To explain the origin and sustainability of magnetism in G(OH)F systems and effect of chemical composition on magnetic features, we applied a high throughput theoretical screening of random structures of C 18 (OH) y F x (that is, with a large number (more than 1,400) of configurations, see Supplementary Table 2 listing abundances of FM and AFM ground states in % of C 18 (OH) y F x ), simulating thus reliably a random nature of the derivatization. We focused on identification of the nature of magnetic motifs driving room temperature magnetism, origin of FM-AFM transition, role of –OH groups in magnetic communication of these motifs and effect of C 18 (OH) y F x (an F/OH ratio) on magnetic properties of the system.

Regarding the magnetism origin, we identified energetically stable diradical motifs, typically consisting of sp2-conjugated islands embedded in an sp3 matrix, which were responsible for the observed magnetic behaviour. A prototypical example is the m-xylylene motif, which comprises eight sp2 carbon atoms and has an FM ground state (GS) with a spin moment S=1 and an FM-AFM spin-flip gap of 0.012 eV (Fig. 5a,b). Another important motif consists of four conjugated sp2 carbon atoms in a triangular configuration that resembles trimethylenemethane (Fig. 5c,d). Structures containing the trimethylenemethane motif have a spin moment S=1 (FM GS) and an FM-AFM spin-flip gap of 0.012 eV. It is worth noting that both m-xylylene and trimethylenemethane are typical organic diradicals that are known sources of molecular magnetism46. Structural details of both prototypical diradical motifs are depicted in Supplementary Fig. 8. The presence of diradical motifs with FM GS and small FM-AFM spin-flip gap is consistent with the experimental FM-AFM transition observed for G(OH)F at ∼62 K.

Figure 5: Spin densities and densities of states. (a,b) The m-xylylene-like motif (green) of G(OH)F embedded in an sp3 lattice with the corresponding FM (a) and AFM (b) phases, with up/down spin densities shown in yellow/blue. (c,d) sp3-embedded trimethylenemethane-like motif with the corresponding FM spin density. Brown/green, blue, red and pink balls represent carbon, fluorine, oxygen and hydrogen atoms, respectively. (e) DOS of the GS FM phase. (f) DOS of the AFM phase. For (e) and (f), orbital contributions of individual atoms (labelled in the inset legend) are presented in both spectra. Electronic states of carbon atoms with up/down magnetic moments are plotted by brown/black line. Electronic states with the same spin direction can hybridize with each other. The hybridization involves the occupied and unoccupied spin-up states (e) and the occupied and unoccupied spin-up or spin-down states (f). Such kind of coupling not involving a finite density of states at E F is termed as the superexchange interaction. Both DOS spectra show a significant contribution of oxygen orbitals to the midgap states, which implies an important role of -OH group in the superexchange interactions. Full size image

The electronic structure displayed as density of states (DOS) of G(OH)F with the m-xylylene-like motif both in the FM and AFM phase (Fig. 5e,f) provides insight into the nature of G(OH)F magnetism. The DOS in the vicinity of the Fermi level (E F ) is dominated by spin-polarized midgap states. Two midgap states per spin channel are visible in the FM phase (Fig. 5e), and only one channel is occupied. The midgap states reflect an imbalance of graphene bipartite lattice, N=N A − N B , where N A and N B are the number of atoms belonging to each sublattice. As the GS spin of imbalanced bipartite lattice is given by 2S=|N A − N B | (ref. 47), both diradical motifs have N=2 and, hence, S=1. The spin-polarized midgap states and bulk of positive (up) spin density reside within the diradical motif on the majority sublattice, while the electronic states of the minority sublattice form a band extending from 2.1 eV above E F . Note that the electronic states with the same spin direction hybridize with each other.

The DOS plot indicates on the superexchange interactions48 in maintaining the GS FM ordering within the diradical motifs. A substantial contribution of the oxygen p states of the bridging hydroxyl group (located between diradical motifs) to the midgap states (Fig. 5e) shows the important role of –OH groups in stabilizing the FM GS through the coupling between magnetic diradical motifs. The importance of –OH functionalization in self-sustainability of magnetic ordering is further demonstrated by the fact that fully fluorinated analogue of the m-xylylene motif, that is, the system comprising m-xylylene-like sp2 island surrounded by a fully fluorinated sp3 network, is predicted to have a paramagnetic GS with an AFM-FM spin-flip energy of 0.001 eV (ref. 43). Introduction of a single –OH group to the supercell only slightly enhances the stability of the m-xylylene motif’s FM state, by about −0.03 eV with respect to its fully fluorinated counterpart. A more significant stabilization of the FM GS was observed when two hydrogen-bonded –OH groups were introduced in close proximity to the sp2 island; this increased the stability of the FM state relative to the AFM state by 0.08 eV. In addition, a strong overlap of the –OH and –F orbitals in a broad binding energy range starting from –18.5 eV highlights the importance of –OH groups preventing migration of fluorine atoms over the graphene surface and suppressing formation of non-magnetic islands, which are formed in partially fluorinated graphenes43,49,50.

