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Tunable magnetism of a single-carbon vacancy in graphene
Journal Pre-proofs Article Tunable magnetism of a single-carbon vacancy in graphene Yu Zhang, Fei Gao, Shiwu Gao, Lin He PII: DOI: Reference:
S2095-9273(19)30668-1 https://doi.org/10.1016/j.scib.2019.11.023 SCIB 888
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Science Bulletin
Received Date: Revised Date: Accepted Date:
30 September 2019 30 October 2019 15 November 2019
Please cite this article as: Y. Zhang, F. Gao, S. Gao, L. He, Tunable magnetism of a single-carbon vacancy in graphene, Science Bulletin (2019), doi: https://doi.org/10.1016/j.scib.2019.11.023
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Tunable magnetism of a single-carbon vacancy in graphene Yu Zhanga,1, Fei Gaob,1, Shiwu Gaob*, and Lin Hea,c* aCenter
for Advanced Quantum Studies, Department of Physics, Beijing Normal
University, Beijing 100875, China bComputational cState
Science Research Center, ZPark II, Beijing 100193, China.
Key Laboratory of Functional Materials for Informatics, Shanghai Institute of
Mocrosystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 1These
*To
authors contributed equally to this work.
whom
correspondence
may
be
addressed
to
Shiwu
Gao
(e-mail:
[email protected]) and Lin He (e-mail: [email protected])
Abstract Creating a single-carbon vacancy introduces (quasi-)localized states for both and electrons in graphene. Theoretically, interactions between the localized electrons and quasilocalized electrons of a single-carbon vacancy in graphene are predicted to control its magnetism. However, experimentally confirming this prediction through manipulating the interactions remains an outstanding challenge. Here we report the manipulation of magnetism in the vicinity of an individual single-carbon vacancy in graphene by using a scanning tunnelling microscopy (STM) tip. Our spin-polarized STM measurements, complemented by density functional theory calculations, indicate that the interactions between the localized and quasilocalized electrons could split the electrons into two states with opposite spins even when they are well above the Fermi level. Via the STM tip, we successfully manipulate both the magnitude and direction of magnetic moment of the electrons with respect to that of the 1
electrons. Three different magnetic states of the single-carbon vacancy, exhibiting magnetic moments of about 1.6 B, 0.5 B, and 0 B respectively, are realized in our experiment.
Keywords: graphene, single-carbon vacancy, magnetic moment, tunable magnetism, scanning tunnelling microscopy.
Received: 30-Sep-2019 Revised: 30-Oct-2019 Accepted: 15-Nov-2019
1. Introduction An outstanding challenge in miniaturization of fabricating data storage devices is to control the magnetism at the atomic scale [1,2]. Very recently, the successful introduction of local magnetic moments in graphene by creating atomic vacancies [3] or adsorbing H atoms [4] shows the ability to achieve such a goal. Different from the H adatoms on graphene, which only introduce a local magnetic moment of electrons [4], creating a single-carbon vacancy introduces local magnetic moments of both the and electrons [5-18]. Theoretically, the interactions between the localized electrons and the quasilocalized electrons of the single-carbon vacancy are predicted to control its magnetic states, either exhibiting local magnetic moments or not [6,8,9,11,12,15,16]. Therefore, such a system provides a unique platform to control the magnetism at the atomic scale. In this work, we experimentally studied how the interactions between the localized electrons and the quasilocalized electrons control the magnetism of the single-carbon vacancy in graphene. Via a scanning tunnelling microscopy (STM) tip, we tuned the interactions between them and realized three different magnetic states of the single-carbon vacancies in graphene. Density functional theory (DFT) calculations revealed the nature of these magnetic states and quantum phase transitions between the three coupling regimes. 2
2. Experimental and computational methods 2.1 STM and scanning tunnelling spectroscopy (STS) measurements The STM system was an ultrahigh vacuum scanning probe microscope (USM-1300 and USM-1500) from UNISOKU. All STM and STS measurements were performed in the ultrahigh vacuum chamber (~10–11 Torr), at liquid-helium temperature (4.2 K) and the images were taken in a constant-current scanning mode. The nonmagnetic STM tips were obtained by chemical etching from a wire of Pt/Ir (80/20%) alloys, and the magnetic STM tips were obtained by electrochemically etching from a wire of Ni. Lateral dimensions observed in the STM images were calibrated using a standard graphene lattice, a Si (111)-(7×7) lattice, and an Ag (111) surface. The dI/dV measurements were taken with a standard lock-in technique by turning off the feedback circuit and using a 793-Hz 5mV A.C. modulation of the sample voltage.
2.2 Computational method Our first-principles calculations are performed within the framework of DFT using Vienna Ab initio Simulation Package (VASP) [19]. The projector augmented-wave (PAW) [20,21] pseudopotentials and the general gradient approximation (GGA) [22] in Perdew-Burke-Ernzerholf form [23] for the exchange-correlation energy are employed. The van der Waals density functional (vdW-DF) recently developed by Dion et al. [24] and parameterized by Klimes et al. [25] is also employed for comparison. A plane wave cutoff of 600 eV is used to expand the wave function. Spin polarization is invoked in all calculations. The geometrical structure and electronic properties of the monovacancy defect in graphene are calculated using the 8 × 8 supercells and the nonmagnetic STM tip is mimicked by a pyramid consisting of 14 Cu atoms. The supercells contain typically a vacuum layer ~ 40 Å along the z axis and the sampling of the Brillouin zone with a 3 × 3 × 1 k-point grid. All atoms except those in the top layer of the tip are allowed to relax until the forces on each atom are less than 0.05 eV/Å. 3
2.3 Synthesis of graphene multilayers on Ni foils A traditional ambient pressure chemical vapor deposition (APCVD) method was adopted to grow graphene multilayers on a Ni foil. The Ni foil was first heated from room temperature to 900 ℃ in 40 min under an argon (Ar) flow of 100 SCCM (SCCM stands for Standard Cubic Centimeters per Minute) and hydrogen (H2) flow of 100 SCCM, and the Ni foil was kept at 900℃ with the Ar and H2 flow for 20 min. In the next process, CH4 gas was introduced with the flow of 20 SCCM holding for 15 min. Then the sample was cooled down to room temperature and transferred into the ultrahigh vacuum condition for further characterizations.
