Determination of the hyperfine magnetic field in magnetic carbon-based materials: DFT calculations and NMR experiments


The prospect of carbon-based magnetic materials is of immense fundamental and practical importance, and information on atomic-scale features is required for a better understanding of the mechanisms leading to carbon magnetism. Here we report the first direct detection of the microscopic magnetic field produced at 13C nuclei in a ferromagnetic carbon material by zero-field nuclear magnetic resonance (NMR). Electronic structure calculations carried out in nanosized model systems with different classes of structural defects show a similar range of magnetic field values (18–21 T) for all investigated systems, in agreement with the NMR experiments. Our results are strong evidence of the intrinsic nature of defect-induced magnetism in magnetic carbons and establish the magnitude of the hyperfine magnetic field created in the neighbourhood of the defects that lead to magnetic order in these materials.


The occurrence of magnetism in carbon materials has been the subject of many investigations and some controversy along the past two decades, given the enormous interest in the possibility of producing carbon-based magnetic materials free from metallic elements1,2,3. These biocompatible magnetic materials find applications in fields such as drug delivery and magnetic resonance imaging, among others1,4. Moreover, the design of graphene-based spintronics devices would greatly benefit from a deeper understanding of magnetism and hyperfine interactions in carbon materials1,5. Recent experimental evidence of magnetic properties (with reports of ferromagnetic order in some cases) of carbon-based materials include irradiated graphite, nanocarbons, fullerenes, oxygen-containing carbons and point defects in graphene1,3,4,6,7,8,9,10,11,12,13,14,15. From the theoretical point of view, magnetism in graphene and related materials has been universally associated with the occurrence of defects such as atomic vacancies, chemisorbed species (such as fluorine, hydrogen and oxygen) and edge sites1,3,4,10,12,16,17. Similar examples of defect-induced magnetism have also been reported in other materials free from transition metal or rare earth elements, such as organic magnets, oxides, nitrides, silicon carbide and others; in all these cases, a common point is the source of magnetism being related to the spin polarization of p orbitals, which is associated with the occurrence of defects of structural or chemical origin2,3,18,19,20,21. In spite of this, there is still some scepticism about the possibility of intrinsic magnetic effects in carbon-based materials, due to the ubiquitously questioned presence of minor amounts of iron or other metallic impurities in experimentally-produced samples that could be the actual source of magnetism4,22,23. However, there are several recent examples of careful analyses that demonstrate in a convincing way the intrinsic nature of magnetism in carbon-derived materials. X-ray magnetic circular dichroism (XMCD) is an element-specific technique that allows the assessment of information about the magnetic moments associated with different elements in the material. XMCD data obtained at the carbon K edge have shown that the magnetization of proton-irradiated samples of carbon films and graphite (as well as for virgin graphite) is indeed associated with the spin polarization of carbon π electrons and also with chemisorbed hydrogen8,24. Similar results were achieved for ion-irradiated SiC crystals, where the ferromagnetic properties of the material were ascribed to electrons in p orbitals of atoms in the neighbourhood of atomic vacancies21. On the other hand, the use of particle-induced X-ray emission (PIXE) has allowed the determination of elemental contents of common magnetic metals (such as Fe, Ni, Cr, etc.) down to sub-ppm levels in samples of graphite and other carbon materials. With this detailed knowledge about the amounts of impurities, it is now possible to ascertain in many well-documented cases of carbon materials that, even when present, the impurities cannot account alone for the magnetization values and also cannot explain the temperature dependence of the magnetic properties of the analysed materials3,24,25,26.

If intrinsic magnetism is indeed a feature of carbon-based materials, then the influence of the local magnetic field on carbon nuclei should be detectable – in the case of systems possessing magnetic order, a strong microscopic field termed the hyperfine field (Bhf) at the atomic nuclei is anticipated. Therefore, evidence for Bhf and measurements of its properties are highly desirable for a better understanding of magnetism in carbon-based materials, providing information on the source of magnetism from a local perspective. Besides its importance from a fundamental point of view, the hyperfine interactions are relevant for applications of graphene and related materials in spintronics and quantum information processing27,28,29,30, leading to numerous theoretical calculations27,28,31 and experimental investigations involving the use of different techniques – electron spin resonance (ESR)11, muon spin rotation (μSR)32 and perturbed angular distribution (PAD)33. In none of these reports, however, any clue about the Bhf value in a truly ferromagnetic carbon material was ever reported. In this work we present a direct measurement of the local magnetic field using 13C nuclear magnetic resonance (NMR), corroborating the intrinsic nature of carbon magnetism and comparing the results to DFT calculations, confirming that the magnetism originates from defects in the structure, and not from ferromagnetic impurities.