The DOS spectra of the AFM phase (Fig. 5f) are virtually identical as those for FM one up to the valence band maximum. The important differences appear in the occupation of the midgap states. The occupied (unoccupied) spin-up (spin-down) states are localized on the C atoms carrying positive spin density, while the opposite occupation resides on the C atoms with negative spin density. As hydroxyl group substantially contributes to the midgap states, we conclude that the AFM superexchange is driven by the magnetic coupling48,51 in which –OH group plays the significant role. Needless to say that the orientation of the hydroxyl group does not affect the FM-AFM transition observed at ∼62 K as both ab initio molecular dynamic simulations and arbitrary rotation of the –OH groups did not induce the phase change. Thus, the experimentally observed FM-AFM transition, inherent to organic-based materials with radical motifs42, is in good agreement with a low-energy gain of superexchange interaction of the FM state, which is inversely proportional52 to the energy difference between hybridized states (∼2.6 eV).

It is worth to mentioning that magnetism of graphene-based materials is intimately related to the appearance of midgap states in their electronic structure28,29. The origin of these midgap states is usually ascribed to defects or edges in the structure of graphene-based materials. Here we first identify the new principal source of magnetism in graphene derivatives based on creation of diradical domains through an appropriate sp3 functionalization. Such diradical motifs embedded in an sp3 lattice are thus clearly necessary but not sufficient for maintenance of the magnetic regime, which is further stabilized by the presence of neighbouring –OH groups. They show multiple roles in the system contributing to formation and stabilization of diradical motifs, superexchange interaction among them and suppression of adatoms lateral diffusion.

To support the principle role of –OH groups on magnetism, we further performed a high-temperature treatment of the G(OH)F sample. If it is exposed to a temperature above 200 °C, the room temperature magnetism is lost (after thermal treatment, G(OH)F behaves in a diamagnetic manner; Supplementary Fig. 9) as –OH groups start to leave the structure of G(OH)F (see, for comparison, Supplementary Fig. 3b). It confirms that –OH groups have an essential role on establishing and maintaining magnetically ordered state up to room temperature. In addition, defects such as vacancies, voids and edges cannot be considered as key factors capable to imprint the observed FM and AFM behaviour at low and room temperature, respectively.

Furthermore, we modelled the effect of the partial 3D layering of G(OH)F sheets on the magnetic features of the G(OH)F system. Here the individual layers in bulk G(OH)F samples were supposed to be bound by both dispersive forces and hydrogen-bonding between –OH groups. The theoretical calculations show that the magnetic properties of bulk G(OH)F are identical to those of the monolayered material (Supplementary Fig. 10). This indicates that magnetism of G(OH)F originates from the individual sheets and is not a consequence of their stacking. In other words, the potential contribution of 3D layering to the observed magnetism can be clearly ruled out.

To address the effect of chemical composition (OH and F contents) on magnetic properties of hydroxofluorographenes, we then constructed the magnetization map based on density functional theory (DFT) calculations for the C 18 (OH) y F x basic studied cell (Fig. 6). The magnetization map shows the propensity for the formation of FM ground states as a function of the F and OH content of the material (as also listed in Supplementary Table 2). Importantly, there are regions corresponding to the magnetically ordered FM ground states ranging from green to magnetically strongest red parts depending on the particular composition. Nevertheless, the blue regions corresponding to non-magnetic states are also present in a significant portion—the fact evidencing for a principal effect of chemical composition on magnetic features of G(OH)F system. In particular, two magnetically interesting islands appear, that is, upper island corresponding to G(OH)F systems with relatively high sp3 functionalization (above ∼50%) and higher OH and F contents and lower island with considerably lower degree of sp3 functionalization, centred at the C 18 F 4 stoichiometry, surprisingly with very low OH content. Importantly, the stoichiometry of the G(OH)F sample, thoroughly discussed above, lies within the region of the upper island (sample denoted as No. 1 in the magnetization map in Fig. 6), where the magnetism originates from the presence of sp2-conjugated diradical motifs embedded in an sp3 matrix. Computational predictions are thus consistent with available experimental data. In this region, the sp3/(sp2+sp3) ratio is above the site percolation limit of honeycomb lattice (0.697)52, which indicates that the number of sp3 atoms is sufficient (above 5.5 for the supercell containing 18 carbon atoms) to cage the sp2 islands.