3. Results and discussion 3.1 The electronic properties of the single-carbon vacancy in graphene. In our experiment, the single-carbon vacancies were generated in the synthesis process of graphene multilayer on Ni foil in a CVD method (see Methods and Figs. S1–S4 (online) for more details) [3,26-29]. Fig. 1a shows a representative atomic STM image of the single-carbon vacancy in the topmost graphene sheet with a characteristic Jahn-Teller distortion [3,8-11,30-32], which can be clearly recognized by the distinctive topographic fingerprint of a triangular
3 × 3 R30° interference
pattern in the STM image that induced by intervalley scattering of the atomic defect (see Figs. S5, S6 online). The STS spectrum recorded on the nearest C of vacant site exhibits two pronounced peaks (Fig. 1b. More data are given in Figs. S7 and S8 (online)), attributing to two spin-polarized states of the quasilocalized electrons V induced by the single-carbon vacancy [3,5] (by combining the Raman measurements and DFT calculations shown in Figs. S9–S14 (online), we can definitely exclude any possible interaction between the single-carbon vacancy and Ni substrate [33-35] or Ni adatoms [36-38] as the origin, and verify that all the experimental phenomena are 4
derived from the intrinsic spin-polarized states of the single-carbon vacancy). The slight energy shift of the two spin-polarized states is induced by the different charge transfer between the substrate and the topmost graphene sheet [39]. Fig. 1c shows a schematic diagram of electronic structure for a single-carbon vacancy in graphene. The crystal field and Jahn-Teller distortion split the localized electrons of the single-carbon vacancy into highly localized V1, V2, and V3 states [3,8-11,30-32]. Both the V2 and V states are half occupied because of the electrostatic Coulomb repulsion U, i.e., when an electron occupies the state, a second electron with opposite spin must overcome an extra energy U. The strength of U, which depends on the spatial localization of the states, determines the spin splitting. The spatial extension of the V state is much larger than that of the V2 state. Therefore, the V2 state has a much larger spin splitting than that of the V state [5,7,30-32] (Fig. 1c). There is usually a single electron occupying the V2 state due to the large spin splitting (the energies of the splitting V2 state are always more than 1 eV away from the Fermi energy, which are beyond our STS detection range). However, the two V states could be double occupied or unoccupied because of the existence of a slight charge transfer from the substrate. Then the spin splitting of the V state should vanish and only one sharp peak is expected to be observed [4]. However, in our experiment, two peaks are still observed for the single-carbon vacancies even when they are well above the Fermi level [3], as shown in Fig. 1b. Our spin-polarized STM measurements, as shown subsequently, demonstrate that the two peaks are the two spin-polarized V states, and we will show that the magnetism of the single-carbon vacancy behaves quite different from that of the adsorbing H atom in graphene.
3.2 The spatial distributions of spin-up and spin-down electrons around the single-carbon vacancy The spin-polarized STM measurements, which can directly reflect spatial distributions of spin-up and spin-down electrons [40,41], provide us an unprecedented insight to identify the magnetism of the single-carbon vacancy. In our experiment, 5
we used electrochemically etched Ni tip (Figs. S15–S17 online) as a spin-polarized STM tip, and its magnetic polarization is always along the tip due to the weak magnetocrystalline anisotropy of Ni and relatively large shape anisotropy of the STM tip [27,42,43]. Before the STM measurements, a magnetic field of 𝐵 = 3.0 T (𝐵 = ―3.0 T) perpendicular to the surface of the sample was applied on and then removed gradually to obtain an up-polarized M↑ (down-polarized M↓) STM tip. As schematically shown in Fig. 2a, we can carry out atomic-resolved STS measurements around the single-carbon vacancy by using spin-polarized STM tip (here the single-carbon vacancy is assumed on the B sublattice). Fig. 2b summarizes four representative spin-resolved STS spectra measured around the single-carbon vacancy (more STS spectra are shown in Figs. S8 and S18 (online)). Because of the spin conservation during the elastic electron tunnelling processes, the differences among
these
STS
spectra
directly
reflect
distributions
of
spin-polarized
density-of-states (DOS) on the A and B sublattices. Our experimental result indicates that the spin-up (spin-down) electrons of the V state are mainly located on the A (B) sublattice around the single-carbon vacancy. However, due to the incomplete polarization of the spin-polarized STM tip and spatial extension of the electron wave functions, there always exists a slight signal on the STS spectra when the polarized orientation of the tip and sample is antiparallel. Such a result is further confirmed by our STS maps recorded at the energies of the two spin-polarized states (Fig. 2c), revealing the site-specific spin polarization around the single-carbon vacancy, as predicted theoretically [5-18]. The above results explicitly demonstrate that the observed two peaks in the spectra are the two spin-polarized V states. We attribute the spin splitting of the V state even when the two spin-polarized states are well above the Fermi level to the interaction between the V state and the V2 state. The existence of local magnetic moment from the localized electrons is the main difference between the magnetism introduced by the atomic vacancies [3] and by the adsorbing H atoms [4] on graphene. If the graphene is not the exact planar configuration around the single-carbon vacancy, the orthogonality between the and states is broken [6,8,9,11,12,15,16]. Then the coupling with the spin-polarized V2 6
state may stabilize the spin splitting of the V state even when it is double occupied or unoccupied. Therefore, the two states of the V electrons induced by the atomic vacancies [3] and by the adsorbing H atoms [4] on graphene show quite different behaviors.
