Manipulating the magnetic moment in phosphorene by lanthanide atom doping: a first-principle study

Abstract

The structure and magnetism of Ln-doped phosphorene (Ln = La, Ce, Pr, Nd, Pm, Eu and Gd) have been investigated using the GGA + U method. It was found that all the single lanthanide atoms can bond strongly to the phosphorene and the Ln-doped phosphorene shows high and tunable magnetism. The magnetic moment in the range from 1 μ_B to 7 μ_B in Ln-doped phosphorene was proportional to the number of spin-parallel 4f electrons in the Ln atoms and achieves the maximum of 7 μ_B for the Eu- and Gd-doped cases, over all the magnetic moments of the known main-group atom and transition metal absorbed or doped phosphorene. Spin density and Bader charge analyses show that the magnetic moments of the Ln-doped systems mainly originate from the 4f electrons of the Ln atoms. Both the band structure and density of states indicate that most of the Ln-doped cases still maintain their semiconductor behavior with band gap values (about 0.90 eV) close to that found for the pristine phosphorene, except the Pm-doped case with the smallest band gap of 0.77 eV. Interestingly, in the Eu-doped case, the Eu atom induces hole doping, which produces a band crossing the Fermi level. The present study suggests that Ln-doped phosphorene can be used as a potential next-generation dilute magnetic semiconductor.

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1. Introduction

Recently, the study of semiconductor materials has attracted increasing attention due to their importance in both fundamental areas and their potential applications in electronics. With the need for different devices ranging from high-performance servers to thin-film display backplanes, two-dimension (2D) layered structure materials have garnered a great deal of interest due to their intriguing physical, chemical and mechanical characters, which are not found in their corresponding bulk materials.^1–3 Among them, graphene has become a very important material due to its high carrier mobility,^4,5 high transparency,⁶ extraordinary electrical and mechanical properties.^7–9 Meanwhile, an increasing number of other 2D materials have been synthesized and characterized, including the monolayers of MoS₂,^10–12 WS₂,¹³ BN,¹⁴ g-N₃C₄,¹⁵ g-C₃N₄ ^16,17 and silicone.¹⁸ Very recently, few-layered phosphorus (garnered phosphorene), a promising 2D semiconductor, was successfully prepared by mechanical exfoliation^19,20 and plasma-assisted fabrication processes.²¹ Different from most of the flat two-dimensional materials, the phosphorene has a puckered hexagonal structure that displays unique electronic and physical properties. For example, the phosphorene has a high carrier mobility (up to 1000 cm² V⁻¹ s⁻¹), large optical conductivity and strong anisotropy along the zig-zag and arm-chair directions.^22–24 Particularly, different from the semi-metallic graphene, the phosphorene is an intrinsic p-type semiconductor with a direct band gap, which is strongly thickness-dependent (∼2 eV for the monolayer).²⁵ It has been reported that the band structure of phosphorene presents highly anisotropic effective masses and electronic properties, which can be transferred from the direct semiconductor to indirect semiconductor by strain.^26,27 Because of these fascinating properties, phosphorene could be potentially used in photodetectors,²⁸ sodium-ion batteries,²⁹ lithium-ion batteries,^30,31 gas sensors,^32,33 transistors^34,35 and p–n diodes.³⁶

In order to controllably modify the structure and property of phosphorene, the adsorption or doping of main group metals,^37,38 transition metals^39–43 and non-metal atoms^38,44,45 as well as clustering⁴⁶ on phosphorene have been extensively explored. Hong's group⁴⁷ found that among the phosphorene with adsorbed main group metals (including Li, Na, Mg and Al) and transition metals (including Cr, Fe, Co, Ni, Mo, Pd, Pt and Au), the Cr-adsorbed phosphorene exhibited the highest magnetic moment (4.89 μ_B). Duan⁴⁰ reported that the 3d transition-metals (TMs) (from Sc to Zn) adsorbed on phosphorene sheets exhibited controllable magnetic properties, which can be controlled by tuning the interaction of the transition metals with phosphorene. Seixas et al.⁴² predicted that the phosphorene monolayer doped with cobalt may be a two-dimensional dilute magnetic semiconductor. Their study showed that the exchange interaction and magnetic order could be engineered and the potential gate may even induce a ferromagnetic-to-anti-ferromagnetic phase transition. Khan et al.⁴⁴ investigated the magnetic states in the Si-, S- and Cl-doped systems and non-spin polarized states in the Al-doped system.

