Tabby is a pattern of short irregular stripes, usually related to domestic cats. We have produced Tabby patterns on graphene by attaching fluorine atoms running as monoatomic chains in crystallographic directions. Separated by non-fluorinated sp 2 carbon ribbons, sp 3-hybridized carbon atoms bonded to zigzag fluorine chains produce sp 2-sp 3 interfaces and spin-polarized edge states localized on both sides of the chains. We have compared two kinds of fluorinated graphite samples C2F x , with x near to 1 and x substantially below 1. The magnetic susceptibility of C2F x (x < 1) shows a broad maximum and a thermally activated spin gap behaviour that can be understood in a two-leg spin ladder model with ferromagnetic legs and antiferromagnetic rungs; the spin gap constitutes about 450 K. Besides, stable room-temperature ferromagnetism is observed in C2F x (x < 1) samples: the crossover to a three-dimensional magnetic behaviour is due to the onset of interlayer interactions. Similarly prepared C2F x (x ≈ 1) samples demonstrate features of two-dimensional magnetism without signs of high-temperature magnetic ordering, but with transition to a superparamagnetic state below 40 K instead. The magnetism of the Tabby graphene is stable until 520 K, which is the temperature of the structural reconstruction of fluorinated graphite.
Magnetism in restricted dimensions can be studied in real bulk crystals if the exchange interactions are much stronger in one or two spatial directions than in the remaining ones1,2. Thus, low dimension magnets have the advantage of bulk materials in providing sufficient intensity for experiments investigating the thermodynamic and spectroscopic characterization of magnetism. Most studies of low dimensional magnetism concentrate on molecular magnets based on organic radicals (see e.g.3,4) or Cu and Ni compounds which have spins ½ or 1, correspondingly5. We have recently synthesized a novel graphene derivative decorated by monoatomic fluorine chains running in crystallographic directions, and have observed clear signs of one-dimensional-like magnetism in this two-dimensional material6. Nanoscale magnetic activity of pure graphene is controlled by the edge geometry. In the present study, graphene fluorination, instead of breaking of the carbon-carbon bonds, is used as an efficient approach to generate edges and, therefore, correlated magnetic states in this material. The fluorine chain running in zigzag direction induces strong spin polarization with a mixed ferro-antiferro-magnetic coupling between locally emerged magnetic moments.
A distinctive characteristic of the novel derivative is that the interfaces form Tabby stripes. Tabby is a pattern of a cat’s coat with tiger stripes and leopard spots. Ideally, if the sp 2-sp 3 interfaces were parallel and evenly spaced lines, they would form embedded graphene nanoribbons. The stoichiometry C4F yields a 3-carbon atom wide nanoribbon, C3F is a 2-atom wide one, and C2F produces monoatomic chains (Fig. 1a). However, this ideal picture is only partially applicable, because the stripes run in all crystallographic directions (Fig. 1b). Still, the Tabby graphene is a unique derivative because the retention of the π-electron system results in different electronic properties of the Tabby graphene compared to fully functionalized graphene derivatives, which are insulators. The Tabby graphene contains confined islands of the π-electron system, it is semiconducting with the band gap 2–2.5 eV, and colour dependent on the C/F ratio7. The most distinct feature is that the Tabby graphene contains up to 10% of stable unpaired spins on carbon atoms. These states interact antiferromagnetically or ferromagnetically, depending on sublattice position.
We implemented the zigzag edge states at sp 2-sp 3 interfaces by slow fluorination of graphite intercalation compounds, which expanded into graphenes during the synthesis. This approach allowed us to obtain single- or bi-layers of fluorinated graphenes. In the case of the fully fluorinated graphene CF, all π-electrons on the basal planes were spent for covalent bonding with fluorine8, whereas deficient fluorination (Fig. 1) preserved the π-system partially, and its electronic properties were sensitive to the fluorine coverage9,10. Spin-half Curie paramagnetism in graphene functionalized with fluorine has been observed previously11. Quite recently, a ferromagnetic-like response has been found in hydroxofluorographenes and interpreted as due to biradical states12.
In this paper, we report on data demonstrating that the π-electron network in carbon nanosegments formed by Tabby fluorine patterns on the basal planes, shows non-Curie paramagnetism and magnetic order, depending on the stacking of graphitic planes and the fluorine coverage. We concentrate on similarities and differences in the magnetic properties of the Tabby graphene for various fluorine contents.