3.3. Tunable atomic configurations and electronic properties of the single-carbon vacancy The interaction between the localized and quasilocalized states determines the magnetism of the single-carbon vacancy in graphene [6,8,9,11,12,15,16]. Previously, it was demonstrated that the sufficient reduction of tip-graphene distance can generate an out-of-plane displacement on graphene through a finite van de Waals (vdWs) force [44-47]. Here we show that it is possible to generate out-of-plane deformation around the single-carbon vacancy and, consequently, tune interactions between the localized and quasilocalized states by using the STM tip under long-time scanning processes. Fig. 3 shows representative results measured on a single-carbon vacancy with three different heights, which are tuned during the scanning process by changing the distance, i.e., the vdWs force, between the STM tip and the single-carbon vacancy (see Figs. S19–S21 (online) for details). Since both the electronic states and topographic features contribute to the measured height, therefore we can only obtain the relative profile heights of the single-carbon vacancy under the same experimental condition for comparison. The single-carbon vacancy with different heights exhibits distinct tunnelling spectra, as shown in Fig. 3a–c and Fig. S22 (online). For the case that the measured height of the protrusion around the vacancy is smaller than 50 pm, the energy separation of the two spin splitting states is ~30 meV (Fig. 3a). The relative intensity of the spin-up (spin-down) peak is obviously larger than the spin-down (spin-up) peak when recorded at A (B) sublattice. Similar features are obtained in tens of the as-grown single-carbon vacancies in graphene by using different STM tips. Here we decrease the tip-graphene distance to about 0.3 nm and scan the studied vacancy for about 30 min (see Figs. S23 and S24 (online) for details), and then the height of the protrusion increases to above 70 pm. Then the energy 7
separation of the two peaks in the spectrum decreases to ~20 meV. Unexpectedly, the electronic states of the left peak (right peak) now are predominantly located on the B (A) sublattice (Fig. 3b), which are exactly opposite to the results obtained in the as-grown single-carbon vacancy. It indicates that the left peak (right peak) of the spectra in Fig. 3b arises from the spin-down (spin-up) state according to the site-specific spin polarization of the quasilocalized electrons. By further decreasing the tip-graphene distance to about 0.1 nm, it is possible to tune the height of the protrusion to above 140 pm under the original measuring conditions (Fig. 3c). In such a case, we only observe a pronounced peak in the spectrum, which is distinct from the previous reported Kondo peak [18]. Similar experimental results can be obtained after heating the sample up to 700 ℃ (the Curie temperature of Ni is 358 ℃) and then gradually cooled down to 4.2 K without external magnetic field, which can help us rule out the influence of remanence in Ni substrate [48] (see the Supplementary materials for more discussion). In Fig. 4a, we summarized the energy separations of the two spin-polarized peaks in the STS spectra as a function of the height of the studied single-carbon vacancy (for the case that there is only one peak, the energy separation is set as zero). The obtained three distinct spectra indicate that there are three different magnetic states of the single-carbon vacancy in graphene, depending on its out-of-plane deformations. To further understand our experimental results, we carried out DFT calculations on the magnetism of the single-carbon vacancy in graphene as a function of its out-of-plane deformations. Our calculations reveal three different magnetic states of the single-carbon vacancy, which are classified as ferromagnetic (FM), quenched antiferromagnetic (QAFM), and nonmagnetic (NM) phases, as shown in Fig. 4b and c. Fig. 4d–4f show the corresponding low-energy DOS of the three phases. Due to the large spin splitting of the V2 state, there usually exists a single electron occupying the V2 state that contributes the local magnetic moment of 1 B. Therefore, we can only concentrate on the direction and magnitude of the magnetic moment. For the FM phase, the single-carbon vacancy exhibits the local magnetic moments of about 1.6 B with 1 B from the localized electrons and about 0.6 B from the 8
quasilocalized electrons. The low energy DOS shows two peaks with the spin-up and spin-down states predominantly on the A and B sublattices respectively. This agrees quite well with our experimental results obtained in the as-grown vacancy (Figs. 2 and 3a). Theoretically, the splitting of the two spin-polarized states depends on the size of the graphene super cell. In our calculation, we used a finite size of the graphene super cell due to the limitation of the calculation ability. Therefore, the theoretical splitting is much larger than that observed in the experiment. By increasing the out-of-plane lattice deformation, the single-carbon vacancy will become the QAFM phase and its local magnetic moment will decrease to only about 0.5 B, which arises from the fact that the magnetic moments from the electrons and the electrons become antiparallel. Then, the spin splitting is smaller than that of the FM phase by using the same graphene super cell in the calculation. More importantly, the spin-up (spin-down) state, which is predominantly located on the A (B) sublattice, changes to the right (left) peak of the low-energy DOS, as shown in Fig. 4e. These features are well accordant with our experimental results. By further increasing the out-of-plane deformation of the single-carbon vacancy, the strong coupling between the localized σ electrons and quasilocalized electrons can completely remove the local magnetic moment of the single-carbon vacancy, resulting in the NM phase. Then, there is only one pronounced peak in the low-energy DOS (Fig. 4f), which is consistent well with our experimental result (Fig. 3c). Therefore, it is reasonable to conclude that the observed three distinct spectra of the single-carbon vacancy correspond to its three magnetic states. Our STM measurements, complemented by DFT calculations, show that the single-carbon vacancy in graphene can exhibit three different magnetic phases depending on the coupling between the localized σ electrons and quasilocalized electrons. This allows for a consistent interpretation of all current data about the magnetism of the single-carbon vacancy. Previously, distinct tunnelling spectra of single-carbon vacancies in graphene are reported [3,12,14,18]. According to our result, the distinct spectra may arise from the different magnetic phases. The single-carbon vacancies generated in the synthesis process of graphene by the CVD 9
method usually have small apparent heights. Therefore, they are mainly in the FM phase and we usually observe two pronounced spin-split peaks in the tunnelling spectra. However, the vacancies generated by irradiation of high-energy ions are predominantly in the NM phase because of the large apparent heights. As a consequence, only a single peak is observed in the spectra [12,14]. In Ref. [13], the average magnetic moment of the single-carbon vacancies generated by irradiation is measured to be about 0.1 B, which is much smaller than the expected value 1.6 B, indicating that most of the single-carbon vacancies generated by irradiation are in the NM state. In our experiment, we found that about 1/4 of the as-grown single-carbon vacancy can be tuned from the FM state to the QAFM state, and about 80% of them can be further tuned from the QAFM state to the NM state. However, we cannot directly change the defects from FM state to the NM state. Our experiments also demonstrated that both the QAFM and the NM states are quite stable at the temperature of 4.2 K in a vacuum. The defects at both QAFM and NM states cannot relax to the FM state during our experiment even we withdraw the STM tip for several hours: more than 2.5 hours for the QAFM state and more than 9 hours for the NM state. The defects at both QAFM and NM states also cannot be tuned to the FM state by using the STM tip (Fig. S20 online). The substrate may help to stabilize the out-of-plane deformation around the single-carbon vacancy.