Although the TM-doped or adsorbed phosphorene displays a relatively high magnetic moment, which mainly originates from the d-orbitals of the doping atoms, practical applications of the TM-doped phosphorene are still limited because of the possible quenching of the d-orbital momentums. Considering that the magnetic moment of an Ln atom depends on the 4f-shell configuration and the 4f-shell has high degeneration with high magnetism, which ensures that the f-orbital momentums can be not quenched, Ln atom doping could prove a promising approach. Ln-doped graphene systems were indeed studied and predicted to be magneto-electric materials for voltage-controlled spintronics⁴⁸ and orbital electronic devices.⁴⁹ Scanning tunneling microscopy (STM) images showed that Gd and Eu grew epitaxially on graphene, which conformed the results predicted by first principle calculations.⁵⁰ Doping Ln atoms in phosphorene may also be achieved in the laboratory and act as potential electronic applications. Therefore, the structure and magnetic properties of Ln-doped phosphorene and their potential applications deserve to be studied further.

In the present paper, a theoretical study was systematically carried out on the structures and magnetic properties of Ln-doped phosphorene (Ln = La, Ce, Pr, Nd, Pm, Eu and Gd) through first-principles calculations. It was found that all the lanthanide atoms strongly bond to the phosphorene and that most of the Ln-doped phosphorene still preserve their semiconductor behavior, showing high magnetic moments and tunable magnetism ranging from 1.0 μ_B to 7.0 μ_B. Especially for the Eu- and Gd-doping cases, the magnetic moment achieves 7.0 μ_B, which was higher than all of the known magnetic moments of the main-group and transition metal-doped systems. The present study is expected to enhance the understanding of the electronic and magnetic properties of Ln-doped phosphorene and facilitate their practical utilization as dilute magnetic semiconductors in the future.

2. Method

To investigate the electronic structure and related properties of Ln-phosphorene, spin-polarized first-principles calculations were performed based on density functional theory (DFT) with the generalized gradient approximation (GGA) in the form of Perdew–Burke–Ernzerhof (PBE) in the Vienna ab initio simulation package (VASP).^51–53 The electronic wave functions were expanded in a plane-wave basis set using a kinetic energy cut-off of 520 eV. All the structures were relaxed until the maximum force exerted on each atom was less than 0.01 eV Å⁻¹. The convergence criteria for energy were set at 0.01 meV. The calculated lattice constant of monolayer phosphorene was a = 3.30 Å and b = 4.62 Å along the zig-zag and arm-chair directions, respectively, which was the same as the previous theoretical study.³⁷ The Monkhorst–Pack (MP) grid of 3 × 3 × 1 was used to sample the Brillouin-zone in the relaxation calculations and 9 × 9 × 1 for the property calculations. For the Ln-doped phosphorene systems, a 4 × 3 orthorhombic supercell containing 47 P and 1 Ln atoms was modeled, which is equivalent to the impurity concentration of 2.08%. A vacuum region of 18 Å in the z direction was adopted to avoid the interaction between two adjacent periodic layers. Besides, Bader charge analysis was adopted to calculate the charge transfer between the Ln atoms and phosphorene.⁵⁴ Different from the common pseudopotentials treating f-electrons as the core to cope with the limitation of DFT in VASP, the unfrozen 4f electron pseudopotentials for Ln atoms were considered in order to obtain more accurate property calculations for the Ln-doped systems in the present study.

For lanthanide atoms, the electron correlation effect may play an important role for their magnetic properties due to the localized 4f-orbitals. The DFT results tend to place the f-states very close to the Fermi level, resulting in a too narrow band gap because DFT calculations usually apply the mean-field approximation to deal with electron–electron interactions. Therefore, the GGA + U correction was used to improve the insufficient description of strongly correlated systems given by DFT,⁵⁵ in which the Hubbard U term was added to the GGA method using the formulation of Dudarev et al.⁵⁶ To the best of our knowledge, there is no fixed experimental or theoretical U value reported for Ln-doped phosphorene. Here, the magnetic and electronic properties calculation with different U value ranging from 0 eV to 7 eV for the Ce-doped case was performed to check the influence of the U value on the description of the 4f-electron localization. When U value was increased from 0 to 7 eV, it was found that the geometrical structure had no significant change, but the 4f states tended to be influenced for U, which was consistent with the related conclusion of a previously theoretical calculation study on 4f-orbitals with GGA + U calculations.^57,58 Therefore, the U value used in the present article was set at 6 eV to perform the GGA + U calculations for Ln-doped phosphorene, which was similar to the previous GGA + U study on Ln-doped systems.^49,59

3. Results and discussion

3.1 The geometrical structure of pure and Ln-doped phosphorene

Before studying the Ln-doped phosphorene, pure phosphorene with supercell 4 × 3 was optimized. Fig. 1 plots the geometrical structure (a) and (b), band structure (c) and density of states (DOS) (c) of the pristine phosphorene layer.

