Lifting the spin degeneracy in Graphene's Dirac cones
Graphene is a one-atom-thick layer of carbon atoms arranged in a honeycomb lattice. This material has garnered significant interest from the scientific community due to the unique properties arising from its particular atomic structure. Notably, graphene's electronic band structure is quite simple, featuring a pair of linearly crossing bands that form what is known as a Dirac cone. Despite extensive experimental and theoretical investigations, graphene still poses several challenges. One major goal is to induce spin polarization in graphene, which is intrinsically a nonmagnetic material. Achieving this would make graphene magnetic and enable spin polarization in the Dirac cone, paving the way for integration of graphene into spintronics. Coupling graphene with common magnetic materials such as iron, cobalt, or nickel induces spin polarization in graphene. Unfortunately, a strong interactions of graphene with these materials significantly alters the shape of the Dirac cone, preventing use of these systems in practical devices. Therefore, it is crucial to identify a system in which graphene can acquire spin polarization while maintaining its unique electronic properties with minimal alteration.
We recently discovered that a graphene-nickel interface can be modified by placing a thin layer of a magnetic rare earth metal europium (Eu) between graphene and nickel (Ni) (Figure 1a). First-principles calculations suggest that Eu attenuates the interaction between graphene and Ni. Moreover, Eu is magnetized by the interaction with Ni, and induces the spin polarization in the graphene's states. Due to a lower interaction with Ni, the electronic states of graphene retain the characteristic shape of the Dirac cone, with the typical gap opening seen in these systems. At the same time, the spin-polarized Dirac states, corresponding to opposite spin channels, interact differently with the spin-polarized Eu states, giving rise to two distinct shapes (Fig. 1b).
Figure 1: (a) Schematic representation of a heterostructure made up of a single layer of graphene, Eu and Ni; (b) first-principle calculations of the electronic band structure of the system with a focus on the Dirac cone. Red and blue colors highlight the two opposite spin directions of graphene, green color marks Eu states. (c) corresponding experimental ARPES data showing two distinct Dirac cones, colored arrows indicate the corresponding spins. (d) experimental spin polarization taken along the dashed line of panel (c), the opposite spin polarizations are indicated by red and blue arrows; (e) spin-resolved photoemission intensity, corresponding to different spin channels. Different Dirac cone gaps are indicated by red and blue arrows. Adapted from P. M. Sheverdyaeva et al., Phys. Rev. Lett. 132, 266401 (2024), with permission from Physical Review Letters.
We validated these predictions using angle-resolved photoemission spectroscopy (ARPES), a powerful technique that directly probes the band structure of materials, and spin-resolved ARPES, which provides information also about the spin polarization of electronic states. The experiments were conducted at the VUV-Photoemission and APE-LE beamlines of the Elettra synchrotron. The ARPES data revealed the emergence of two distinct graphene states, both exhibiting gapped conical dispersion (Fig. 1c), in a very good agreement with theoretical predictions. Additionally, the spin-ARPES data confirmed that these two Dirac cones indeed possess opposite spin polarizations (Fig. 1d), with the gap magnitudes for each spin channel differing by 2-3 times (Fig. 1e). The presence of a spin-dependent gap in graphene’s Dirac states can be employed in spintronic applications, for example, in the realization of graphene-based spin-filtering devices.
We furthermore explored theoretically whether the spin polarization in graphene may open the way to the manifestation of other, more exotic transport phenomena. As theory predicts, the Dirac cone states in the proximity of the gap have a locally nontrivial topology, characterized by a finite Berry curvature (Figure 2a). The calculations show that these topological properties of the gap would lead to a quantum anomalous Hall effect (Fig. 2b). This effect is characterized by currents flow without losing energy, opening up exciting possibilities for advanced electronics, and leading to more efficient and faster devices.
Figure 2: Theoretical topological analysis of a simplified system, built of graphene and Eu (a) wave-vector resolved Berry curvature in the proximity of the Dirac cone. The energy scale is referred to the Dirac point. (b) corresponding quantum anomalous Hall effect. Red arrows mark the Dirac states corresponding to the previous figure. Adapted from P. M. Sheverdyaeva et al., Phys. Rev. Lett. 132, 266401 (2024), with permission from Physical Review Letters.
This research was conducted by the following research team:
P. M. Sheverdyaeva1, G. Bihlmayer2, E. Cappelluti1, D. Pacilé3, F. Mazzola4,5, N. Atodiresei2, M. Jugovac6, I. Grimaldi3, G. Contini7, Asish K. Kundu1,8,9, I. Vobornik5, J. Fujii5, P. Moras1, C. Carbone1, and L. Ferrari7
1 CNR-ISM, Trieste, Italy
2 Forschungszentrum Jülich and JARA, Jülich, Germany
3 Dipartimento di Fisica, Università della Calabria, Arcavacata di Rende, Italy
4 Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venice, Italy
5 CNR-IOM, Trieste, Italy
6 Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy
7 CNR-ISM, Rome, Italy
8 ICTP, Trieste, Italy
9 NSLS II, New York, USA.
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Reference
P.M. Sheverdyaeva, G. Bihlmayer, E. Cappelluti, D. Pacilé, F. Mazzola, N. Atodiresei, M. Jugovac, I. Grimaldi, G. Contini, Asish K. Kundu, I. Vobornik, J. Fujii, P. Moras, C. Carbone, and L. Ferrari, “Spin-Dependent Spin-Dependent ππ* Gap in Graphene on a Magnetic Substrate", Phys. Rev. Lett. 132, 266401 (2024);
DOI: 10.1103/PhysRevLett.132.266401. The article was chosen as Editor’s suggestion.