Introduction

Unexpected ferromagnetism has been observed or theoretically predicted for numerous defective carbon based materials and wide-band gap semiconductors such as highly oriented pyrolytic graphite (HOPG), graphene, oxides and SiC1,2,3,4,5,6,7,8,9,10,11,12, which provides an alternative for organic and semiconductor spintronics. As the origin of the ferromagnetism is different from that in conventional d-electron ferromagnets, any experimental evidence to reveal its origin will be crucial. Červenka et al.13 demonstrated direct evidence that localized electron states at grain boundaries were one of the origins to induce ferromagnetism in HOPG. Ohldag et al.14 proved that the ferromagnetism found in graphite originates from carbon π-states and hydrogen-mediated electronic states. Ugeda et al.15 explained the formation of local magnetic moments by single vacancies in graphite. Recently, defect-induced ferromagnetism was found in SiC8,16,17,18. Divacancies (VSiVC) are proven to exist in neutron irradiated and neon implanted SiC8,17. Thus a question arises whether it is possible to establish a one-to-one correlation between the local moments and the specific orbitals/electrons in SiC.

On the other hand, SiC has been well known as a kind of economical and practical abrasive and a semiconductor for its application in high-temperature and high-voltage semiconductor electronics. As to our work, the good crystalline quality and the low concentration of impurities (please compare the relevant data in Refs. 8,19,20) can remove the concerns whether the observed ferromagnetism originates from extrinsic factors (e.g. magnetic contamination, see Refs. 21,22). Moreover, the dynamics of defects and their charge states in SiC upon ion irradiation can be obtained by ab initio molecular dynamics simulations23, rendering SiC an ideal testbed for the investigation of defect-induced ferromagnetism. Recent studies reveal that SiC could be a material with potential for applications in quantum optics and quantum information24,25,26,27. Therefore, direct experimental evidence for defect-induced ferromagnetism in SiC will have significant impact on other scientific areas related to defects.

In this paper, 6H-SiC single crystals irradiated with xenon ions are investigated to reveal the origin of its ferromagnetism. We present the results of X-ray absorption near-edge structure (XANES) and X-ray magnetic circular dichroism (XMCD) experiments at both the silicon and carbon K-edges in conjunction with sensitive magnetization measurements and first-principles calculations. These results show that the p electrons of the nearest-neighbor carbon atoms of VSiVC are mainly responsible for the long-range ferromagnetic coupling. Our results provide important evidence for the origin of defect-induced ferromagnetism in SiC.

Results

Magnetization measurements and sample selection

As a prerequisite step, the pristine SiC wafer was checked for trace elements by using particle induced X-ray emission. The amount of transition metal impurities (Fe, Co and Ni) proves to be below the detection limit of around 1 μg/g (result shown in Fig. S1 in the supplementary material). Figure 1(a) exhibits the hysteresis loops of all implanted samples after subtraction of the diamagnetic background. The inset of Fig. 1(a) shows magnetization vs. field for sample 5E12 and the pristine SiC measured at 5 K. The pristine SiC is primarily diamagnetic with a weak paramagnetic contribution (see Figs. S2–S4 in the supplementary material for details). As shown in Fig. 1(a), SiC becomes ferromagnetic upon Xe ion irradiation. The strongest magnetization occurs for the sample 5E12, which is the sample subjected to the lowest fluence and with the least damage to the crystallinity (refer to Fig. S5). With rising fluence, the saturation magnetization (Ms) decreases from 0.72 μB/vacancy to around 0.02 μB/vacancy. The decrease of Ms at large defect concentrations has also been observed in proton irradiated graphite2,28. This is very probably due to damage to the crystalline order or due to the unfavorable spin-polarization when the defects are too close to each other29. The hysteresis loops measured for the sample 5E12 at 5 K and 300 K after subtracting the magnetic background from the pristine sample are shown in Fig. 1(b), indicating Ms at 300 K is still around half of Ms at 5 K and the transition temperature is higher than 300 K. Therefore, we focus on the sample 5E12 in the following investigation.

Figure 1
figure 1

(a) Ferromagnetic hysteresis loops of samples 5E12, 1E13, 5E13, 1E14 at 5 K after subtracting the magnetic background from the pristine sample. The inset shows the as-measured magnetization vs. field of the sample 5E12 and the pristine sample at 5 K. (b) Hysteresis loops of the sample 5E12 at 5 K and 300 K.