Fig. 1 The optimized structure: (a) side-view, (b) top-view, (c) band structure, and (d) DOS of the pristine phosphorene.

The two calculated P–P bond distances between the nearest two P atoms are 2.221 Å and 2.258 Å in phosphorene, respectively, which are close to the reported experimental and theoretical values.^39,60 The ground state of phosphorene has no magnetic moment. The band structure of the pristine phosphorene (Fig. 1c) reveals a direct bandgap of 0.91 eV and both the top of valence band and the bottom of conduction band are located at the Γ point of the reciprocal space, which is in good agreement with other theoretical works.^22,61 Also, Fig. 1c shows that there is a high anisotropic band dispersion around the band gap, which implies that monolayered phosphorene may possess the feature of giant phononic anisotropy and anisotropic electrical conductance.⁶²

Using the above pristine phosphorene as a template, one Ln atom was used to substitute a P atom to form the Ln-doped phosphorene. Fig. 2 displays a schematic representation of the optimized geometrical structure of the Ln-doped phosphorene and Table 1 lists the calculated bond distances and binding energies of the optimized structure for each Ln-doped case.

Fig. 2 A schematic of the geometrical structure of the Ln-doped phosphorene: (a) top-view and (b) lateral-view.

Table 1 The optimized bond lengths (Ln–P₁ = Ln–P₂, Ln–P₃ = Ln–P₄ and Ln–P₅ in Å) and binding energies (E_b in eV) of the Ln-doped phosphorene systems

Phosphorene	Ln–P1	Ln–P3	Ln–P5	Eb
Pristine	2.221	3.542	2.258	—
La-doped	2.852	3.118	2.811	−8.03
Ce-doped	2.831	3.077	2.780	−7.20
Pr-doped	2.817	3.058	2.760	−6.81
Nd-doped	2.804	3.043	2.748	−6.51
Pm-doped	2.798	3.025	2.734	−4.87
Eu-doped	2.887	3.176	2.970	−4.45
Gd-doped	2.761	2.981	2.680	−7.22

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The results indicate that there exists an obviously in-plane distortion, which may be caused by the much larger diameter of the lanthanide atom when compared to the phosphorous atom, leading to a change in the lattice constants Δa = 0.017–0.076 Å and Δb = −0.042–0.091 Å. Meanwhile, an outward relaxation of the Ln atom occurs from the phosphorene surface and the P₅ atom directly connected to the doped Ln atom moves downward into the lower sublayer. The three Ln–P bond distances between the Ln atom and the neighboring P atoms decrease from La to Gd, except Eu as shown in Table 1. This phenomenon mainly originates from lanthanide contraction in which the radius of the Ln atom reduces with increasing atomic number. The Eu atom displays different behavior when compared with the rest of the Ln atoms because of its special valence electron configuration 4f⁷6s². The half-filled 4f-orbital configuration of the Eu atom was relatively stable and the large Eu atomic radius results in relatively long Eu–P bond distances.

The binding energy (E_b) of each Ln-doped case was calculated as follows:

E_b = E_m/p − E_v − E_m

where E_m/p is the total energy of the Ln-doped phosphorene, E_m denotes the energy of an isolated Ln atom and E_v stands for the energy of the Ln-doped phosphorene framework moving the Ln atom. All the calculated binding energies are in the range of ∼4.4 to ∼8.0 eV, indicating the strong bonds between the Ln atom and phosphorene. The La-doped phosphorene has the largest value (−8.03 eV), while the Eu-doped system has the smallest (−4.45 eV), corresponding to its +2 valence. Enhanced binding energies were found in the Ln-doped phosphorene when compared with the TM-doped phosphorene or the Ln-doped graphene. For example, the binding energies of the Fe- and Mn-doped phosphorene were −3.98 eV and −2.96 eV, respectively.³⁹

To verify the structural stability of the Ln-doped phosphorene, the formation energy E_f was calculated according to the following formula:

E_f = (E_doped + μ^P) − (E_pure + μ^Ln)

where E_doped and E_pure are the total energies of the Ln-doped cases (Ln = La, Ce, Pr, Nd, Pm, Eu and Gd) and the pure phosphorene, respectively; μ^P and μ^Ln denote the chemical potential of the P atom (taken from pure phosphorene) and Ln atom. If the μ^Ln was taken as the energy of an atom in bulk Ln, the formation energies of the Ln-doped phosphorene are −0.95 eV, −0.84 eV, −0.27 eV, −0.24 eV, 0.95 eV, −0.56 eV and −0.87 eV, respectively. The negative values and small positive value indicate that the doping of Ln atom in phosphorene was energetically favorable.⁶³ Furthermore, all the formation energies become negative if μ^Ln was taken at their respective upper limits, for example, the atomic energies.^38,64 The calculated formation energies obtained for La, Ce, Pr, Nd, Pm, Eu and Gd doped phosphorene are plotted as a function of Δμ^Ln in Fig. 3. Therefore, it can be confirmed that doping of La, Ce, Pr, Nd, Eu and Gd can be easily achieved experimentally. Although the formation energy of the Pm-doped case was somewhat higher than other Ln atoms, the Pm-doped system may be synthesized under appropriate experimental conditions³⁸ such as the atomic deposition rate, pressure and temperature.

Fig. 3 The calculated formation energies of Ln-doped phosphorene (Ln = La, Ce, Pr, Nd, Pm, Eu and Gd) as a function of the chemical potential difference of each dopant atom. The reference of Δμ^Ln = 0 represents the chemical potential obtained from bulk Ln. The formation energies calculated from the atomic energies of each Ln atom are marked with squares.

The different charge density has been calculated to check the charge transfer between the doped Ln atom and phosphorene as shown in Fig. 4, in which the gold color surrounding the atoms represents the charge accumulation and the cyan color represents the charge loss area. Fig. 4 shows that there exists a high bonding charge density in the region between the lanthanide atom and neighboring phosphorus atoms, indicating the covalent interaction between the lanthanide atom and its neighboring phosphorous atoms. A similar charge density feature for Ln-doped phosphorene further confirms the enhanced binding energy in the Ln-doped phosphorene.

Fig. 4 The difference in charge density of Ln-doped phosphorene with an iso-surface value of 0.002 e A⁻³. The gold color represents an increase in the electron density after doping and the cyan color indicates an electron density depletion.

3.2 Magnetic properties

Table 2 lists the calculated magnetic moments of the Ln-doped phosphorene. When a Ln atom is doped into the phosphorene, the magnetic moments from the Ce- to Pm-doped systems increase from 1 μ_B to 4 μ_B. Especially, for the Eu- and Gd-doped cases, the magnetic moments were calculated to be as high as ∼7.0 μ_B, higher than all the known magnetic moments of the main group element and TM-doped systems. Fig. 5 presents the predicted spin charge density of the Ln-doped phosphorene using the GGA + U method, which reveals that the Ln atom induces the significant spin charge density and the P atom has no obvious contribution to the magnetism. The spin charge density in Fig. 5 exhibits a different distribution of 4f-electrons, corresponding to a different 4f-electron configuration. In the Ce-doped system, the computed shape of the spin charge density distribution was similar to that of the f_z³ electronic orbital. In the Pr-, Nd- and Pm-doped systems, the spin charge density distribution corresponds to the hybrid of the corresponding 4f electronic orbitals. Interestingly, a regular spherical spin charge density distribution was observed in the Eu- and Gd-doped systems, which indicates that the magnetism originates from the half-filled electron configuration of the 4f-orbitals. Generally, the magnetic moments of the Ln-doped systems are almost proportional to the number of the spin-parallel 4f-electrons. For instance, isolated Ce and Gd atoms have one and seven spin-parallel 4f-electrons, respectively, and their corresponding doped systems exhibit spin configurations with a total magnetic moment of 1 μ_B and 7 μ_B, respectively. The other Pr, Nd and Pm atoms with +3 valence state possess two, three or four spin-parallel 4f-electrons in the corresponding doped systems, leading to the magnetic moments from 2 μ_B to 4 μ_B. Therefore, Table 2 and Fig. 5 both imply that the magnetic moment of the Ln-doped system was mainly derived from the Ln atom and contributed by the localized spin-parallel 4f-orbital electrons of the doped Ln atom.

Table 2 The magnetic moment of the Ln-doped phosphorene (in μ_B) computed using the GGA + U method and electron transfer from Ln atom to P atom in Ln-doped phosphorene measured using Bader charge analysis

Doped atom	La	Ce	Pr	Nd	Pm	Eu	Gd
μB (GGA + U)	0	1.0	2.0	3.0	4.0	7.1	7.0
Isolated	1.0	2.0	3.0	4.0	5.0	7.0	7.2
Charge transfer	1.61	1.61	1.56	1.58	1.42	1.33	1.60

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Fig. 5 The calculated spin charge density of Ln-doped phosphorene using the GGA + U functional. The iso-surface value was set to 0.004 e A⁻³.