Figure 6: Magnetic properties as a function of C 18 (OH) y F x stoichiometry. (a) The mean magnetization map indicates which C 18 (OH) y F x (x=0–8, y=0–8) stoichiometries are likely to exist in ferromagnetic and non-magnetic ground states. Both –F and –OH groups are assumed to be randomly distributed across the sample (as suggested by STEM–HAADF elemental mapping, cf. Fig. 3) at zero temperature and the possibility of kinetically controlled –F/–OH migration is not considered. The white circles indicate experimentally studied samples: 1—C 18 (OH) 1.8 F 7.2 (ferromagnetic in the ground state), 2—C 18 (OH) 1.5 F 6 (ferromagnetic in the ground state), 3—C 18 (OH) 2 F 3 (diamagnetic in the ground state), 4—C 18 (OH) 2.6 F 4.7 (ferromagnetic in the ground state), 5—C 18 (OH) 2.4 F 7 (ferromagnetic in the ground state), 6—C 18 F 2.5 (diamagnetic in the ground state), 7—C 18 F 4 (ferromagnetic in the ground state) and 8—C 18 F 6.3 (diamagnetic in the ground state). (b) The isothermal magnetization (M) curve of C 18 (OH) 1.8 F 7.2 (Sample No. 1) as a function of an external magnetic field (H), recorded at a temperature of 5 K. (c) M versus H curve of C 18 (OH) 1.5 F 6 (Sample No. 2), recorded at a temperature of 5 K. (d) M versus H curve of C 18 (OH) 2 F 3 (Sample No. 3), recorded at a temperature of 5 K. (e) M versus H curve of C 18 (OH) 2.6 F 4.7 (Sample No. 4), recorded at a temperature of 5 K. (f) M versus H curve of C 18 (OH) 2.4 F 7 (Sample No. 5), recorded at a temperature of 5 K. (g) M versus H curve of C 18 F 2.5 (Sample No. 6), recorded at a temperature of 5 K. (h) M versus H curve of C 18 F 4 (Sample No. 7), recorded at a temperature of 5 K. (i) M versus H curve of C 18 F 6.3 (Sample No. 8), recorded at a temperature of 5 K. The insets in panel (b,c,e,f and h) show the behaviour of the respective hysteresis loops around the origin with the saturation magnetization (M S ) indicated. Full size image

To confirm the presence of diradical motifs experimentally, we prepared and measured the electron paramagnetic resonance (EPR) spectra (Supplementary Fig. 11) for the C 18 F 11.5 sample whose sp3/(sp2+sp3) ratio was above the percolation limit (0.735), favouring the emergence of diradical motifs according to our theory. This sample exhibited a similar level of sp3 functionalization like G(OH)F sample, which is, however, antiferromagnetic (S=0) and thus EPR silent. The EPR resonances recorded at two different temperatures clearly indicate the presence of radical species. In particular, overlapping signals originating from uncoupled S=1/2 centres (strong resonance signals around g≈2) together with spin-coupled S=1/2 systems were observed, leading to the formation of triplet species (S=1). The EPR signatures of S=1 systems exhibited small E/D ratios (about 0.1) and became clearly visible upon lowering the temperature. The axial zero-field-splitting parameter (D) for the S=1 system was found to be equal to ∼790 MHz, which corresponds to an average distance of ∼4.6 Å between the interacting S=1/2 spins (point-dipole approach). Note that the distance between the two interacting S=1/2 spins corresponds well with the distance between the methylene groups in the m-xylylene motif (∼4.887 Å). The EPR data thus unambiguously confirmed the presence of diradical motifs in fluorographene systems of sufficiently high sp3 content.

To validate the theoretical magnetization map, we further prepared four additional samples (samples denoted as No. 2–No. 5 in Fig. 6) exploiting various reaction conditions and –OH sources (for details, see ‘Methods’ section below) and determined their chemical composition by XPS (Supplementary Figs 12 and 13). Here it is worth noting that the experimental scope for preparing the strongest magnetic systems will be limited by thermodynamics (Supplementary Fig. 14) and ability to prepare hydroxofluorographene systems with suitable and stable distributions of –OH and –F moieties (in this context, the facile migration of fluorines in lightly fluorinated graphenes may be problematic43). Nevertheless, the magnetic properties of all four additional derivatives with chemical compositions of C 18 (OH) 1.5 F 6 , C 18 (OH) 2 F 3 , C 18 (OH) 2.6 F 4.7 and C 18 (OH) 2.4 F 7 fit to the magnetization map with an excellent correlation and confirm the profound influence of the C 18 (OH) y F x stoichiometry (Fig. 6 and Supplementary Figs 12 and 13). In particular, C 18 (OH) 2 F 3 is a diamagnet, in full accordance with the map (it lies in one of the blue regions in Fig. 6). Conversely, C 18 (OH) 1.5 F 6 , C 18 (OH) 2.6 F 4.7 and C 18 (OH) 2.4 F 7 are magnetically sustainable 2D materials with an FM GS (all lying in green-yellow region) and very similar transition temperature to the AFM state at ∼62 K. The identical transition temperature, thus independent on chemical composition, is viewed as another proof of the same source of magnetism based on diradical motifs. The slight changes in saturation magnetization (from ∼0.9 to ∼1.2 emu g–1; Fig. 6) stem from different strength of superexchange interactions associated to the content of –OH groups.