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Direct evidence for the origin of magnetism

XMCD spectroscopy as an element-specific technique has been used to measure the magnetic contribution from different elements with partially occupied 3d or 4f subshells30,31. Ohldag et al.28 successfully applied this technique to investigate the magnetism at the carbon K-edge in proton irradiated HOPG. As it is possible to investigate the bonding state in SiC single crystals using XANES spectroscopy32,33, it is also possible to explore the magnetic contribution in defect-induced ferromagnetism in SiC with soft X-ray spectroscopy. Figure 2(a) shows the XANES spectra of the silicon K-edge for selected samples to investigate the source of the observed ferromagnetism. Comparing with the pristine sample, the peak positions of samples after implantation are not changed, but the relative strength of the peak at 1848 eV decreases, which suggests an increase of defect density34. As shown in Fig. 2(b), the strength of the XMCD signal at the silicon K-edge is below the detection noise level in both the pristine sample and the sample 5E12. We may conclude that no spin-polarized states of 3p electrons occur at silicon atoms and thus silicon centers do not contribute to the ferromagnetism observed in the sample 5E12. Figure 2(c) shows the XANES spectra at the carbon K-edge of the sample 5E12 and the pristine sample measured at 300 K. Resonances around 285 eV and 290 eV correspond to the transition of carbon 1s core-level electrons to π* and σ* bands, respectively14,28. The resonance at 285 eV of the sample 5E12 is sharper than that of the pristine sample, indicating that the orbital hybridization at carbon is modified from the diamond-like sp3-type carbon in pure SiC towards a more planar, graphitic sp2-type carbon center, which leaves the orthogonal pz orbital unchanged and gives rise to the peak of π* bands32. This reflects a change of the local coordination from the tetrahedrally coordinated carbon atom in pristine SiC to the three-fold bound carbon site. In sharp contrast to the silicon K-edge, a clear XMCD signal appears at the carbon K-edge as shown in Fig. 2(d). Therefore, the defect-induced ferromagnetism originates from a spin-polarized partial occupancy of the pz orbitals at carbon atoms close to defect sites in SiC. It is worth noting that an XMCD peak at around 280 eV Fig. 2(d) appears well below the onset of the π* resonance. This peak was also observed in graphite14. This intriguing feature is not yet fully understood.

Figure 2
figure 2

X-ray absorption spectra measured in EY (electron yield) mode for the sample 5E12 and the pristine sample: (a) XANES of the silicon K-edge at 77 K, (b) XMCD at the silicon K-edge at 77 K, (c) XANES of the carbon K-edge at 300 K. (d) XMCD at the carbon K-edge at 300 K.

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Discussion

According to the results provided by positron annihilation spectroscopy (see Figure S6 in the supplementary material), divacancies VSiVC are the dominating defect type in our samples. Note that the nearest-neighbor atoms of VSiVC include three carbon atoms as well as three silicon atoms. Why is the magnetic signal observed only at the carbon sites? To answer this question, first-principles calculations were employed. As shown in Fig. 3(a), 90% of the spin polarization with a total moment of 2 μB due to one divacancy VSiVC is contributed by the valence states of the carbon atoms. This explains why XMCD is only observable at the carbon K-edge. Furthermore, when comparing the partial spin-resolved DOS of nearest-neighbor carbon atoms with that of other carbon atoms, it is visible [see Figure 3(b)] that 85% of the magnetic moments originate from the three nearest-neighbor carbon atoms. In the Si-C system, as carbon has higher electronegativity than silicon, unpaired electrons around carbon atoms should be more localized than those around silicon. A Mulliken population analysis indicates that in the unperturbed SiC bulk the Si-C bonds are already polar in accordance with the respective electronegativities: Partial charges of −0.32 e on carbon atoms and of +0.32 e on silicon atoms are calculated for the pristine bulk at the Mulliken level. In the vicinity of the divacancy carbon atoms show a trend towards larger partial charges (−0.38 e), whereas the silicon partial charges close to the divacancy are nearly unchanged. Spin polarization thus mainly appears at those carbon atoms that are located around the divacancies. According to Fig. 3(c), our calculation indicates that most of the magnetic moments (90%) originate from the p states of nearest-neighbor carbon atoms of VSiVC. Due to the attraction of the remaining adjacent silicon atoms, the nearest-neighbor carbon atoms will slightly move away from the VSiVC. This structure change from the unperturbed four-fold bulk coordination to a more planar three-fold bound state is connected with s-p-rehybridization at the C atoms in the close vicinity of VSiVC. Concomitantly, this distortion will modify the electronic structure locally towards a higher degree of sp2 bonding orbitals and a singly occupied p-type lone pair at the C atoms. Thus those outermost orbitals will acquire significant π character and the magnetic moments are mainly contributed by p electrons, as shown in Fig. 3(d). This analysis corroborates our interpretation of the XMCD experiment: the XMCD signal of SiC after irradiation is thus assigned to p electrons.

