasing the spin correlation length. FMR opens new possibilities for investigations of these issues in carbon-based magnetic nanostructures. References [1] V.L.J. Joly, K. Takahara, K. Takai, K. Sugihara, T. Enoki, M. Koshino, H. Tanaka, Phys. Rev. B 81 (2010) 245428. [2] X. Jia, J. Campos-Delgado, M. Terrones, V. Meuniere, M.S. Dresselhaus, Nanoscale 3 (2011) 86. [3] M. Acik, Y.J. Chabal, Jpn. J. Appl. Phys. 50 (2011) 070101. [4] T. Enoki, Phys. Scr. T146 (2012) 014008. [5] Y.W. Son, M.L. Cohen, S.G. Louie, Nature 444 (2006) 347. [6] S. Bhowmick, V.B. Shenoy, J. Chem. Phys. 128 (2008) 244717. [7] W.L. Wang, S. Meng, E. Kaxiras, Nano Lett. 8 (2008) 241. [8] O.V. Yazyev, M.I. Katsnelson, Phys. Rev. Lett. 100 (2008) 047209. [9] N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17 (1966) 1133. [10] P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, W. Eberhardt, K. Kern, C. Carbone, Nature 416 (2002) 301. [11] A. Dato, V. Radmilovic, Z. Lee, J. Philips, N. Frenklach, Nano Lett. 8 (2008) 2012. [12] M.A. Augustyniak-Jabłokow, K. Tadyszak, M. Mac´kowiak, Y.V. Yablokov, Phys. Status Solidi RRL 5 (2011) 271. [13] H. Feldner, Z.Y. Meng, T.C. Lang, F.F. Assaad, S. Wessel, A. Honecker, Phys. Rev. Lett. 106 (2011) 226401. [14] M.E. Fisher, Am. J. Phys. 32 (1964) 343. [15] L. Chen, L. Guo, Z. Li, H. Zhang, J. Lin, J. Huang, S. Jin, X. Chen, Scientific Reports 3 (2013) 2599, http://dx.doi.org/10.1038/srep02599. [16] L.A. Ponomarenko, R. Yang, R.V. Gorbachev, P. Blake, A.S. Mayorov, K.S. Novoselov, M.I. Katsnelson, A.K. Geim, Phys. Rev. Lett. 105 (2010) 136801. [17] J. Kunstmann, C. Ozdogan, A. Quandt, H. Feshke, Phys. Rev. B 83 (2011) 045414. [18] D. Gao, M. Si, J. Li, J. Zhang, Z. Zhang, Z. Yang, D. Xue, Nanoscale Res. Lett. 8 (2013) 129, http://dx.doi.org/10.1186/1556-276X-8-129.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
FMR evidence of ferromagnetic correlations at zigzag edge states in single-layer graphene Krzysztof Tadyszak, Mariusz Mac´kowiak ⇑, Maria A. Augustyniak-Jabłokow, Roman Strzelczyk ´ , Poland Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowski Str 17, 60-179 Poznan
h i g h l i g h t s Magnetism of zigzag edges of single layer graphene can be studied by FMR/ESR method. Ferromagnetic spin correlation lengths were evidenced. Magnetic order in low-dimensional systems is sensitive to thermal fluctuations. ESR spectra of conduction electrons show Pauli type behavior.
a r t i c l e
i n f o
Article history: Received 16 April 2014 Received in revised form 17 July 2014 Accepted 17 July 2014 Available online 23 July 2014 Keywords: Graphene Ferromagnetism of graphene Ferromagnetic resonance Electron spin resonance
a b s t r a c t Magnetic properties of zigzag edges of single-layer graphene were investigated by ferromagnetic resonance (FMR)/electron spin resonance (ESR) technique. We observed the FMR lines in single-layer graphene, which provide the most direct experimental proof of the theoretical prediction of ferromagnetic correlations at zigzag edges. To explain the observed temperature dependence of the FMR lines we analyzed the magnetic spin correlation length, which is responsible for magnetic ordering in these quasi-1D ferromagnetic nanodomains formed by zigzag edges. ESR spectra of conduction electrons were also studied. Ó 2014 Elsevier B.V. All rights reserved.