To further validate our theory, provide additional support for the essential role of –OH groups in the magnetism of hydroxofluorographenes, and explore the potentially different origins of magnetism in fluorographene and hydroxofluorographene systems, we also synthesized three partially fluorinated fluorographenes without –OH groups by simple thermal defluorination of the exfoliated C 1 F 1 sample (for details on synthesis, see the ‘Methods’ section). The stoichiometries of these new systems are C 18 F 2.5 , C 18 F 4 and C 18 F 6.3 and the samples are denoted as No. 6, 7 and 8, respectively, in the magnetization map in Fig. 6 (for detailed XPS and magnetic characterization, see Supplementary Figs 15, 16 and 17). In full agreement with the magnetization map derived from our computational studies (Fig. 6), C 18 F 2.5 is diamagnetic but contains some paramagnetic centres in perfect correspondence with the work by Nair et al.43 reporting such behaviour for fluorographenes with lower fluorine coverages. Importantly, beyond the study by Nair et al.43, the C 18 F 4 exhibits even an FM GS as predicted by our magnetic model and experimentally confirmed (Fig. 6). However, it undergoes a transition to a paramagnetic state with the Curie temperature of 22 K. The different nature of transition temperature and inability to maintain magnetic ordering up to room temperature imply the different origin of magnetism in fluorographenes compared with hydroxofluorographenes. In particular, the structure of C 18 F 4 can be considered as sp3 structural defect in the sp2 graphene lattice (Supplementary Fig. 18). This is further confirmed experimentally by detailed magnetic analysis of C 18 F 4 (Supplementary Fig. 17). In particular, the temperature evolution of coercivity and saturation magnetization of C 18 F 4 agrees very closely with predictions based on theoretical expressions for magnetism due to d-electrons (that is, models based on Brillouin and Bloch functions), implying that its magnetism is due to localized defect-induced magnetic moments53,54. These results starkly contrast with our observations for G(OH)F systems that exhibit room temperature magnetic ordering, whose experimental saturation magnetization and coercivity data cannot be fitted using models based on expressions for d-electron magnetism. Finally, the C 18 F 6.3 sample is again diamagnetic with some paramagnetic centres in agreement with the theoretical magnetization map (Fig. 6). Here the magnetic ordering is lost due to a lack of conduction electrons related to the increased degree of functionalization.

The comparison of magnetic behaviour of GF and G(OH)F systems demonstrates the differences between the ‘defect-induced magnetism’ observed for GF systems with lower levels of sp3 functionalization and the ‘diradical motif-based magnetism’ observed in the highly functionalized G(OH)F system. At the same time, these data show that our theoretical model (that is, the magnetization map presented in Fig. 6) is robust, universal and capable of explaining the behaviour of both system types with different origins of magnetism.

In summary, we report a new class of graphene derivatives, which behave as antiferromagnetic materials at room temperature, representing examples of sp-based systems with room temperature magnetism. They become ferromagnets as the temperature is lowered showing remarkable magnetization. These organic magnets are prepared via simple, scalable and controllable reactions of fluorographene with suitable –OH-containing organic precursors. An interplay between thermodynamically preferred defluorination and nucleophilic substitution affects the products’ final stoichiometry and thus their magnetic features. The magnetism in hydroxofluorographenes with an appropriate stoichiometry stems from the presence of diradical motifs coupled via superexchange interactions and stabilized by –OH groups, which also mediate the coupling. The newly constructed theoretical model addresses the effect of system stoichiometry on magnetic features in an excellent agreement with experimental data. More importantly, this robust model has a universal character covering the aspects of the ‘defect-induced magnetism’ and ‘diradical motif-triggered magnetism’ appearing in the field of graphene magnetism depending on degree of sp3 functionalization.

We believe that this work would open the doors for preparing a wider family of graphene-based 2D room temperature magnets whose magnetic properties can be tuned by controlling the sp3 functionalization. Definitely, the theoretical model based on diradical motifs communicating through superexchange interactions should be further extended also for other graphene-based systems. The developed room temperature carbon magnets also offer a huge space for testing in potential applications in various fields including, for example, spintronics and magnetically separable nanocarriers.