4. Conclusion In summary, we demonstrated that the magnetism of the single-carbon vacancy is determined by interactions between the localized σ electrons and quasilocalized electrons. Via an STM tip, we successfully tuned the σ- interactions and realized three magnetic states of the single-carbon vacancy in graphene. Our theoretical calculations further revealed the nature of the three magnetic states. The realized tunable magnetism at atomic scale may have potential applications in graphene-based spintronics.
Conflict of interest 10
The authors declare that they have no conflict of interest.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974050, 11674029). L.H. also acknowledges support from “the Fundamental Research Funds for the Central Universities”, and “Chang Jiang Scholars Program”. S. G. acknowledges supports from MOST through the National Key R&D Program of China (2017YFA0303404 and 2016YFB0700700), the Science Challenge Project No. TZ2018004, and the NSFC through grant NSAF U-1530401 and No. 21403081. We acknowledge the allocated computer time at the supercomputer facility TH2-JK at Beijing Computational Science Research Center (CSRC).
Author contributions Yu Zhang synthesized the samples, performed the STM experiments, and analyzed the data. Fei Gao and Shiwu Gao performed the theoretical calculations. Lin He conceived and provided advice on the experiment, analysis, and the theoretical calculation. Lin He and Yu Zhang wrote the paper. All authors participated in the data discussion.
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Figure Legends
Fig. 1. (Color online) The electronic properties of the single-carbon vacancy in graphene. (a) STM topography of a single-carbon vacancy in the topmost graphene sheet (Vb: 200 mV, I: 200 pA). (b) STS spectrum recorded exactly on the nearest C of vacant site (A site, marked by the red dot in panel (a). The two peaks reflect the DOS with opposite spin polarizations. (c) Left panel: schematic diagram of the electronic structure at a single-carbon vacancy in graphene. The removal of a C atom creates three sp2σ dangling bonds and introduces a localized state Vσ, which further splits into highly localized Vσ1, Vσ2, and Vσ3 states due to the crystal field and Jahn– Teller distortion. Meanwhile, a quasilocalized state Vπ is also introduced in the band structure. Both the V2 and V states further split because of the electrostatic Coulomb repulsion U. Right panel: illustration of the spin-split states of V2 and V. The strength of U depends strongly on the spatial localization of the states. 15
Fig. 2. (Color online) The spatial distributions of spin-up and spin-down electrons in the vicinity of the single-carbon vacancy. (a) Schematic diagram of the spin-polarized STM measurements. The black dashed circle shows the position of the missing C atom, and the arrows reflect the spin directions. (b) The spin-polarized dI/dV spectra measured with tip polarization M↑ (M↓) on A (B) sublattice respectively. (c) The spin-polarized STS maps at the bias voltages of the spin-up and spin-down states respectively. Fig. 3. (Color online) Tunable atomic configurations and electronic properties of the single-carbon vacancy. (a–c) Up panel: schematic side view of the configurations around the vacancy, which can be tuned by the vdWs force between the STM tip and graphene. Middle panel: typical heights of the single-carbon vacancy (Vb: 500 mV, I: 150 pA). Bottom panel: the corresponding dI/dV spectra recorded at A and B sublattices of the single-carbon vacancy. The relative intensities of two localized peaks reflect the distributions of the DOS with opposite spin polarizations.
Fig. 4. (Color online) Theoretical calculations of the three magnetic states of the single-carbon vacancy. (a) The energy separations of the two spin-polarized DOS peaks in STS spectra as a function of the height of the studied vacancy in STM images. (b) Theoretical calculations of the localized magnetic moments of the single-carbon vacancy in graphene as a function of its out-of-plane deformation. The localized magnetic moments of the FM, QAFM and NM states are ~1.6 μB, ~0.5 μB, and ~0 μB, respectively. The blue dots indicate the intrinsic magnetic moments of the vacancy in graphene, and the red dots indicate the induced magnetic states by considering the interaction between the V state and STM tip. (c) Schematic diagram of the spin alignment of V and V moments in the three states. (d–f) The theoretical calculations of the localized DOS of the single-carbon vacancy in the FM, QAFM, and NM states respectively. The spin-up and spin-down electrons are indicated by blue and red lines, respectively. 16
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Yu Zhang is currently a Ph.D. candidate at the Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University. She received her M.S. degree at Beijing Normal University in 2016. Her research mainly focuses on the scanning tunnelling microscopy (STM) study of magnetism in graphene.
Shiwu Gao received his Ph.D. degree in Solid State Theory from the Institute of Physics, CAS in 1990. He is now a chair professor in Beijing Computational Science 20
Research Center. His main research interests are materials theory and computational physics with focus on the electronic excitations, surface dynamics, and nanoplasmonics.
Lin He received his Ph.D. degree in Physics from Peking University in 2009. He is now a professor in the Center for Advanced Quantum Studies, Department of Physics at Beijing Normal University. His research focuses on scanning tunnelling microscopy (STM) study of electronic properties and exotic quantum phases in graphene, including novel broken-symmetry states, superconductivity, magnetism, and topology.