In order to explore the underlying magnetic mechanism, the electron transfer was calculated using Bader charge analysis as shown in Table 2. The number of electrons transferred from the Ln atom to the P atoms was in the range of 1.42 to 1.61 e, except for the Eu atom (1.33 e) due to its low valence state +2. The similar electron transfer numerically reveals almost the same bonding characteristic between each Ln atom and P atom. After the electron transfer of no more than 1.6, the different numbers of the spin-parallel 4f-electrons ranging from 1 to 7 in the Ln atom produce corresponding magnetic moments ranging from 1 μ_B to 7 μ_B. The isolated La atom with a magnetic moment of 1 μ_B has an empty 4f-shell. However, forming the La–P bonds in the La-doped phosphorene causes no magnetic moment by losing its 5d- and 6s-electrons. These results conform the previous conclusion that the magnetic moment mainly originates from the 4f-electrons of the Ln atoms and is proportional to the number of spin-parallel 4f-electrons in the Ln-doped phosphorene. The magnetic behavior of the Ln-doped case was different from that of the TM-doped phosphorene in which the different number of the spin-parallel d-electrons was the main origination producing their corresponding magnetism.⁴⁰ Specially, there might exist the quenching of the d-orbital momentum in the TM-doped cases. Higher f-orbital degeneration than that of d-orbital will ensure that the f-orbital momentums are not quenched in the Ln-doped phosphorene, maintaining high magnetism.

3.3 The band structures and density of states

Fig. 6 gives the calculated band structure of each Ln-doped phosphorene. It was found that doping La, Ce, Pr, Nd and Gd atoms only have a small effect on the band structure of the pristine phosphorene, which leads to the result that the Ln-doped systems still show a semiconducting feature with similar band gap values (about 0.90 eV) close to the band gap value 0.91 eV of the pristine phosphorene. For the La-doped system, both the spin-up bands and spin-down bands are all overlapped, suggesting no spin-polarized state. This is different from the other four Ln atoms with localized spin-parallel 4f-orbitals located away from the Fermi level, displaying the magnetic states of Ln-doped phosphorene. Then, it is observed that the spin polarized states obviously appear in the Pm-doped system, which are at the bottom edge of the conduction band, while near the top edge of the valence band has no significant change. This results in an indirect band gap of 0.77 eV, which is the smallest bandgap among the calculated Ln-doped systems. Noticeably, for the Eu-doped phosphorene, a valence band crossing the Fermi level was found in the range between the Γ-point and X-point, which originates from the unoccupied states of the Eu-affected phosphorus atom P₅ due to Eu with the +2 valence state rather than +3 valence state. When compared with pristine phosphorene, the up-shifted Fermi level of Ln-doped phosphorene was found due to charge transfer from the Ln atom to the phosphorene. For the Eu-doped case, its Fermi level was not up-shifted, but down-shifted because of the lower electron transfer than those of other calculated Ln-doped phosphorene, which was attributed to the +2 valence state of Eu rather than +3. Therefore, the Eu atom can induce hole doping in the Eu-doped phosphorene, increasing the hole carrier concentration of the semiconducting phosphorene. The calculated band gap value, at least larger than 0.77 eV, of the Ln-doped phosphorene indicates that the Ln-doped phosphorene could be used as potential dilute magnetic semiconductors.

Fig. 6 The calculated band structure of Ln-doped phosphorene. The blue lines imply the spin-up bands while the red lines stand for the spin-down bands. The horizontal solid line located at 0 eV represents the Fermi level.