Figure 3
figure 3

The electronic structure of Si95(VSi)C95(VC): (a) The total spin-resolved DOS and the partial spin-resolved DOS of silicon atoms and carbon atoms, respectively. (b) Comparison of partial spin-resolved DOS of nearest-neighbor carbon atoms and others. (c) Comparison of the partial spin-resolved DOS of s and p electrons of nearest-neighbor carbon atoms of VSiVC. (d) The structure and spin density isosurface (0.08 e/Å3, in purple) around one of the nearest-neighbor carbon atoms. The carbon atom is in grey in the middle and silicon atoms are in yellow. The arrows indicate the bond angles of Si-C-Si. The dashed line and square indicate the direction and the location of the adjacent silicon vacancy part (VSi) within VSiVC, respectively.

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In conclusion, in this work we investigated the magnetic properties of 6H-SiC after xenon irradiation. X-ray absorption spectroscopy at both the silicon and carbon K-edges combined with sensitive magnetization measurements and first-principles calculations are used to understand the origin of defect-induced ferromagnetism. The results give strong evidence that the p electrons of the nearest-neighbor carbon atoms of VSiVC are mainly responsible for the observed ferromagnetism. These results provide valuable insight into comprehending the phenomena of defect-induced ferromagnetism in SiC, graphitic and other carbon-based materials and will encourage the exploration of the origin of defect-induced ferromagnetism in other promising materials such as graphene and oxides.

Methods

Sample preparation

A commercial one-side-polished semi-insulating 6H-SiC (0001) single crystal wafer was cut into pieces for ion irradiation. The concentrations of transition metal impurities (Fe, Co and Ni) prove to be below the detection limit of particle induced X-ray emission (see Fig. S1 in the supplementary material). Four SiC pieces were implanted by xenon ions with fluence values of 5 × 1012, 1 × 1013, 5 × 1013, 1 × 1014 cm−2 at an energy of 500 keV at room temperature, which were subsequently labelled as 5E12, 1E13, 5E13 and 1E14, respectively. During implantation, the samples were tilted by 7 degrees to reduce the channelling effect. The corresponding displacements per atom (DPA) values have been calculated by Stopping and Range of Ions in Matter (SRIM)35 to be 0.023, 0.047, 0.23 and 0.47, respectively. The distribution of irradiation-induced damage predicted by SRIM for xenon ions is more uniform and closer to the surface than that produced by 140 keV neon ions17.

Measurements

All samples were measured with a superconducting quantum interference device (SQUID-MPMS or SQUID-VSM, Quantum Design). The magnetization is determined according to the total vacancies calculated using SRIM35. Both XANES and XMCD spectroscopies at the silicon and carbon K-edges were obtained at the Advanced Light Source (Berkeley Lab). The spectra of the silicon K-edge were measured at BL6.3.1 under a magnetic field of −2 and 2 T at 77 K, while the carbon K-edge spectra were measured at BL4.0.2 with the possibility of using a X-ray photon energy as low as 100 eV (note that the carbon K-edge is around 285 eV) and applying an external field of −0.5 and 0.5 T at 300 K. The typical spectral resolution for both beamlines is E/ΔE ~ 5000 (see Ref. 14). In the measurements, total electron yield (EY) mode is chosen, which usually collects the signal from the topmost 5–10 nm of the sample36.

Calculation parameters

First-principles calculations were performed using the Cambridge Serial Total Energy Package37. Spin-polarized electronic structure calculations were performed using the Perdew-Burke-Ernzerhof functional38 for the exchange-correlation potential based on the generalized gradient approximation. The core-valence interaction was described by ultrasoft pseudopotentials39 and to represent the self-consistently treated valence electrons the cutoff energy of the plane-wave basis was set to 310 eV. We calculated the total spin-resolved density of states (DOS) and the partial spin-resolved DOS of silicon atoms and carbon atoms in a 4 × 4 × 1 6H-SiC supercell containing one axial VSiVC [Si95(VSi)C95(VC)]. The calculation presented in this paper is for neutral VSiVC. With the minimum distance between adjacent VSiVC larger than 12 Å, this structure allows long-range ferromagnetic coupling8. The content of the spin polarization contribution is determined by comparing the integrated DOS below the Fermi level.