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S2095-9273(19)30668-1 https://doi.org/10.1016/j.scib.2019.11.023 SCIB 888
To appear in:
Science Bulletin
Received Date: Revised Date: Accepted Date:
30 September 2019 30 October 2019 15 November 2019
Please cite this article as: Y. Zhang, F. Gao, S. Gao, L. He, Tunable magnetism of a single-carbon vacancy in graphene, Science Bulletin (2019), doi: https://doi.org/10.1016/j.scib.2019.11.023
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Tunable magnetism of a single-carbon vacancy in graphene Yu Zhanga,1, Fei Gaob,1, Shiwu Gaob*, and Lin Hea,c* aCenter
for Advanced Quantum Studies, Department of Physics, Beijing Normal
University, Beijing 100875, China bComputational cState
Science Research Center, ZPark II, Beijing 100193, China.
Key Laboratory of Functional Materials for Informatics, Shanghai Institute of
Mocrosystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 1These
*To
authors contributed equally to this work.
whom
correspondence
may
be
addressed
to
Shiwu
Gao
(e-mail:
[email protected]) and Lin He (e-mail: [email protected])
Abstract Creating a single-carbon vacancy introduces (quasi-)localized states for both and electrons in graphene. Theoretically, interactions between the localized electrons and quasilocalized electrons of a single-carbon vacancy in graphene are predicted to control its magnetism. However, experimentally confirming this prediction through manipulating the interactions remains an outstanding challenge. Here we report the manipulation of magnetism in the vicinity of an individual single-carbon vacancy in graphene by using a scanning tunnelling microscopy (STM) tip. Our spin-polarized STM measurements, complemented by density functional theory calculations, indicate that the interactions between the localized and quasilocalized electrons could split the electrons into two states with opposite spins even when they are well above the Fermi level. Via the STM tip, we successfully manipulate both the magnitude and direction of magnetic moment of the electrons with respect to that of the 1
electrons. Three different magnetic states of the single-carbon vacancy, exhibiting magnetic moments of about 1.6 B, 0.5 B, and 0 B respectively, are realized in our experiment.
Keywords: graphene, single-carbon vacancy, magnetic moment, tunable magnetism, scanning tunnelling microscopy.
Received: 30-Sep-2019 Revised: 30-Oct-2019 Accepted: 15-Nov-2019
1. Introduction An outstanding challenge in miniaturization of fabricating data storage devices is to control the magnetism at the atomic scale [1,2]. Very recently, the successful introduction of local magnetic moments in graphene by creating atomic vacancies [3] or adsorbing H atoms [4] shows the ability to achieve such a goal. Different from the H adatoms on graphene, which only introduce a local magnetic moment of electrons [4], creating a single-carbon vacancy introduces local magnetic moments of both the and electrons [5-18]. Theoretically, the interactions between the localized electrons and the quasilocalized electrons of the single-carbon vacancy are predicted to control its magnetic states, either exhibiting local magnetic moments or not [6,8,9,11,12,15,16]. Therefore, such a system provides a unique platform to control the magnetism at the atomic scale. In this work, we experimentally studied how the interactions between the localized electrons and the quasilocalized electrons control the magnetism of the single-carbon vacancy in graphene. Via a scanning tunnelling microscopy (STM) tip, we tuned the interactions between them and realized three different magnetic states of the single-carbon vacancies in graphene. Density functional theory (DFT) calculations revealed the nature of these magnetic states and quantum phase transitions between the three coupling regimes. 2
2. Experimental and computational methods 2.1 STM and scanning tunnelling spectroscopy (STS) measurements The STM system was an ultrahigh vacuum scanning probe microscope (USM-1300 and USM-1500) from UNISOKU. All STM and STS measurements were performed in the ultrahigh vacuum chamber (~10–11 Torr), at liquid-helium temperature (4.2 K) and the images were taken in a constant-current scanning mode. The nonmagnetic STM tips were obtained by chemical etching from a wire of Pt/Ir (80/20%) alloys, and the magnetic STM tips were obtained by electrochemically etching from a wire of Ni. Lateral dimensions observed in the STM images were calibrated using a standard graphene lattice, a Si (111)-(7×7) lattice, and an Ag (111) surface. The dI/dV measurements were taken with a standard lock-in technique by turning off the feedback circuit and using a 793-Hz 5mV A.C. modulation of the sample voltage.
2.2 Computational method Our first-principles calculations are performed within the framework of DFT using Vienna Ab initio Simulation Package (VASP) [19]. The projector augmented-wave (PAW) [20,21] pseudopotentials and the general gradient approximation (GGA) [22] in Perdew-Burke-Ernzerholf form [23] for the exchange-correlation energy are employed. The van der Waals density functional (vdW-DF) recently developed by Dion et al. [24] and parameterized by Klimes et al. [25] is also employed for comparison. A plane wave cutoff of 600 eV is used to expand the wave function. Spin polarization is invoked in all calculations. The geometrical structure and electronic properties of the monovacancy defect in graphene are calculated using the 8 × 8 supercells and the nonmagnetic STM tip is mimicked by a pyramid consisting of 14 Cu atoms. The supercells contain typically a vacuum layer ~ 40 Å along the z axis and the sampling of the Brillouin zone with a 3 × 3 × 1 k-point grid. All atoms except those in the top layer of the tip are allowed to relax until the forces on each atom are less than 0.05 eV/Å. 3
2.3 Synthesis of graphene multilayers on Ni foils A traditional ambient pressure chemical vapor deposition (APCVD) method was adopted to grow graphene multilayers on a Ni foil. The Ni foil was first heated from room temperature to 900 ℃ in 40 min under an argon (Ar) flow of 100 SCCM (SCCM stands for Standard Cubic Centimeters per Minute) and hydrogen (H2) flow of 100 SCCM, and the Ni foil was kept at 900℃ with the Ar and H2 flow for 20 min. In the next process, CH4 gas was introduced with the flow of 20 SCCM holding for 15 min. Then the sample was cooled down to room temperature and transferred into the ultrahigh vacuum condition for further characterizations.