Experimental approach

As a sensitive probe of local magnetic fields, nuclear magnetic resonance is ideally suited for gaining information on the hyperfine field in magnetic carbon-based materials. In NMR experiments, nuclear spin transitions between energy levels are excited and detected, with the transition frequency being characteristic of the type of nucleus and dependent on the local magnetic field according to:

where γ is referred to as the gyromagnetic ratio of the studied nucleus (in our case 13C) and B is the net magnetic field at the nucleus site. Local, internal magnetic fields thus contribute to the transition frequency, but in the majority of cases these fields are tiny, so that an additional large external field is necessary to perform the experiment. The net field is then , with B0 the external field and Bhf the local hyperfine field. However, in a magnetically ordered material the local field itself is large enough to enable the experiment to be performed without external field. This is referred to as zero-field NMR, and is a well-known effect in ferromagnetic materials such as iron, nickel and cobalt34,35,36. In the case of zero-field NMR the net field is simply the hyperfine field Bhf, and the NMR frequency is proportional to it. Thus a detection of a zero-field 13C NMR signal provides direct evidence of intrinsic carbon magnetism and presents a straightforward method of measuring the hyperfine field.

Another important feature of NMR in magnetic materials is a strong signal enhancement due to the coupling of nuclear and (ferromagnetically ordered) electronic spins. This ferromagnetic enhancement is largest in magnetic domain walls37, meaning that in zero-field NMR experiments one usually observes the signals from nuclei in the walls. The enhancement can be measured easily if the pulsed NMR method is employed for detecting the zero-field NMR signal. In pulsed NMR, short high power radio-frequency pulses are used to rotate the nuclear magnetization, and the subsequent magnetization precession is detected. In conventional single-pulse NMR experiments performed in non-magnetic materials, the signal amplitude is

where B1 is the amplitude of the radio-frequency field, and τ the duration of the pulse. For more complex pulse sequences the equivalent expressions become more involved, but the dependence on γB1τ remains qualitatively similar. However, ferromagnetic enhancement increases the field seen by the nuclei in a single domain wall by a factor η: B1 → ηB1, implying that a measurement of the amplitude in dependence on B1 can yield the value of η and provide insight into domain wall physics. Usually simple relations similar to equation (2) are not obeyed in ferromagnetic powders because of the random orientations of domain walls; more complicated dependences of the signal on B1 are then observed.

The material chosen for this investigation was ferromagnetic graphite, produced by controlled oxidation of high-purity graphite (details about sample preparation are given in Methods and Supplemental Material). As previously described13,14,38, this material can be produced in bulk quantities (~50 mg) and presents ferromagnetic order at room temperature and below. The maximum amounts of metallic impurities detected in the samples are well below the limits required to account for its overall magnetization, pointing to a genuinely carbon-originated magnetism14. (See also Supplemental material.) The magnetic properties of the material are related to the defects introduced in the graphite lattice by the oxygen attack, as suggested by recent theoretical calculations performed in graphite nanoribbons with edges partially passivated by oxygen atoms12. The sample selected for the NMR experiments showed a well-defined hysteresis loop in a magnetization versus applied magnetic field measurement conducted at low temperature (1.8 K), with coercive field of ca. 500 Oe, clearly indicating its ferromagnetic character (Supplemental Figure S1).
Electronic structure calculations

Without any a priori information about the hyperfine field, it would be difficult to find the zero-field nuclear resonance signal. Thus a series of first-principles calculations based on the density functional theory (DFT) was carried out to guide the NMR experiment. Calculations were performed in nanosized model systems built to somewhat reproduce the local features of the structure of ferromagnetic graphite (Fig. 1) (details of the DFT calculations are given in the Methods section). The model systems included graphene sheets with isolated or multiple single atomic vacancies, as well as graphite nanoribbons with oxygen atoms adsorbed at the zigzag edge sites. These systems are known from previous reports4,9,10,11,12,16,17,39 to give rise to magnetic moments localized at carbon atoms, with indications of a ferromagnetic ground state in some cases11,12,39, and thus they were considered good candidates for the initial calculations of Bhf at 13C nuclei. A summary of the results of the DFT calculations is presented in Table 1. The first noticeable aspect of these results is that all Bhf values fall into the same range, ~18–21 T, despite the different types of defects giving rise to magnetism in vacancy-containing graphene sheets and in oxygen-containing graphite nanoribbons. This is an indication that the Bhf values here reported are indeed characteristic of carbon sites with localized magnetic moments in carbon-based systems. As it should be expected, the largest Bhf values in each system were found at the sites also presenting the highest net spin densities and, thus, the largest atomic magnetic moments, as illustrated in Fig. 2 for some of the studied systems.

Figure 1: Relaxed structures of the systems used in the DFT calculations:
Figure 1

(a) Graphene sheet with one single vacancy: supercell with 71 carbon atoms and 1 atomic vacancy. (b) Graphene sheet with one single vacancy: Supercell with 161 carbon atoms and 1 atomic vacancy. (c) Graphene sheet with two single vacancies: Supercell with 160 carbon atoms and 2 atomic vacancies ca. 11 Å apart. (d) Graphene sheet with two single vacancies: Supercell with 160 carbon atoms and 2 atomic vacancies ca. 4.5 Å apart. (e) Graphite nanoribbon: Supercell with 48 carbon atoms (indicated as brown spheres) in each layer, with 8 oxygen atoms (indicated as red spheres) at the zigzag edges.