Fig. 7 plots the total DOSs (TDOSs) and the projected DOSs (PDOSs) of corresponding 4f-orbitals with the Fermi level set at 0 eV for the Ln-doped phosphorene, respectively. In Fig. 7, it was found that the overall DOS of the Ln-doped phosphorene mainly depends on the property of the corresponding doping Ln atom and the magnetic moment originates from the spin-parallel electrons in the 4f-orbitals of the Ln atom. For the f-orbitals, the locations move towards the lower energy with an increasing number of 4f-electrons in the Ln-doped phosphorene, except for the Eu-doped case with a low valence state +2, which results in the location of 4f-orbital close to the Fermi level. In fact, the imbalance between the occupied spin-up and spin-down states implies the production of a net magnetic moment with the range from 1.0 μ_B to 7.0 μ_B. Interestingly, in the Pm-doped system, the spin polarized states contributed by the 4f-orbitals of the Pm atom can be observed at the edge of the conduction band. In addition, in the Eu-doped phosphorene appears hole doping due to existing a band crossing the Fermi level, as shown in Fig. 7h. In the pristine phosphorene, there are five valence electrons and four sp³ valence hybridization orbitals, one of which was occupied by a lone pair of electrons and the remaining three sp³ valence hybridization orbitals with three valence electrons form three covalent P–P bonds with neighboring P atoms. In the Ln-doped system, the Ln atom of substituting the P atom in phosphorene can still offer three valence electrons for bonding with the neighboring P atoms in most Ln-doped cases, which leads to the results that the Ln atom has +3 valence state and the Ln-doped phosphorene can still reserve its semiconducting features as before. However, the Eu atom can only offer two valence electrons to bond with the neighboring P atoms, showing the +2 valence state, which directly leads to the hole doping feature observed in the Eu-doped case, different from that of the other Ln-doped cases. Obviously, it is also not difficult to understand why the La-doped phosphorene does not produce any magnetism. In the La-doped system, there exists no 4f-electrons and the three electrons of the 5d¹6s² valence orbital configuration form three valence bonds with the neighboring P atoms, which was similar to the corresponding P atom in the pristine phosphorene. Therefore, the La-doped phosphorene displays non-magnetic properties. These results further explain the calculated magnetic properties of the Ln-doped cases described above.

Fig. 7 The calculated total density of states (TDOS) and projected density of states (PDOS) for the Ln-doped phosphorene systems: (a) Ce-doped phosphorene, (b) Pr-doped phosphorene, (c) Nd-doped phosphorene, (d) Pm-doped phosphorene, (e) Eu-doped phosphorene, (f) Gd-doped phosphorene and (g) La-doped phosphorene. (h) The projected density of states of P₅ and Eu atom in the Eu-doped phosphorene. The vertical black dotted line represents the Fermi level set at 0 eV.

4. Conclusions

In the present article, the structure and magnetic properties of Ln-doped phosphorene (Ln = La, Ce, Pr, Nd, Pm, Eu and Gd) have been calculated using the GGA + U method with the model of a 4 × 3 orthorhombic supercell containing 47 P and 1 Ln atoms, equivalent to an impurity concentration of 2.08%. In the optimized Ln-doped phosphorene configuration, an obvious in-plane distortion was observed and the calculated binding energies are in the range from ∼4.4 to ∼8.0 eV, implying strong bonding between the lanthanide atom and phosphorene. When compared with the TM-doped phosphorene or Ln-doped graphene, an enhanced binding energy was found in the Ln-doped phosphorene. Also, Bader charge analysis revealed that the number of electrons transferred from the Ln to the P atoms was in the range of 1.42 to 1.61 e, except for the low valence state (+2) Eu with 1.33 e. In addition, the negative or small positive values obtained for the formation energies imply that doping Ln atoms in phosphorene was energetically favorable and the Ln-doped system may be synthesized under appropriate experimental conditions. The predicted magnetic moments are in the range from 1.0 μ_B to 7.0 μ_B, which was proportional to the number of spin-parallel 4f-electrons in the Ln-doped phosphorene. In addition, the magnetic moment was as high as 7.0 μ_B for the Eu- and Gd-doped cases, higher than all the known magnetic moments of the main-group and transition metal-doped systems. The spin charge density further displays the origination of the magnetism was mainly contributed by the 4f-orbital electrons of the doped Ln atoms in the Ln-doped phosphorene. The calculated band structure shows that the doping of the La, Ce, Pr, Nd and Gd atoms has a little effect on the band structure of the pristine phosphorene and DOS analysis further points out that the location of 4f states moves towards the lower energy with an increasing number of 4f-electrons, which leads to the result that the Ln-doped phosphorene still reserves its semiconducting features with band gap values (about 0.90 eV) close to pristine phosphorene. The Pm-doped case has the smallest band gap of 0.77 eV because the spin polarized bands are close to the bottom edge of the conduction band and no significant change appears near the top edge of the valence band. Interestingly, in the Eu-doped case, a valence band crossing the Fermi level was observed, which was caused by the low valence state (+2) of the Eu atom increasing the hole carrier concentration of the semiconducting phosphorene.