3. Results and discussion 3.1 The electronic properties of the single-carbon vacancy in graphene. In our experiment, the single-carbon vacancies were generated in the synthesis process of graphene multilayer on Ni foil in a CVD method (see Methods and Figs. S1–S4 (online) for more details) [3,26-29]. Fig. 1a shows a representative atomic STM image of the single-carbon vacancy in the topmost graphene sheet with a characteristic Jahn-Teller distortion [3,8-11,30-32], which can be clearly recognized by the distinctive topographic fingerprint of a triangular
3 × 3 R30° interference
pattern in the STM image that induced by intervalley scattering of the atomic defect (see Figs. S5, S6 online). The STS spectrum recorded on the nearest C of vacant site exhibits two pronounced peaks (Fig. 1b. More data are given in Figs. S7 and S8 (online)), attributing to two spin-polarized states of the quasilocalized electrons V induced by the single-carbon vacancy [3,5] (by combining the Raman measurements and DFT calculations shown in Figs. S9–S14 (online), we can definitely exclude any possible interaction between the single-carbon vacancy and Ni substrate [33-35] or Ni adatoms [36-38] as the origin, and verify that all the experimental phenomena are 4
derived from the intrinsic spin-polarized states of the single-carbon vacancy). The slight energy shift of the two spin-polarized states is induced by the different charge transfer between the substrate and the topmost graphene sheet [39]. Fig. 1c shows a schematic diagram of electronic structure for a single-carbon vacancy in graphene. The crystal field and Jahn-Teller distortion split the localized electrons of the single-carbon vacancy into highly localized V1, V2, and V3 states [3,8-11,30-32]. Both the V2 and V states are half occupied because of the electrostatic Coulomb repulsion U, i.e., when an electron occupies the state, a second electron with opposite spin must overcome an extra energy U. The strength of U, which depends on the spatial localization of the states, determines the spin splitting. The spatial extension of the V state is much larger than that of the V2 state. Therefore, the V2 state has a much larger spin splitting than that of the V state [5,7,30-32] (Fig. 1c). There is usually a single electron occupying the V2 state due to the large spin splitting (the energies of the splitting V2 state are always more than 1 eV away from the Fermi energy, which are beyond our STS detection range). However, the two V states could be double occupied or unoccupied because of the existence of a slight charge transfer from the substrate. Then the spin splitting of the V state should vanish and only one sharp peak is expected to be observed [4]. However, in our experiment, two peaks are still observed for the single-carbon vacancies even when they are well above the Fermi level [3], as shown in Fig. 1b. Our spin-polarized STM measurements, as shown subsequently, demonstrate that the two peaks are the two spin-polarized V states, and we will show that the magnetism of the single-carbon vacancy behaves quite different from that of the adsorbing H atom in graphene.
3.2 The spatial distributions of spin-up and spin-down electrons around the single-carbon vacancy The spin-polarized STM measurements, which can directly reflect spatial distributions of spin-up and spin-down electrons [40,41], provide us an unprecedented insight to identify the magnetism of the single-carbon vacancy. In our experiment, 5
we used electrochemically etched Ni tip (Figs. S15–S17 online) as a spin-polarized STM tip, and its magnetic polarization is always along the tip due to the weak magnetocrystalline anisotropy of Ni and relatively large shape anisotropy of the STM tip [27,42,43]. Before the STM measurements, a magnetic field of 𝐵 = 3.0 T (𝐵 = ―3.0 T) perpendicular to the surface of the sample was applied on and then removed gradually to obtain an up-polarized M↑ (down-polarized M↓) STM tip. As schematically shown in Fig. 2a, we can carry out atomic-resolved STS measurements around the single-carbon vacancy by using spin-polarized STM tip (here the single-carbon vacancy is assumed on the B sublattice). Fig. 2b summarizes four representative spin-resolved STS spectra measured around the single-carbon vacancy (more STS spectra are shown in Figs. S8 and S18 (online)). Because of the spin conservation during the elastic electron tunnelling processes, the differences among
these
STS
spectra
directly
reflect
distributions
of
spin-polarized
density-of-states (DOS) on the A and B sublattices. Our experimental result indicates that the spin-up (spin-down) electrons of the V state are mainly located on the A (B) sublattice around the single-carbon vacancy. However, due to the incomplete polarization of the spin-polarized STM tip and spatial extension of the electron wave functions, there always exists a slight signal on the STS spectra when the polarized orientation of the tip and sample is antiparallel. Such a result is further confirmed by our STS maps recorded at the energies of the two spin-polarized states (Fig. 2c), revealing the site-specific spin polarization around the single-carbon vacancy, as predicted theoretically [5-18]. The above results explicitly demonstrate that the observed two peaks in the spectra are the two spin-polarized V states. We attribute the spin splitting of the V state even when the two spin-polarized states are well above the Fermi level to the interaction between the V state and the V2 state. The existence of local magnetic moment from the localized electrons is the main difference between the magnetism introduced by the atomic vacancies [3] and by the adsorbing H atoms [4] on graphene. If the graphene is not the exact planar configuration around the single-carbon vacancy, the orthogonality between the and states is broken [6,8,9,11,12,15,16]. Then the coupling with the spin-polarized V2 6
state may stabilize the spin splitting of the V state even when it is double occupied or unoccupied. Therefore, the two states of the V electrons induced by the atomic vacancies [3] and by the adsorbing H atoms [4] on graphene show quite different behaviors.