Magnetic properties of Tabby graphene C2F x with x < 1
The magnetic properties of Tabby graphenes are tightly connected with their structure, which changes during the sample history. Immediately after the synthesis, the samples were diamagnetic with only a Curie-like paramagnetic tail at low temperatures13. Unexpectedly, the measurements performed in several months, during which the samples were stored in a desiccator at room temperature, revealed qualitative changes: in addition to spin-half paramagnetism (Fig. 2a), the magnetic susceptibility as a function of temperature exhibited a maximum at ~250 K (Fig. 2b). The contribution of this non-Curie paramagnetism increased during further ageing (Fig. 2c), and in about one year the broad maximum followed by an activation-like drop on cooling (Fig. 2d) became a dominating feature in the magnetic susceptibility. Remarkably, the magnetization increased by 50 times after one year of storage.
The linear magnetic susceptibility χ(T) in Fig. 2 can be split as χ = χ0 + χCurie + χspin into a temperature-independent term χ0, a small Curie-like part χCurie = C/T identified by the low-T upturn, and a spin contribution χspin. The term χspin(T), that is the nontrivial part of the magnetic response, shows a non-monotonous temperature dependence with a broad maximum. This feature cannot be understood in the frames of independent magnetic moments. As shown in Fig. 2, non-monotonous temperature dependence of magnetic susceptibility χspin is the hallmark of low dimensional magnetism and is typical for both chain- and ladder-structured materials14. The position of the maximum in the plot of χspin (T) establishes an energy scale related to the strength of antiferromagnetic (AF) spin-spin interaction which favours spin pairing, and therefore, opposes the spin alignment parallel to an external magnetic field15.
To extract the strength of the interaction from the data and to estimate the amount of interacting spins, one may think in terms of localized spins with the Heisenberg Hamiltonian, H = Σij J ij S i·S j where S i is the spin located at site i and J ij denotes the strength of the exchange interaction. As in the case of molecule-based materials, various models can be tried out: the Heisenberg chain with anisotropic antiferromagnetic coupling (Bonner-Fisher16), the Hatfield model17 of a 1D spin chain with modulated coupling, a dimerised chain (Bleaney-Bowers18), and a spin ladder with antiferromagnetic interactions (Troyer-Tsunetsugu-Würtz19). However, none of these models which assume various modifications of only antiferromagnetic couplings, could give satisfactory agreement with our experiment. Indeed, the picture of the spin interactions that was predicted by the discoverers of the peculiar edge states of zigzag graphene nanoribbons in the seminal work by Wakabayashi et al.20, is characterized by ferromagnetic exchange coupling J FM ~ 103 K within a zigzag edge and an antiferromagnetic edge-edge coupling of the order J AFM ~ 10–100 K, depending on the nanoribbon width21. It is therefore reasonable to interpret the experimental results in the frames of the spin ladder model with ferromagnetic legs (J FM) and antiferromagnetic rungs (J AFM). We calculated the magnetic susceptibility of this model for the number of spins in a leg, Ns, changing from 1 to 126, and found that this model could be used successfully to fit a large batch of samples. As an example, the solid line in Fig. 2d corresponds to a combination of Ns = 3 and Ns = 8.
On the basis of the analysis of the susceptibility curves obtained on the different samples, we have arrived at the following quantitative conclusion: (i) with the maximum at T = 200–280 K, the exchange interaction strength (J AFM) value is in the range J AFM = 300–450 K22; (ii) the concentration of the exchange-coupled spins is rather large, being in the range 1–20% per CnF structural unit; (iii) the residual concentration of isolated spins ½ does not exceed 0.1%. The J AFM value confirms quantitatively that the AFM interactions within the graphene planes are much stronger than those in the organic radical crystals (e.g. nitroxide-based radicals, verdazyl radical crystals, or thiazyl radicals3), making the Tabby graphene an ideal candidate for 2D behaviour studies of pure organic materials.
Evolution of the magnetism of C2F x (x < 1) on ageing and annealing
A remarkable property of the Tabby graphene is the development of macroscopic magnetic order during ageing. Figure 3a shows that the behaviour of as-prepared samples is accurately described by the Brillouin function, which provides a good fit for total angular momentum quantum number J = S = ½ (free isolated electron spin). The saturation value in the magnetization curve shown in Fig. 3b corresponds to 0.3% of localized spins participating in the long-range magnetic order.
As the samples were purely organic, their magnetism was prone to thermal effects. We observed a sharp drop of paramagnetic response (Fig. 3c,d) and saturated magnetization (Fig. 3e) as a result of short-term heating up to the fluorine detachment temperature (520 K). This confirms that the magnetism of the Tabby graphene has pure organic origin and is determined by the fluorine arrangement on the basal plane.