The magnetic behavior of the Ln-doped phosphorene was different from that of TM-doped phosphorene. In TM-doped graphene or phosphorene, the magnetism is mainly produced by the 3d-electrons of the transition metals. In addition, it is well-known that there exists the quenching of d-orbital momentum. However, the higher f-orbital degeneration than the d-orbital can effectively avoid the orbital momentum quenching, maintaining the high magnetism of the Ln-doped system. We expect that the Ln-doped phosphorene with high and tunable magnetic moment will become a next-generation candidate as a potential dilute magnetic semiconductor.

Acknowledgements

We are indebted to Beijing Natural Science Foundation (2132033), Beijing Higher Education Young Elite Teacher Project (YETP1177), the open Foundation of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology Grant No. KFJJ13-8M).

References

1. A. D. Franklin, Science, 2015, 349, 6249.
2. F. Xia, H. Wang, D. Xiao, M. Dubey and A. Ramasubramaniam, Nat. Photonics, 2014, 8, 899.
3. P. Miro, M. Audiffred and T. Heine, Chem. Soc. Rev., 2014, 43, 6537.
4. P. Avouris, Z. Chen and V. Perebeinos, Nat. Nanotechnol., 2007, 2, 605.
5. F. Schwierz, Nat. Nanotechnol., 2010, 5, 487.
6. S. Bae, H. Kim, Y. Lee, X. Xu, J. S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y. J. Kim, K. S. Kim, B. Ozyilmaz, J. H. Ahn, B. H. Hong and S. Iijima, Nat. Nanotechnol., 2010, 5, 574.
7. A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183.
8. Y. B. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, Nature, 2005, 438, 201.
9. A. K. Geim, Science, 2009, 324, 1530.
10. O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic and A. Kis, Nat. Nanotechnol., 2013, 8, 497.
11. T. Cao, G. Wang, W. P. Han, H. Q. Ye, C. R. Zhu, J. R. Shi, Q. Niu, P. H. Tan, E. Wang, B. L. Liu and J. Feng, Nat. Commun., 2012, 3, 177.
12. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147.
13. L. Cheng, C. Yuan, S. D. Shen, X. Yi, H. Gong, K. Yang and Z. Liu, ACS Nano, 2015, 9, 11090.
14. Y. Lin and J. W. Connell, Nanoscale, 2012, 4, 6908.
15. A. Hashmi and J. S. Hong, Sci. Rep., 2014, 4, 65.
16. Y. Zheng, J. Liu, J. Liang, M. Jaroniec and S. Z. Qiao, Energy Environ. Sci., 2012, 5, 6717.
17. X. Wang, K. Maeda, A. Thomas, K. Takanabe, G. Xin, J. M. Carlsson, K. Domen and M. Antonietti, Nat. Mater., 2009, 8, 76.
18. A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang and Y. Yamada-Takamura, Phys. Rev. Lett., 2012, 108, 245501.
19. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen and Y. Zhang, Nat. Nanotechnol., 2014, 9, 372.
20. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. F. Xu, D. Tomanek and P. D. Ye, ACS Nano, 2014, 8, 4033.
21. W. L. Lu, H. Y. Nan, J. H. Hong, Y. M. Chen, C. Zhu, Z. Liang, X. Y. Ma, Z. H. Ni, C. H. Jin and Z. Zhang, Nano Res., 2014, 7, 853.
22. R. X. Fei and L. Yang, Nano Lett., 2014, 14, 2884.
23. F. N. Xia, H. Wang and Y. C. Jia, Nat. Commun., 2014, 5, 289.
24. J. S. Qiao, X. H. Kong, Z. X. Hu, F. Yang and W. Ji, Nat. Commun., 2014, 5, 4475.
25. O. Prytz and E. Flage-Larsen, J. Phys.: Condens. Matter, 2010, 22, 15502.
26. Y. Li, S. Yang and J. Li, J. Phys. Chem. C, 2014, 118, 23970.
27. X. H. Peng, Q. Wei and A. Copple, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 90, 085402.
28. H. T. Yuan, X. G. Liu, F. Afshinmanesh, W. Li, G. Xu, J. Sun, B. Lian, A. G. Curto, G. J. Ye, Y. Hikita, Z. X. Shen, S. C. Zhang, X. H. Chen, M. Brongersma, H. Y. Hwang and Y. Cui, Nat. Nanotechnol., 2015, 10, 707.