3.3. Tunable atomic configurations and electronic properties of the single-carbon vacancy The interaction between the localized and quasilocalized states determines the magnetism of the single-carbon vacancy in graphene [6,8,9,11,12,15,16]. Previously, it was demonstrated that the sufficient reduction of tip-graphene distance can generate an out-of-plane displacement on graphene through a finite van de Waals (vdWs) force [44-47]. Here we show that it is possible to generate out-of-plane deformation around the single-carbon vacancy and, consequently, tune interactions between the localized and quasilocalized states by using the STM tip under long-time scanning processes. Fig. 3 shows representative results measured on a single-carbon vacancy with three different heights, which are tuned during the scanning process by changing the distance, i.e., the vdWs force, between the STM tip and the single-carbon vacancy (see Figs. S19–S21 (online) for details). Since both the electronic states and topographic features contribute to the measured height, therefore we can only obtain the relative profile heights of the single-carbon vacancy under the same experimental condition for comparison. The single-carbon vacancy with different heights exhibits distinct tunnelling spectra, as shown in Fig. 3a–c and Fig. S22 (online). For the case that the measured height of the protrusion around the vacancy is smaller than 50 pm, the energy separation of the two spin splitting states is ~30 meV (Fig. 3a). The relative intensity of the spin-up (spin-down) peak is obviously larger than the spin-down (spin-up) peak when recorded at A (B) sublattice. Similar features are obtained in tens of the as-grown single-carbon vacancies in graphene by using different STM tips. Here we decrease the tip-graphene distance to about 0.3 nm and scan the studied vacancy for about 30 min (see Figs. S23 and S24 (online) for details), and then the height of the protrusion increases to above 70 pm. Then the energy 7
separation of the two peaks in the spectrum decreases to ~20 meV. Unexpectedly, the electronic states of the left peak (right peak) now are predominantly located on the B (A) sublattice (Fig. 3b), which are exactly opposite to the results obtained in the as-grown single-carbon vacancy. It indicates that the left peak (right peak) of the spectra in Fig. 3b arises from the spin-down (spin-up) state according to the site-specific spin polarization of the quasilocalized electrons. By further decreasing the tip-graphene distance to about 0.1 nm, it is possible to tune the height of the protrusion to above 140 pm under the original measuring conditions (Fig. 3c). In such a case, we only observe a pronounced peak in the spectrum, which is distinct from the previous reported Kondo peak [18]. Similar experimental results can be obtained after heating the sample up to 700 ℃ (the Curie temperature of Ni is 358 ℃) and then gradually cooled down to 4.2 K without external magnetic field, which can help us rule out the influence of remanence in Ni substrate [48] (see the Supplementary materials for more discussion). In Fig. 4a, we summarized the energy separations of the two spin-polarized peaks in the STS spectra as a function of the height of the studied single-carbon vacancy (for the case that there is only one peak, the energy separation is set as zero). The obtained three distinct spectra indicate that there are three different magnetic states of the single-carbon vacancy in graphene, depending on its out-of-plane deformations. To further understand our experimental results, we carried out DFT calculations on the magnetism of the single-carbon vacancy in graphene as a function of its out-of-plane deformations. Our calculations reveal three different magnetic states of the single-carbon vacancy, which are classified as ferromagnetic (FM), quenched antiferromagnetic (QAFM), and nonmagnetic (NM) phases, as shown in Fig. 4b and c. Fig. 4d–4f show the corresponding low-energy DOS of the three phases. Due to the large spin splitting of the V2 state, there usually exists a single electron occupying the V2 state that contributes the local magnetic moment of 1 B. Therefore, we can only concentrate on the direction and magnitude of the magnetic moment. For the FM phase, the single-carbon vacancy exhibits the local magnetic moments of about 1.6 B with 1 B from the localized electrons and about 0.6 B from the 8
quasilocalized electrons. The low energy DOS shows two peaks with the spin-up and spin-down states predominantly on the A and B sublattices respectively. This agrees quite well with our experimental results obtained in the as-grown vacancy (Figs. 2 and 3a). Theoretically, the splitting of the two spin-polarized states depends on the size of the graphene super cell. In our calculation, we used a finite size of the graphene super cell due to the limitation of the calculation ability. Therefore, the theoretical splitting is much larger than that observed in the experiment. By increasing the out-of-plane lattice deformation, the single-carbon vacancy will become the QAFM phase and its local magnetic moment will decrease to only about 0.5 B, which arises from the fact that the magnetic moments from the electrons and the electrons become antiparallel. Then, the spin splitting is smaller than that of the FM phase by using the same graphene super cell in the calculation. More importantly, the spin-up (spin-down) state, which is predominantly located on the A (B) sublattice, changes to the right (left) peak of the low-energy DOS, as shown in Fig. 4e. These features are well accordant with our experimental results. By further increasing the out-of-plane deformation of the single-carbon vacancy, the strong coupling between the localized σ electrons and quasilocalized electrons can completely remove the local magnetic moment of the single-carbon vacancy, resulting in the NM phase. Then, there is only one pronounced peak in the low-energy DOS (Fig. 4f), which is consistent well with our experimental result (Fig. 3c). Therefore, it is reasonable to conclude that the observed three distinct spectra of the single-carbon vacancy correspond to its three magnetic states. Our STM measurements, complemented by DFT calculations, show that the single-carbon vacancy in graphene can exhibit three different magnetic phases depending on the coupling between the localized σ electrons and quasilocalized electrons. This allows for a consistent interpretation of all current data about the magnetism of the single-carbon vacancy. Previously, distinct tunnelling spectra of single-carbon vacancies in graphene are reported [3,12,14,18]. According to our result, the distinct spectra may arise from the different magnetic phases. The single-carbon vacancies generated in the synthesis process of graphene by the CVD 9
method usually have small apparent heights. Therefore, they are mainly in the FM phase and we usually observe two pronounced spin-split peaks in the tunnelling spectra. However, the vacancies generated by irradiation of high-energy ions are predominantly in the NM phase because of the large apparent heights. As a consequence, only a single peak is observed in the spectra [12,14]. In Ref. [13], the average magnetic moment of the single-carbon vacancies generated by irradiation is measured to be about 0.1 B, which is much smaller than the expected value 1.6 B, indicating that most of the single-carbon vacancies generated by irradiation are in the NM state. In our experiment, we found that about 1/4 of the as-grown single-carbon vacancy can be tuned from the FM state to the QAFM state, and about 80% of them can be further tuned from the QAFM state to the NM state. However, we cannot directly change the defects from FM state to the NM state. Our experiments also demonstrated that both the QAFM and the NM states are quite stable at the temperature of 4.2 K in a vacuum. The defects at both QAFM and NM states cannot relax to the FM state during our experiment even we withdraw the STM tip for several hours: more than 2.5 hours for the QAFM state and more than 9 hours for the NM state. The defects at both QAFM and NM states also cannot be tuned to the FM state by using the STM tip (Fig. S20 online). The substrate may help to stabilize the out-of-plane deformation around the single-carbon vacancy.