We made an attempt to determine the Curie temperature for this organic magnet by measuring the isothermal M(H) loops and plotting the saturated magnetization at each temperature point (Fig. 3f). The Curie temperature was higher than the room temperature, but its exact value could not be determined because the magnetism falled irreversibly due to thermal destruction of the samples.
Magnetic properties of C2F x with x ≈ 1
The Tabby graphenes of the composition C2F x (x ≈ 1) were prepared by using similar technological procedures as in the case of C2F x , x < 1 (see the supplementary information for more details). All samples were Curie-like paramagnetic at room temperatures without any sign of ferromagnetism. However, on cooling, a strong increase in the magnetic moment was observed, pointing out at a ferromagnetic-like transition near 40 K (Fig. 4a). This transition was registered by both Superconducting Quantum Interference Device (SQUID) and Electron Paramagnetic Resonance (EPR). The double integrated intensity (EPR susceptibility) followed the ZFC magnetization protocols. The zero field–cooled (ZFC) and the field-cooled (FC) magnetizations diverged below 16 K, indicating a slow relaxation (blocking) of magnetization (Fig. 4a). This low-temperature behaviour was sensitive to the applied magnetic fields (H), and at H = 1000 Oe the difference between the ZFC and FC magnetizations was undetectable (Fig. 4c). The position of the shifts to lower temperatures as the field increased, yielding the anisotropy field H A = 2600 Oe and a zero-field value of the blocking temperature, T 0 max = 10.5 K. M(H) isothermal dependencies (Fig. 4d), confirmed that below 40 K we observed superparamagnetism, and the numerical fits of the data in Fig. 4c,d give an average spin quantum number S ≅ 1000.
Keeping the samples at room temperature for a year caused strong changes to the magnetic response (Fig. 4b). The magnetism of the aged samples looked similar at first glance, but really it was not. First, the values of magnetic moment below the ferromagnetic-like transition were 40–50 times smaller in the aged samples. Second, on cooling from room temperature, the magnetic susceptibility passed through a maximum around 280 K and approached zero at low temperatures. This indicates clearly that the temperature dependence of magnetic susceptibility exhibits an activated behaviour below a broad maximum, which is characteristic of thermal excitation from a nonmagnetic ground state with a spin gap. Annealing the samples in a dynamic vacuum at T = 373 K for 24 hours resulted in full restoration of the magnetic properties shown in Fig. 4a. This resulted in the reduction of the oxygen and water content from 0.47% to 0.19%, and from 1.21% to 0.75% correspondingly, as verified by X-ray photoelectron spectroscopy. This led probably to the increase of interlayer interactions and development of 3D superparamagnetic ordering below 40 K. Apparently, both oxygen and water pushed the graphene planes apart, and the magnetic response was dominated by short-range 2D antiferromagnetic interactions.
EPR study of C2F x with x ≈ 1
The EPR technique, which allows selective tracking of different magnetic entities, diagnoses the magnetic units responsible for the described phenomena. For all the studied samples, the room temperature EPR spectra revealed two main constituents: (a) narrow lines within the region of g = 2.00, typical for fluorinated carbon, and (b) asymmetric broad lines with g ~ 2. The total spin densities were found to be 1018–1020 spin/g with only 1–2% contribution coming from the narrow signals. We focused the attention on the broad lines. For all samples, doubly integrated intensities for the broad lines which corresponded to EPR susceptibility followed the trends for SQUID susceptibility (see Fig. 4a,b), while the differences between the FC and ZFC measurements followed the shift of the resonant field positions H r broad. At each temperature, the position of a broad EPR line (i.e., resonant field H r broad) for this paramagnetic entity was determined by the origin of the entities (g-factor) and the internal magnetic fields (like hyperfine one etc.). Thus, the developing temperature shift of H r broad manifested progressive strengthening of the internal magnetic field. It is worth mentioning here that the resonant field of the narrow EPR line, attributed to fluorinated carbon, remained the same within the entire temperature region of 4–300 K. This may have reflected both the inhomogeneity of the samples and the local nature of magnetic ordering in the corresponding entities.
