Engineering Magnetic Anisotropy of Rhenium Atom in Nitrogenized Divacancy of Graphene

The effects of charging on the magnetic anisotropy energy (MAE) of rhenium atom in nitrogenized-divacancy graphene (Re@NDV) are investigated using density functional theory (DFT) calculations. High-stability and large MAE of 71.2 meV are found in Re@NDV. The more exciting finding is that the magnitude of MAE of a system can be tuned by charge injection. Moreover, the easy magnetization direction of a system may also be controlled by charge injection. The controllable MAE of a system is attributed to the critical variation in dz2 and dyz of Re under charge injection. Our results show that Re@NDV is very promising in high-performance magnetic storage and spintronics devices.


Introduction
A fundamental obstacle to the downscaling of spintronics devices is the spin-reorientation transition (SRT), induced by thermal fluctuations at room temperature. To prevent the occurrence of SRT, magnetic materials should possess large magnetic anisotropy energy (MAE) [1][2][3]. Therefore, the search for magnetic materials possessing large MAE is of both fundamental interest and technological merit for future spintronics device applications. In general, MAE originates in large spin-orbit coupling (SOC) interactions. Recently, the two-dimensional materials containing 5d transition-metal (TM) atoms have been paid more attention in magnetic storage areas, due to strong SOC in 5d TM atoms [4][5][6][7][8][9][10][11][12].
To stabilize a magnetic bit against thermal agitation, a material is required to possess large MAE. Meanwhile, to reduce energy consumption, a material is desired to have low MAE in the process of writing information. To solve this confliction, the MAE of magnetic materials should be manipulated. Previous studies have suggested that the MAE of magnetic materials can be controlled by an electric field [13][14][15][16][17], surface charging [11,[18][19][20], and biaxial strain [8,15,[21][22][23][24][25]. Experimental studies demonstrated that the electric field can manipulate magnetization orientation of a ferromagnetic semiconductor [26]. First principles calculations predicted that MAE could be tuned in an Fe(001) monolayer by an applied electric field [27]. A recent study of Fe-Pt multilayers suggested that the magnitude of MAE and the magnetization direction can be controlled simultaneously by surface charging [18].
Although there are extensive investigations on the modulation of MAE of magnetic materials, few stable materials that have large MAE and are easily affected by ambient conditions have been found so far. Recent studies have indicated that graphene-based materials can be easily tuned by external conditions [7,28,29]. To firm the TM atom and reduce the probability of forming cluster [30,31], one may introduce defects, such as single vacancies and nitrogenized divacancies, into graphene [12,[32][33][34]. In this work, we investigate the stability, electronic and magnetic properties of rhenium atom in nitrogenized Nanomaterials 2023, 13, 829 2 of 8 divacancy of graphene (Re@NDV). We found that Re@NDV is highly stable and possesses large MAE of 71.2 meV. Moreover, the MAE of Re@NDV can be manipulated by charge injection. The physical mechanism of tunable MAE is discussed. The charge injection not only changes the intensity of Re@NDV MAE, but it also changes the direction of the easily magnetized axis. The control of the easily magnetized axis is beneficial to information storage and erasure. We hope that our computational results can help future experimental scientists synthesize two-dimensional Re@NDV materials. Additionally, we also consider some new materials as candidates for spintronic devices [35][36][37][38][39].

Computational Methods
The structural and electric properties were calculated using the density functional theory (DFT) in the Vienna ab initio simulation package (VASP) [40,41], the VASP is a simulation software package developed by Hafner's group at the University of Vienna. We used VASP version 5.5.4. The generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE) was used [42]. The interactions between electrons and nuclei were described by the projector augmented wave (PAW) method [43]. The kinetic energy cutoff of the plane wave is 500 eV. A 3 × 3 × 1 k-point mesh was adopted to relax the supercell. Geometric structural relaxations were performed until residual force per atom was smaller than 0.01 eV/Å. A 6 × 6 supercell was chosen along the x and y directions of graphene layer. The vacuum region of 15 Å perpendicular to the NDV of Re@NDV was built.
The MAE value was calculated by a noncollinear mode [44]. The atomic positions were fully relaxed until the total energy was converged to smaller than 10 −7 eV. MAE is defined as MAE = E z − E x/y , where E z and E x/y are the total energies for the z axis and x/y axis magnetizations, respectively. The positive and negative MAEs indicate the easy axis, parallel and perpendicular to the graphene plane, respectively.