29. J. Sun, H. W. Lee, M. Pasta, H. Yuan, G. Zheng, Y. Sun, Y. Li and Y. Cui, Nat. Nanotechnol., 2015, 10, 980.
30. W. Li, Y. Yang, G. Zhang and Y. W. Zhang, Nano Lett., 2015, 15, 1691.
31. Q. S. Yao, C. X. Huang, Y. B. Yuan, Y. Z. Liu, S. M. Liu, K. M. Deng and E. J. Kan, J. Phys. Chem. C, 2015, 119, 6923.
32. A. N. Abbas, B. L. Liu, L. Chen, Y. Q. Ma, S. Cong, N. Aroonyadet, M. Kopf, T. Nilges and C. W. Zhou, ACS Nano, 2015, 9, 5618.
33. L. Z. Kou, T. Frauenheim and C. F. Chen, J. Phys. Chem. Lett., 2014, 5, 2675.
34. H. Wang, X. Wang, F. Xia, L. Wang, H. Jiang, Q. Xia, M. L. Chin, M. Dubey and S. J. Han, Nano Lett., 2014, 14, 6424.
35. J. Na, Y. T. Lee, J. A. Lim, D. K. Hwang, G. T. Kim, W. K. Choi and Y. W. Song, ACS Nano, 2014, 8, 11753.
36. Y. X. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. J. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. F. Xu and P. D. Ye, ACS Nano, 2014, 8, 8292.
37. Y. Ding and Y. Wang, J. Phys. Chem. C, 2015, 119, 10610.
38. W. Yu, Z. Zhu, C. Niu, C. Li, J. Cho and Y. Jia, Phys. Chem. Chem. Phys., 2015, 17, 16351.
39. A. Hashmi and J. Hong, J. Phys. Chem. C, 2015, 119, 9198.
40. X. Sui, C. Si, B. Shao, X. Zou, J. Wu, B.-L. Gu and W. Duan, J. Phys. Chem. C, 2015, 119, 10059.
41. P. Srivastava, K. P. S. S. Hembram, H. Mizuseki, K.-R. Lee, S. S. Han and S. Kim, J. Phys. Chem. C, 2015, 119, 6530.
42. L. Seixas, A. Carvalho and A. H. Castro Neto, Phys. Rev. B: Condens. Matter Mater. Phys., 2015, 91, 155138.
43. H. Wang, S. Zhu, F. Fan, Z. Li and H. Wu, J. Magn. Magn. Mater., 2016, 401, 706.
44. I. Khan and J. Hong, New J. Phys., 2015, 17, 023056.
45. L. J. Kong, G. H. Liu and Y. J. Zhang, RSC Adv., 2016, 6, 10919.
46. A. Srivastava, M. S. Khan, S. K. Gupta and R. Pandey, Appl. Surf. Sci., 2015, 356, 881.
47. T. Hu and J. Hong, J. Phys. Chem. C, 2015, 119, 8199.
48. Y. Lu, T. G. Zhou, B. Shao, X. Zuo and M. Feng, AIP Adv., 2016, 6, 055708.
49. Y.-J. Li, M. Wang, M. Y. Tang, X. Tian, S. Gao, Z. He, Y. Li and T. G. Zhou, Phys. E, 2016, 75, 169.
50. X. Liu, C. Z. Wang, M. Hupalo, Y. X. Yao, M. C. Tringides, W. C. Lu and K. M. Ho, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 245408.
51. G. F. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169.
52. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15.
53. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
54. W. Tang, E. Sanville and G. Henkelman, J. Phys.: Condens. Matter, 2009, 21, 084204.
55. W. Setyawan and S. Curtarolo, Comput. Mater. Sci., 2010, 49, 299.
56. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57, 1505.
57. W. Cen, Y. Liu, Z. Wu, H. Wang and X. Weng, Phys. Chem. Chem. Phys., 2012, 14, 5769.
58. C. L. Ma, S. Picozzi, X. Wang and Z. Q. Yang, Eur. Phys. J. B, 2007, 59, 297.
59. W. Chen, P. Yuan, S. Zhang, Q. Sun, E. Liang and Y. Jia, Phys. B, 2012, 407, 1038.
60. Y. Takao and A. Morita, Physica B+C, 1981, 105, 93.
61. R. Zhang, B. Li and J. Yang, J. Phys. Chem. C, 2015, 5, 119.
62. X. M. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. C. Jia, H. Zhao, H. Wang, L. Yang, X. D. Xu and F. N. Xia, Nat. Nanotechnol., 2015, 10, 517.
63. H. Zheng, J. Zhang, B. Yang, X. Du and Y. Yan, Phys. Chem. Chem. Phys., 2015, 17, 16341.
64. G. Gao, G. Ding, J. Li, K. Yao, M. Wu and M. Qian, Nanoscale, 2016, 8, 8986.

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