An unambiguous attribution of the magnetic unit can be done for as-prepared C2F x (x ≈ 1). There we observed clear transformation of the same broad EPR signal that was observed at room temperatures, into a multicomponent ferromagnetic resonance (FMR) signal (Fig. 5). Below 40 K the broad EPR signal grew abruptly in integral intensity, broadened and then split into low and high field components, which shifted towards opposite directions on further temperature decrease. The low field component kept shifting to the zero field region and then disappeared below 25 K, whereas the high field component at T = 15 K turned back to lower resonance field values, still remaining within the high field region (Fig. 6c). All the above features are typical for ferromagnetic (FMR) signals originated from partially oriented ferromagnetic subsystems with different magnetic anisotropies. Thus, the subsystem of exchange-coupled magnetic entities responsible for the short-range in-plane interactions, was also responsible for the ferromagnetism observed in these systems at low temperatures. This subsystem was present in all the studied samples: as-prepared, aged and annealed. Its magnetic behaviour was rich: it demonstrated 2D antiferromagnetic interactions, room temperature magnetic ordering, and the development of low-temperature superparamagnetism. We note that superparamagnetic behaviour below 25 K have been observed in EPR studies of nanosized graphite prepared by ball milling23 and of ultrathin graphitic particles obtained by heavy sonication of graphite powder24.
In the case of Tabby graphenes C2F x with x < 1, the position of the broad line, H r broad, was shifted to the low field region and changed its position smoothly on cooling. This indicates a decrease of an internal spontaneous magnetic field (Fig. 6a). For the case of Tabby graphenes with x < 1, the same behaviour of H r broad was observed within the temperature range of 100–300 K. However, below 100 K, the H r broad in this sample shifted abruptly to the higher field region (Fig. 6b corresponds to the sample depicted in Fig. 4b), indicating significant change in the internal magnetic field on cooling.
Fluorination is well known to be an effective method for introducing localized spin centres into graphene. When the attached fluorine atoms are arranged as monoatomic chains running in crystallographic directions (Tabby pattern), the sp 2-sp 3 interfaces created by the fluorine chain play the same role as zigzag edges. The graphene bipartite lattice consists of inequivalent A and B sublattices. In the case of a zigzag chain, one expects a set of localized spin states in sublattice A on one side of the nanochain and sublattice B on the other side. Density functional theory (DFT) calculations for well-separated fluorine chains clearly reveal the emergence of magnetism in fluorinated graphene6. The calculated complex magnetic configuration combines the strong ferromagnetic interaction between the local magnetic moments of C atoms within each side of the CF chain with the antiferromagnetic coupling between the magnetic moments of C atoms located on the opposite sides of the CF chain.
The parallels in the magnetic behaviour of Tabby graphenes with different stoichiometry and stacking sequences lead to a conclusion that the magnetic unit responsible for the ordering effects originates from the π-electron system in the nanosegments created by the Tabby patterns with the magnetic moments localized at the zigzag interfaces. DFT calculations confirm that edge states near a single zigzag chain are preserved in disordered networks of densely packed interfaces6. Strong differences in the magnetic behaviour of the described samples are explained by their structural differences.
Several graphene derivatives are known, e.g. graphene oxide, hydrogenated graphene, fluorographene, and chlorographene. Functionalization opens the band gap of graphene, which is desirable for on/off electronics. However, at full graphene coverage, the possibilities for manipulation of electronic properties are limited because the π electrons are already spent to the attached atoms. Extensive studies are done on releasing the π electrons by producing single-side C2F and C2H (still not synthesized), or “digging” the wide-gap derivatives, removing extra atoms and forming one-dimensional graphene regions: point defects, quantum dots, nanoribbons, superlattices.
In the synthesis of the Tabby graphene, the method of slow fluorination provides conditions where adsorbates tend to align in a chain sequence in which F adatoms are located on alternating sides of the graphene plane. Fluorine has the highest electronegativity of all elements. If the synthesis is made slowly at low temperature, quasi-equilibrium conditions allow fluorine to attach to the thermodynamically preferable places. Fluorinated carbon tends to separate spatially from non-fluorinated carbon. If one F is attached to the graphene, the next F will most preferably attach close to it, to another side in the ortho-position. The adsorption of an odd number of F atoms disturbs the π-electron system, so the adjacent atom attaches as close as possible, but to another side due to strong repulsion. The meta-position is unfavourable because it creates unpaired radicals.
We observed 2D spin gap -activated magnetism of C2F x (x < 1) samples after prolonged ageing (Fig. 2). It can be speculated that this feature is related to the bilayer-like structure of fluorinated graphite (x < 1). During the gas-phase synthesis, simultaneous F adsorption at multiple sites resulted in seeding of the chains in a random distribution across the graphene planes. Apparently, the chains were not long enough to produce the zigzag-inherited edge states. The honeycomb lattice of graphene is a bipartite lattice. Sublattices A and B are identical in a single layer. In a bilayer, atom attachment on B sites is energetically more preferable than on A sites. The chain grown in a certain direction of a graphite layer may dictate the rule for the pattern formation in the adjacent layer. The C−F bonds in graphene are dynamic, with a low energy barrier for the migration of F atom to the nearest C atom. The fluorine chains repeal and arrange in two neighbouring layers like the teeth of a comb. This creates an additional discriminating mechanism leading to the formation of regular Tabby patterns where crossing and branching are suppressed, which is presumably favourable for magnetic coupling.