Structure and Stability of Re@NDV
We first investigated the optimized structure of Re@NDV, as displayed in Figure 1a,b. The optimized stable structure of Re@NDV involved the Re atom located on the top site of NDV. The distance between Re and NDV was 0.303 Å, which is much lower than that of Re@Gr (1.686 Å). To examine the stability of the Re atom at the nitrogenized divacancy, we estimated the binding energy, which is expressed as: where E[Re@NDV], E[Re] and E[NDV] represent the total energies of Re@NDV, the Re atom and NDV, respectively. The large binding energy of 6.94 eV (see Table 1) and the short distance between Re and N atoms (0.30 Å) indicate that the Re atom can be strongly stable on the NDV surface.  To illuminate the strong interaction between Re and NDV, Figure 2a,b present the charge density difference for Re@NDV. One can see that electrons deplete from the Re atom and accumulate in regions between the Re-N bonds. This indicates that there is a covalent interaction between Re and N atoms, resulting in strong binding between Re and NDV. The Bader charge of Re atom amounted to 1.36e (see Table 1), suggesting that the electron transfers from Re to N atoms, which is consistent with the results of charge density difference.  To illuminate the strong interaction between Re and NDV, Figure 2a,b present the charge density difference for Re@NDV. One can see that electrons deplete from the Re atom and accumulate in regions between the Re-N bonds. This indicates that there is a covalent interaction between Re and N atoms, resulting in strong binding between Re and NDV. The Bader charge of Re atom amounted to 1.36e (see Table 1), suggesting that the electron transfers from Re to N atoms, which is consistent with the results of charge density difference. To illuminate the strong interaction between Re and NDV, Figure 2a,b present the charge density difference for Re@NDV. One can see that electrons deplete from the Re atom and accumulate in regions between the Re-N bonds. This indicates that there is a covalent interaction between Re and N atoms, resulting in strong binding between Re and NDV. The Bader charge of Re atom amounted to 1.36e (see Table 1), suggesting that the electron transfers from Re to N atoms, which is consistent with the results of charge density difference.  Charge density difference isosurfaces of Re@NDV under neutral and adding 0.2e/unit cell, respectively.
(a,c) Top view; (b,d) side view. The yellow color represents charge accumulation, while the cyan color represents the charge depletion zone.

Magnetic Properties of Re@NDV
We now discuss the magnetic properties of Re@NDV. As shown in Table 1, Re@NDV has a large spin magnetic moment of 3.02µ B . Figure 1c,d display the spin density of Re@NDV. It can be seen that the spin density of Re@NDV mostly comes from the Re atom. This suggests that the Re atom provides a major magnetic moment of Re@NDV. Furthermore, adsorption of the Re atom to NDV induces strong magnetocrystalline anisotropy with MAE values of 71.20 meV and an easy axis along the y axis. This value is far greater than that of Re atom adsorption on divacancy-defect graphene (DV) (about 2.67 meV), which is derived from the increase in the magnetic moment of the Re atom in Re@NDV. Re@NDV structure with high stability and large MAE has potential applications in information storage.

Charge Manipulation of MAE in Re@NDV
We next study the surface charging effect on the MAE of a system. The magnetic moments and MAE of a system with respect to charging are shown in Figure 3a,b, respectively. At zero charge, the magnetic moment is 3.012µ B and MAE reaches its maximum value (~71.2 meV with an in-plane axis of magnetization). The magnetic moment and MAE remarkably reduce by adding electrons. Bader analysis shows that the electron charge of Re is in the range of 5.74~6.02e, which is 5.64e in the neutral form. This indicates only a small part of the injected electron charge transfers to the Re atom, and more electrons transfer to C atoms than neutral atoms, which may be visualized from the charge density difference under −0.2e per unit cell (see Figure 2c,d). The addition of electrons to the Re atom led to more pairing for spin-down electrons of d z 2 orbitals, and then the magnetic moments of Re decrease. Removing the electrons from a system makes the magnetic moment of Re increase but the MAE reduce, accompanying the sign change. Bader analysis suggests that the electrons of Re are about 5.21e~5.55e, which decreases the spin-down electron of the d yz pair and enhances the magnetic moment of Re. As mentioned above, the MAE of a system strongly depends on the ∆l value. Figure 3c gives the ∆l value with respect to charging, and one can see that the injecting charges led to a ∆l decrease, except for −0.2e per unit cell. On the whole, small ∆l may result in small MAE, which indicates that the Bruno relationship is still valid [45].