Introduction Graphene, a two-dimensional form of carbon, has attracted considerable attention due to its unique physical properties and potential technological applications. Nanographene, whose shape is described in terms of a combination of armchair and zigzag edges, has spin-polarized nonbonding p-electron state (edge-state) localized in the zigzag-edge region in spite of the absence of such state in armchair edges, as suggested by theoretical predictions and scanning tunneling microscope/scanning tunneling spectroscopy (STS) experiments [1–4]. According to theoretical studies [5], the edge-state spins are strongly coupled in parallel with each other in a zigzag edge through strong intrazigzag-edge ferromagnetic interaction J0 having a strength of 103 K. In a nanographene sheet with zigzag-edge regions separated by the presence of armchair edges, the ferromagnetically coupled edge-state spins in a zigzag edge are interacting with those in other zigzag edge through interzigzag-edge ⇑ Corresponding author. Tel.: +48 61 8695 208. E-mail address: [email protected] (M. Mac´kowiak). http://dx.doi.org/10.1016/j.molstruc.2014.07.047 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
ferromagnetic/antiferromagnetic interaction J1 having a strength of (101–102) J0 and mediated by conduction p carriers. There have been a large number of theoretical efforts investigating edge state magnetism [6–8] in graphene nanostructures terminated by zigzag edges. However, we are not aware of any direct experimental observation of these phenomena in single-layer graphene. The intrinsic magnetic properties of graphene in finite sizes are far from being understood, because magnetic signal from one piece of graphene in finite sizes is too weak to be detected by macro-magnetic measurement. Therefore, a massive amount of high-purity graphene (at least in milligram-scale) is an essential prerequisite to unveil the intrinsic magnetism contributed from graphene edges or vacancy defects. Even the possibilities of such phenomena were questioned by the fact that no true long-range magnetic ordering in 1D systems is possible at finite temperatures [9]. Nevertheless, nanometer range spin correlation lengths in certain 1D systems have been achieved in practice [10]. Establishing the range of magnetic order at graphene edges as well as the underlying physical mechanisms is thus crucial for understanding and practical realization of the nanoelectronic and spintronic devices.
32
K. Tadyszak et al. / Journal of Molecular Structure 1076 (2014) 31–34
In this work, we study the magnetic correlations at zigzag edges of single-layer graphene by investigating the FMR/ESR measurements. In particular, the use of ferromagnetic resonance (FMR) is noticeable. We found the FMR signal in the sample of a single layer graphene in a high vacuum. The ferromagnetically coupled edge spins gave a broad FMR signal, and as the edges are one-dimensional, the signal is shifted to the low magnetic field. One of the advantages of FMR over conventional magnetization measurements is that it yields information on the dynamics of the system. A mixture of microscopic phases containing a ferromagnetic contribution and a paramagnetic one is not easy to discriminate in a DC magnetization measurement, while it should be clearly distinguished in an FMR experiment. The zigzag edges exhibit ferromagnetic behavior when their size is sufficiently large, wherein the internal field undergoes ferromagnetic ordering revealing FMR lines. We observed the FMR lines in single-layer graphene, which provide the most direct experimental proof of the theoretical prediction of ferromagnetic correlations at zigzag edge states so far.
Material and methods We investigated graphene produced by the substrate-free gasphase synthesis with an average flake size of 550 nm, supplied by Graphene Supermarket in the form of graphene suspension in pure ethanol and declared to be monolayer. This material was reported to be free of functional groups and to have low defect concentration [11]. However, we established [12] the presence of quite a significant amount of paramagnetic defects in the sample prepared by deposition of about 0.02 mg of the graphene flakes on amorphous SiO2 of highly developed surface. It should be noted, that conventional magnetization measurements require much larger sample. Graphene deposition and the sample transfer to the measuring tube were performed in the chamber filled with the protective argon atmosphere prepared by repeated filling of chamber by pure argon followed by its removal. This procedure was applied to minimize pollution with traces of paramagnetic oxygen and water molecules. As argon is heavier than air, the fast transfer of the measuring tube from the chamber with protective atmosphere to the vacuum pump should not cause contact of the sample (graphene deposited on SiO2) with the atmospheric oxygen or moisture. The spectra recorded before switching on the pump and during first hours of pumping did not show any traces of the ESR signal. A weak signal appeared only 60 h after attaining high dynamic vacuum (105 Pa). Several days of sample storage under static vacuum in the closed ampoule resulted in a significant increase in signal intensity and in its narrowing. Such delay in signal appearance can be understand under assumption that the potentially paramagnetic defects were blocked by some kind of functional groups or adatoms attached to graphene surface and edges. Storage in vacuum caused gradual detachment of the adatoms and/or functional groups resulting in release of paramagnetic defects and the appearance of ESR signal. The spin content was established by the use of K3NbO8:Cr5+ standard. After several day storage in vacuum the spin concentration reached the value of 3 1013 spin/cm2 (4 1020 spin/g) then a gradual decrease in the signal intensity was observed. If the observed ESR signal is assigned to the magnetic moments localized on carbon vacancies, a decrease in the signal intensity should be related to the reconstruction of these vacancies resulting in a decrease in the magnetic moment. After several months and additional annealing at 400 °C for 12 h the ESR signal associated with localized states disappeared completely. The sample exposed to such a long conservation in high vacuum and annealing reveals ESR spectrum of conduction electrons and low-frequency FMR lines.