When the layers in the Tabby graphene are substantially spaced, as in C2F x (x ≈ 1), the compound can be considered as a stack of monolayers. In this case the discriminating mechanism for chain formation is absent. Although fluorination does produce localized spins, the chain length is not enough for the development of zigzag edge states with measurable magnetic interactions on the 2D plane, or the development of high-temperature long-range magnetic ordering. High-temperature long-range magnetic ordering was absent in the samples of our study. Instead, we observed transition to 3D superparamagnetic behaviour at low temperatures. A low temperature ferromagnetic transition was seen in the multicomponent FMR signal, with the features typical for partially oriented ferromagnetic subsystems having different magnetic anisotropies. Ageing of the samples led to 50-fold reduction in the 3D magnetism, whereas transition to 2D behaviour was detected from the broad maximum and low-temperature activated behaviour of magnetic susceptibility.
To sum up, fluorination of graphene in such a way that the attached fluorine atoms formed monoatomic stripes running in crystallographic directions produced a special type of graphene derivative, which we call the Tabby graphene. The sp 2 –sp 3 interfaces produced by the fluorine atoms attached in the zigzag directions gave rise to numerous magnetic phenomena. Graphene is a two-dimensional material, whereas the fluorine chain patterns reduce the effective dimensionality to 1D. Magnetic susceptibility shows a behaviour typical for low-dimensional quantum spin-ladder systems, which is characterized by spin ordering along the zigzag edges and their antiparallel alignment between opposite zigzag edges. The existence of a gap in the spin excitation spectra of graphene ribbons with zigzag edges has been theorized since their discovery in 1998. We produced magnetically active fluorinated graphite samples and showed that this type of low-dimensional magnetism can be realized experimentally in a graphene-based system. We observed magnetic dimensional crossover with changes in the fluorine loading and interlayer distance, the parameters that can be controlled by synthesis conditions, sample ageing, and annealing. The Tabby graphene is a promising material with tuneable electronic and magnetic properties, and it provides a playground for the exploration of new quantum many-body states as well.
Samples of fluorinated graphite C2F x with the fluorine content x, 0.5 ≤ x ≤ 1, were produced by room temperature synthesis25,26,27. The starting material for the synthesis of the fluorinated graphite samples was natural graphite from the Zaval’evo deposit (Ukraine). To remove metal and silicate impurities, the material was purified by double acid treatment (HNO3:HCl 1:3 and concentrated HF). The grain size of the samples was about 100 × 100 × 20 μm, and the content of 3d metal impurities was below 1 ppm. Detailed description of sample preparation can be found in Supplementary Information.
DC magnetic measurements were performed at a Quantum Design SQUID magnetometer (MPMS-XL-1) in -1 T–+1 T magnetic fields. The DC magnetic susceptibility data were collected in the 1.76–400 K range in a 10 mT magnetic field. Electron Paramagnetic Resonance (EPR) measurements within the temperature range 4 K < T < 300 K were carried out by using a Bruker EMX-200 X-band (ν~9 GHz) EPR spectrometer equipped with Oxford Instrument ESR900 cryostat and Agilent 53150 A frequency counter at microwave power (P MW) levels ranging from 50 µW to 200 mW. The structure and composition of the fluorinated graphite samples were studied by means of X-ray diffraction (XRD) on a DRON-SEIFERT-RM4 diffractometer by using CuK α radiation and X-ray photoelectron spectroscopy (XPS) on a Phoibos 150 SPECS spectrometer using monochromatized AlK α radiation with the energy of 1486.7 eV. The results of structure and composition analysis are given in Supplementary Information.
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This research was supported by the Russian Science Foundation (Grant #14–13–00813) and European FP7 IRSES project 295180 MagNonMag. We are grateful to Dr I.P. Asanov for the XPS measurements and Dr Yu. V. Shubin for the XRD patterns. This study has been performed in the research group of Tatiana Makarova. Fighting with her illness, Tatiana was able to prepare the first version of the manuscript, working to the very last hours of her life. We, colleagues and friends of Tatiana, will miss her warm personality and highest expertise in physics.