4. Conclusion In summary, we demonstrated that the magnetism of the single-carbon vacancy is determined by interactions between the localized σ electrons and quasilocalized electrons. Via an STM tip, we successfully tuned the σ- interactions and realized three magnetic states of the single-carbon vacancy in graphene. Our theoretical calculations further revealed the nature of the three magnetic states. The realized tunable magnetism at atomic scale may have potential applications in graphene-based spintronics.
Conflict of interest 10
The authors declare that they have no conflict of interest.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974050, 11674029). L.H. also acknowledges support from “the Fundamental Research Funds for the Central Universities”, and “Chang Jiang Scholars Program”. S. G. acknowledges supports from MOST through the National Key R&D Program of China (2017YFA0303404 and 2016YFB0700700), the Science Challenge Project No. TZ2018004, and the NSFC through grant NSAF U-1530401 and No. 21403081. We acknowledge the allocated computer time at the supercomputer facility TH2-JK at Beijing Computational Science Research Center (CSRC).
Author contributions Yu Zhang synthesized the samples, performed the STM experiments, and analyzed the data. Fei Gao and Shiwu Gao performed the theoretical calculations. Lin He conceived and provided advice on the experiment, analysis, and the theoretical calculation. Lin He and Yu Zhang wrote the paper. All authors participated in the data discussion.
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Figure Legends
Fig. 1. (Color online) The electronic properties of the single-carbon vacancy in graphene. (a) STM topography of a single-carbon vacancy in the topmost graphene sheet (Vb: 200 mV, I: 200 pA). (b) STS spectrum recorded exactly on the nearest C of vacant site (A site, marked by the red dot in panel (a). The two peaks reflect the DOS with opposite spin polarizations. (c) Left panel: schematic diagram of the electronic structure at a single-carbon vacancy in graphene. The removal of a C atom creates three sp2σ dangling bonds and introduces a localized state Vσ, which further splits into highly localized Vσ1, Vσ2, and Vσ3 states due to the crystal field and Jahn– Teller distortion. Meanwhile, a quasilocalized state Vπ is also introduced in the band structure. Both the V2 and V states further split because of the electrostatic Coulomb repulsion U. Right panel: illustration of the spin-split states of V2 and V. The strength of U depends strongly on the spatial localization of the states. 15
Fig. 2. (Color online) The spatial distributions of spin-up and spin-down electrons in the vicinity of the single-carbon vacancy. (a) Schematic diagram of the spin-polarized STM measurements. The black dashed circle shows the position of the missing C atom, and the arrows reflect the spin directions. (b) The spin-polarized dI/dV spectra measured with tip polarization M↑ (M↓) on A (B) sublattice respectively. (c) The spin-polarized STS maps at the bias voltages of the spin-up and spin-down states respectively. Fig. 3. (Color online) Tunable atomic configurations and electronic properties of the single-carbon vacancy. (a–c) Up panel: schematic side view of the configurations around the vacancy, which can be tuned by the vdWs force between the STM tip and graphene. Middle panel: typical heights of the single-carbon vacancy (Vb: 500 mV, I: 150 pA). Bottom panel: the corresponding dI/dV spectra recorded at A and B sublattices of the single-carbon vacancy. The relative intensities of two localized peaks reflect the distributions of the DOS with opposite spin polarizations.
Fig. 4. (Color online) Theoretical calculations of the three magnetic states of the single-carbon vacancy. (a) The energy separations of the two spin-polarized DOS peaks in STS spectra as a function of the height of the studied vacancy in STM images. (b) Theoretical calculations of the localized magnetic moments of the single-carbon vacancy in graphene as a function of its out-of-plane deformation. The localized magnetic moments of the FM, QAFM and NM states are ~1.6 μB, ~0.5 μB, and ~0 μB, respectively. The blue dots indicate the intrinsic magnetic moments of the vacancy in graphene, and the red dots indicate the induced magnetic states by considering the interaction between the V state and STM tip. (c) Schematic diagram of the spin alignment of V and V moments in the three states. (d–f) The theoretical calculations of the localized DOS of the single-carbon vacancy in the FM, QAFM, and NM states respectively. The spin-up and spin-down electrons are indicated by blue and red lines, respectively. 16
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Yu Zhang is currently a Ph.D. candidate at the Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University. She received her M.S. degree at Beijing Normal University in 2016. Her research mainly focuses on the scanning tunnelling microscopy (STM) study of magnetism in graphene.
Shiwu Gao received his Ph.D. degree in Solid State Theory from the Institute of Physics, CAS in 1990. He is now a chair professor in Beijing Computational Science 20
Research Center. His main research interests are materials theory and computational physics with focus on the electronic excitations, surface dynamics, and nanoplasmonics.
Lin He received his Ph.D. degree in Physics from Peking University in 2009. He is now a professor in the Center for Advanced Quantum Studies, Department of Physics at Beijing Normal University. His research focuses on scanning tunnelling microscopy (STM) study of electronic properties and exotic quantum phases in graphene, including novel broken-symmetry states, superconductivity, magnetism, and topology.
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