Decrease in the localized states concentration to the amount below the detection level weakens the exchange coupling and the conduction electrons can be observed separately. ESR measurements were performed with the RADIOPAN SX spectrometer with Oxford CF935 cryostat allowing the measurements in the temperature range of 4.2–300 K.
Results and discussion FMR lines Temperature variation of the FMR/ESR spectra in single-layer graphene is shown in Fig. 1. The presence of a distinct FMR lines situated at ca. 210 mT with a peak-to-peak width of ca. 20 mT is evident up to T = 50 K. The FMR lines are typical to ferromagnetic quasi-1D nanodomains formed by zigzag edges. Between 50 K and 65 K the FMR line disappears. Above 125 K the wide FMR lines characterized by low values of widely distributed effective local fields are visible. To understand this behavior we have to analyze the magnetic spin correlation length, which is responsible for magnetic ordering in ferromagnetic nanodomains formed by zigzag edges. The spectrum in Fig. 1 in the vicinity of g 2 is overmodulated and the measurements for these regions were repeated in proper conditions. The resonant microwave absorption in ferromagnetic materials for a given frequency is controlled by an effective field Beff, which is a vector sum of an external applied field and various contributions of internal magnetization. The localized edge-state spins in nanographene contribute to the formation of an unconventional carbon-based magnetic system, as the edge state is strongly spin polarized. The resonance center field (Bcenter) for the ferromagnetic resonance signals shifts to a lower value (about 210 mT). It can be understood from the condition for resonance in the presence of local magnetic field (BA): hf/lBg = Bcenter + BA, where h is the Planck’s constant, g 2 for a free electron, f (8.970 GHz) is the fixed frequency of the applied microwave magnetic field, and lB is the Bohr magneton, respectively. Magnetic order in low-dimensional systems is exceptionally sensitive to thermal fluctuations. In particular, the Mermin–Wagner theorem excludes long range order
Fig. 1. Temperature variation of the FMR/ESR spectra in single-layer graphene.
K. Tadyszak et al. / Journal of Molecular Structure 1076 (2014) 31–34
in one-dimensional magnetic systems (such as the magnetic graphene edges) at any finite temperature [9]. Nevertheless, a recent theoretical report using quantum Monte Carlo supports the existence of such a long spin–spin correlation length along the zigzag edge and justifies the picture obtained from the oneelectron theories [13]. Despite these spectacular theoretical predictions, the experimental demonstration of this long-range spin order in graphene is still missing. One of the most appealing experimental examples of 1D magnetism is monoatomic Co chains on Pt substrate characterized by a ferromagnetic order range of 4 nm at 45 K [10]. The range of magnetic order is limited by the temperaturedependent spin correlation lengths na (a = x, y, z) which define the decay law of the spin correlation:
a a a a ^si ^siþl ¼ ^si ^si expðl=na Þ;
ð1Þ
where ^sai are the components of magnetic moment unit vector ^si at site i. In principle, the spin correlation length imposes the limitations on the spintronic device dimensions. In order to establish this parameter one has to determine the energetics of the spin fluctuations contributing to the breakdown of the ordered ground-state configuration. The energetics of the transverse and longitudinal spin excitations have been explored using DFT calculations [8]. The magnetic correlation parameters in the presence of spin-wave fluctuations, the dominant type of spin disorder in this case, were obtained with the help of one-dimensional Heisenberg model Hamiltonian:
H ¼ J 0
X X X ^si ^siþ1 d ^szi^sziþ1 mH ^si ; i
i
ð2Þ
i
where ^si is the magnetic moment unit vector at site i, H is the external magnetic field vector, and m is the total magnetic moment per unit cell of zigzag edge. At a zigzag edge of graphene, the total magnetic moment of the outermost edge atoms was estimated as m = 0.30 lB per unit cell [8]. The estimated small anisotropy parameter d/J0 104 originates from the weak spin–orbit interaction in carbon. This simple model Hamiltonian has known analytic solutions and determines the spin correlation lengths calculated for our particular case. As shown in [8], above the crossover temperature Tx 10 K, weak magnetic anisotropy does not play any role and the spin correlation length n / T1. However, below Tx the spin correlation length grows exponentially with decreasing temperature. At T = 300 K the spin correlation length n 1 nm. From a practical point of view, this means that the dimensions of spintronic devices based on the magnetic zigzag edges of graphene and operating at normal temperature conditions are limited to several nanometers. Nevertheless, one has to keep in mind that there is room for improvement. Achieving control over the magnetic anisotropy d/J0 could possibly raise the crossover temperature Tx above 300 K and thus significantly extend n [8]. Possible approaches for reaching this goal include chemical functionalization of the edges with heavy-element functional groups or coupling graphene to a substrate. For the Heisenberg model, the enhancement factor for the susceptibility in comparison with one of noninteracting spins reads [14]:
v 1 þ u 2J0 ¼ ¼ ; v0 1 u T
ð3Þ
where u = coth(J0/T) T/J0 and the approximation being valid at J0 T. At temperature 125 K the susceptibility enhancement factor vv0 12. This yields a ferromagnetic coupling J0 750 K, which is close to the theoretical predictions [5]. Recently, the intrinsic magnetism of graphene edge states based on unidirectional aligned graphene sheets derived from completely carbonized SiC crystals
33
was studied [15]. The value of ferromagnetic coupling 820 ± 80 K was found, which is close to our result. As shown in Fig. 1, the local field determining the FMR frequency is practically constant up to T = 50 K. The local field is created mainly by the nearest neighbor spins in the quasi-1D ferromagnetic nanodomains formed by zigzag chains. As far as the rapidly decreasing with temperature magnetic correlation lengths are longer than ferromagnetic nanodomains, the local effective spin is constant. Above 50 K (between 50 K and 65 K) magnetic correlations become too short to produce stable local field and fast magnetic spin fluctuations lead to averaging of the effective field. The presence of wide FMR lines at temperatures above 125 K, characterized by low values of widely distributed effective local fields, is a consequence of the development of spin glass state [4]. In general, a spin glass state develops when the strengths of exchange interaction vary randomly in space. At this temperature region the magnetic correlation lengths are very short and rapid fluctuations of a frustrated spin system take place. Bhowmick and Shanoy [6] calculated that the zigzag edges of single layer graphene nanostructures that are longer than three to four repeat units are always magnetic, irrespective of other regular or irregular edges. Therefore, the edge irregularities and defects of the bounding edges do not destroy the edge state magnetism. We should admit that after another year of storage in vacuum, the signal from the coupled edge states disappears. The fundamental question for future application in spintronics and nanoelectronics is the stability in time and tuning of required magnetic and electric properties of graphene. This problem has been considered in many papers. In [17] the stability of edge states and edge magnetism in zigzag edge graphene nanoribbons is critically discussed. It was pointed out that magnetic edge states might not exist in real systems and showed that there are at least three very natural mechanisms—edge reconstruction, edge passivation, and edge closure—which dramatically reduce the effect of edge states or even totally eliminate them. Charge doping and the presence of edge defects further destabilize the intrinsic magnetism of such systems. Edge states may be passivated by functional groups or adatoms like oxygen, O–H groups, and other groups used in sonification process in the production of graphene. The existence of residual gas in vacuum may be also responsible for the observed decrease of magnetization. Time evolution of magnetization in single-layer graphene flakes was described in our previous paper [12]. We have shown that paramagnetic centers in graphene are sensitive to the atmospheric oxygen – samples must be tested in vacuum or in some inert environment. Quality of graphene flakes is important – even small contamination with nanographite can strongly influence ESR spectra. The signal disappears presumably due to coupling between graphene flakes (aggregation). This instability of the signal is, paradoxically, the proof that the observed signal is related to the graphene and not due to the presence of ferromagnetic impurities. However, suitable chemical modification of the graphene edges can result in the stable magnetic properties. Currently we are successfully working in this field. Graphene obtained by us from graphite by exfoliation/sonification in paraffin has very stable magnetic properties and strong FMR spectrum. Ferromagnetic resonance lines were also observed at about 200 mT and related to the presence of ferromagnetically correlated edge spins on the edges of the MoS2 nanosheets [18]. ESR lines The annealing induced disappearance of the narrow signal associated with localized electrons of carbon vacancies revealed a much broader and very weak signal shown in Fig. 2. This signal, corresponding to a spin concentration of about 4 1011 spin/ cm2, can be attributed to the conduction electrons in graphene.
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coupling between the ferromagnetic edge states and conduction electrons, which show Pauli type behavior. Conclusions
Fig. 2. Temperature dependence of the normalized ESR susceptibility vESR measured for the weak signal assigned to the conducting electrons. The solid line corresponds to the Curie law. The spectrum shown in the inset was recorded at 100 K with 64 accumulations.