Magnetic Properties of Re@NDV
We now discuss the magnetic properties of Re@NDV. As shown in Table 1, Re@NDV has a large spin magnetic moment of 3.02μB. Figure 1c,d display the spin density of Re@NDV. It can be seen that the spin density of Re@NDV mostly comes from the Re atom. This suggests that the Re atom provides a major magnetic moment of Re@NDV. Furthermore, adsorption of the Re atom to NDV induces strong magnetocrystalline anisotropy with MAE values of 71.20 meV and an easy axis along the y axis. This value is far greater than that of Re atom adsorption on divacancy-defect graphene (DV) (about 2.67 meV), which is derived from the increase in the magnetic moment of the Re atom in Re@NDV. Re@NDV structure with high stability and large MAE has potential applications in information storage.

Charge Manipulation of MAE in Re@NDV
We next study the surface charging effect on the MAE of a system. The magnetic moments and MAE of a system with respect to charging are shown in Figure 3a,b, respectively. At zero charge, the magnetic moment is 3.012μB and MAE reaches its maximum value (~71.2 meV with an in-plane axis of magnetization). The magnetic moment and MAE remarkably reduce by adding electrons. Bader analysis shows that the electron charge of Re is in the range of 5.74~6.02e, which is 5.64e in the neutral form. This indicates only a small part of the injected electron charge transfers to the Re atom, and more electrons transfer to C atoms than neutral atoms, which may be visualized from the charge density difference under −0.2e per unit cell (see Figure 2c,d). The addition of electrons to the Re atom led to more pairing for spin-down electrons of dz 2 orbitals, and then the magnetic moments of Re decrease. Removing the electrons from a system makes the magnetic moment of Re increase but the MAE reduce, accompanying the sign change. Bader analysis suggests that the electrons of Re are about 5.21e~5.55e, which decreases the spindown electron of the dyz pair and enhances the magnetic moment of Re. As mentioned above, the MAE of a system strongly depends on the Δl value. Figure 3c gives the Δl value with respect to charging, and one can see that the injecting charges led to a Δl decrease, except for −0.2e per unit cell. On the whole, small Δl may result in small MAE, which indicates that the Bruno relationship is still valid [45].   To illuminate the origin of manipulating MAE by injecting charge, Figure 4 plots the projected density of states (PDOS) of Re-5d orbitals with charging of −0.15e and 0.2e per unit cell, respectively. Based on the second-order perturbation formula [1,40], the MAE value can be expresses as where ξ is the coefficient of SOC, and µα and o β are the energy levels of the unoccupied spin α and occupied spin β state, respectively. From the denominator of Equation (2), it can be seen that the most dominant contribution to MAE comes from the orbitals around the Fermi level. As displayed in Figure 4, the main contribution to MAE is the coupling between spin-down occupied d yz and spin-down unoccupied d x occupation result in a change in easy magnetization direction and a reduction in the MAE of a system when removing electrons. Re@NDV is a good candidate for a magnetic storage device because it has large MAE and can be regulated by charge injection. Large MAE can ensure long-term stable storage of stored data, while small MAE can reduce energy consumption for writing information. In the future, it can be used as a storage medium for high-performance mobile devices.

Conclusions
We investigated the stability, magnetic properties and modification of Re@NDV using an applied external electric field and charging using DFT calculations. It was found that Re@NDV possesses high stability and large MAE. External electric fields do not influence the MAE much, while charge injection can bring dramatic changes to the magnitude of MAE and easy magnetization direction. The orbital-resolved PDOS demonstrates that there is critical variation in d z 2 and d yz of Re under an external electric field and charge injection, which is responsible for the change in MAE. The high-stability, large MAE and controllable MAE of Re@NDV means it has potential applications in high-performance magnetic storage and spintronics devices. With the continuous miniaturization of spintronic devices, it is crucial to improve magnetic storage density. In the future, we will explore two-dimensional magnetic materials with larger MAE to meet the needs of people's practical applications and to regulate MAE through various methods, such as strain, adding an electric field, etc.  Data Availability Statement: All data is contained within the manuscript.
Acknowledgments: Thank you very much for Ge's help.

Conflicts of Interest:
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.