We have assigned the signal shown in Fig. 2 to itinerant spins on basis of the Pauli type of temperature dependence of the ESR susceptibility. The observed signal is very weak, and as for now, we did not try to induce the spin echo. Moreover, the estimated short relaxation time of order of 30 ns indicates that the pulse methods do not allow observation of neither the echo nor the FID signal. We noted that the spin concentration determined by ESR was the same as that of conduction electrons determined from capacity measurements [16]. The observed weak temperature dependence can be a consequence of the interactions with the localized states on the zigzag edges. This supposition concerning the origin of the signal is confirmed by the signal shape, which can be fitted as the perpendicular component of the anisotropic powder spectrum with g|| > g\, as observed for the conduction electrons in graphite and expected for graphene. Because of a low spin concentration and a small amount of graphene in the sample, the signal is too weak to record its parallel component. For the fitting procedure we used the room temperature g-values typical of graphite (g\ = 2.0023, g|| = 2.051). In this procedure the linewidth in the perpendicular direction (in the graphene plane), in the temperature range 4.2– 300 K, varied between 0.39 mT and 0.45 mT. Yazyev and Katsnelson [8] have calculated spin density of states for the collinear domain wall excitation at a zigzag edge of graphene. They found that for the ferromagnetically coupled outermost edge atoms the spin energy is different than that for single zigzag edge or conduction electrons. That is why we do not observe a
In this study we provided the direct experimental evidence of ferromagnetic ordering in the zigzag edges of graphene. On the basis of our investigations we can conclude about the existence of the magnetic edges in graphene and presence of the ferromagnetic correlations between edge spins. The FMR technique requires much smaller sample comparing to conventional magnetometric measurements. Magnetic ordering is determined by the spin correlation length. Magnetic order in low-dimensional systems is exceptionally sensitive to thermal fluctuations. Several approaches have been proposed for extending the range of magnetic order by increasing the spin correlation length. FMR opens new possibilities for investigations of these issues in carbon-based magnetic nanostructures. References [1] V.L.J. Joly, K. Takahara, K. Takai, K. Sugihara, T. Enoki, M. Koshino, H. Tanaka, Phys. Rev. B 81 (2010) 245428. [2] X. Jia, J. Campos-Delgado, M. Terrones, V. Meuniere, M.S. Dresselhaus, Nanoscale 3 (2011) 86. [3] M. Acik, Y.J. Chabal, Jpn. J. Appl. Phys. 50 (2011) 070101. [4] T. Enoki, Phys. Scr. T146 (2012) 014008. [5] Y.W. Son, M.L. Cohen, S.G. Louie, Nature 444 (2006) 347. [6] S. Bhowmick, V.B. Shenoy, J. Chem. Phys. 128 (2008) 244717. [7] W.L. Wang, S. Meng, E. Kaxiras, Nano Lett. 8 (2008) 241. [8] O.V. Yazyev, M.I. Katsnelson, Phys. Rev. Lett. 100 (2008) 047209. [9] N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17 (1966) 1133. [10] P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, W. Eberhardt, K. Kern, C. Carbone, Nature 416 (2002) 301. [11] A. Dato, V. Radmilovic, Z. Lee, J. Philips, N. Frenklach, Nano Lett. 8 (2008) 2012. [12] M.A. Augustyniak-Jabłokow, K. Tadyszak, M. Mac´kowiak, Y.V. Yablokov, Phys. Status Solidi RRL 5 (2011) 271. [13] H. Feldner, Z.Y. Meng, T.C. Lang, F.F. Assaad, S. Wessel, A. Honecker, Phys. Rev. Lett. 106 (2011) 226401. [14] M.E. Fisher, Am. J. Phys. 32 (1964) 343. [15] L. Chen, L. Guo, Z. Li, H. Zhang, J. Lin, J. Huang, S. Jin, X. Chen, Scientific Reports 3 (2013) 2599, http://dx.doi.org/10.1038/srep02599. [16] L.A. Ponomarenko, R. Yang, R.V. Gorbachev, P. Blake, A.S. Mayorov, K.S. Novoselov, M.I. Katsnelson, A.K. Geim, Phys. Rev. Lett. 105 (2010) 136801. [17] J. Kunstmann, C. Ozdogan, A. Quandt, H. Feshke, Phys. Rev. B 83 (2011) 045414. [18] D. Gao, M. Si, J. Li, J. Zhang, Z. Zhang, Z. Yang, D. Xue, Nanoscale Res. Lett. 8 (2013) 129, http://dx.doi.org/10.1186/1556-276X-8-129.