NiX₂ (X = Cl and Br) sheets as promising spin materials: a first-principles study

Abstract

In order to achieve paper-like spin devices, it is rather critical to develop new two-dimensional (2D) spin materials. In this study, the geometrical structure, stability, and electronic and magnetic properties of 2D nickel dihalides of NiX₂ (X = Cl and Br) type were investigated using density functional theory (DFT) calculations. We found that after optimization, geometries of NiCl₂ and NiBr₂ sheets that are obtained from their bulk counterparts are well kept. Phonon dispersion calculations demonstrated that both NiCl₂ and NiBr₂ sheets are dynamically stable. Magnetism calculations showed that ferromagnetic (FM) coupling is ground state for both structures in which per NiCl₂ and NiBr₂ unit cells can possess the moments of 1.91 and 1.88 μ_B, respectively. Density of states (DOS) and band structure calculations revealed that both structures are magnetic semiconductors with large band gaps. In addition, strain effect also showed that the moments of NiCl₂ and NiBr₂ sheets can be effectively tuned by applying the biaxial strain. A unique combination of integrated geometry, dynamical stability, intrinsic ferromagnetism, a magnetic semiconductor and tunable magnetism makes NiCl₂ and NiBr₂ sheets promising candidates for next-generation paper-like spin devices.

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Introduction

Driven by the enormous demand of the microprocessor market all over the world, a paper-like spin device has become one of the most exciting and challenging research areas. Paper-like spin devices can not only utilize spin degree of freedom of the electron to sense, store, process and transfer information with high density and high sensitivity but can also overcome the fundamental limits, such as heat dissipation and energy loss, of the device architecture caused by the diminishing size of the devices in current semiconductor technologies. Thus, the development of paper-like spin devices is important to both fundamental scientific research and industrial applications. It is well known that the performance of a device strongly depends on the properties of the material. Consequently, the progress of paper-like spin devices drives us to further develop advanced 2D spin materials.

Thus far, different families of 2D materials, such as the group IVA family (graphene, silicene and germanene),^1,2 group IIIA (boronene),³ group VA family (phosphorene, arsenene and antimonene),^4,5 group IIIA–VA family (BN sheet),^6,7 group IVA–VIA family (GeS, GeSe, SnS and SnSe sheets),⁸ transition metal dichalcogenides (MoS₂, MoSe₂, WS₂, WSe₂, TaS₂, TaSe₂, VS₂, VSe₂, NbS₂ and NbSe₂ sheets),^9–11 MXenes (Ti₂C, V₂C, Cr₂C, Nb₂C, Zr₂C, Hf₂C and Ta₂C sheets),^12,13 organo-metal porous materials (Co-PP, Cr-PP, Cu-PP, Fe-PP, Mn-PP, Ni-PP and Zn-PP sheets),^14,15 metal-halides¹⁶ and metal-oxides,^17,18 have been reported theoretically and experimentally. Among these, all IVA, IIIA, VA, IIIA–VA, IVA–VIA groups and most transition metal dichalcogenides in their pristine forms are nonmagnetic, thus hindering their applications in spin-based devices. Great efforts have been made in order to explore the application of 2D structures in this field.^19–27 For example, creating carbon vacancies in graphene,¹⁹ doping metallic or nonmetallic atoms in graphene,^20,21 silicone,²² germanene²² and phosphorene,²³ and using strain in defect-interacted MoS₂ sheet,²⁵ have been confirmed as effective methods to generate spin. Particularly, FM, the important property for the application of 2D materials in spintronic devices, was predicted in half-brominated silicone²⁶ and half-fluorinated BN and ZnO sheets.²⁷ Nevertheless, experimental realisation of promising spin with the methods mentioned above still is difficult because precise modulations of vacancy, doping, strain and surface-functionalization on 2D structures is still challenging. Recently, there has been an increasing interest for exploring 2D structures with intrinsic magnetism.^28–31 Some MXenes,²⁸ organo-metallic porous sheets,²⁹ metal-halide sheets³⁰ and metal-oxide sheets³¹ have been identified as excellent spin materials. In particular, robust FM was reported in pristine Ti₂C,³² Ti₂N,³² Cr₂C,³³ FeC₂,³⁴ VCl₃,³⁵ VI₃ (ref. 35) and NiCl₃ (ref. 36) sheets. While great efforts have been made in previous studies, researching new promising 2D spin structures is still important for further development of paper-like spin devices.

NiCl₂ and NiBr₂ crystals have been prepared for several years with methods such as vapor phase dynamical transport method,³⁷ laser beam^38,39 and thermal evaporation.⁴⁰ It should be noted that NiCl₂ and NiBr₂ crystals are formed by the stacking of layers with the interlayer separations of 3.08 and 3.24 Å, respectively. The existence of large interlayer separation in such two materials provides a possibility of their exfoliations into single-layer sheets, as reported in graphene¹ and MoS₂.⁹ Thus, in this study, we focused on the study of stability, geometrical structure, electronic and magnetic properties of NiCl₂ and NiBr₂ sheets. As mentioned above, NiCl₂ and NiBr₂ sheets can be viewed as 2D counterparts of NiCl₂ and NiBr₂ crystals, respectively.⁴¹ Our paper is organized as follows: (1) we first discuss the geometric structures of NiCl₂ and NiBr₂ sheets; (2) the stabilities of NiCl₂ and NiBr₂ sheets are then examined by performing phonon dispersion curve calculations; (3) next, magnetic properties of NiCl₂ and NiBr₂ sheets, including magnetic moment, magnetic coupling, exchange parameter and Curie temperature, are studied in detail; (4) finally, based on the calculations of DOS and band structures, we analyze the electronic properties of NiCl₂ and NiBr₂ sheets; (5) in addition, we also explore the effect of strain on the magnetic properties of NiCl₂ and NiBr₂ sheets. Our aim in so doing is to assess the suitability of NiCl₂ and NiBr₂ sheets as excellent spin materials.

Theory and methods

First principles calculations were performed using projector augmented wave (PAW) type potentials⁴² executed in the Vienna ab initio Simulation Package (VASP).^43,44 The Perdew–Burke–Ernzerhof (PBE)⁴⁵ pseudo potential inside the general gradient approximation (GGA) was chosen for the exchange correlation. The 3s²3p⁵, 4s²4p⁵ and 3d⁸4s² atomic orbitals are treated as valence states for Cl, Br and Ni atoms, respectively. A plane wave basis set with threshold value of 600 eV was used. In order to avoid the interactions between neighboring sheets, we set a vacuum space of about 17 Å for NiCl₂ and NiBr₂ sheets. The k-point sampling in reciprocal space was represented with 10 × 10 × 1 grid meshes. The convergence criterion for the atomic position and lattice vector optimizations was set as 1 × 10⁻⁴ eV in energy. To account for strong correlation of the unfilled d orbitals of the Ni atom, the U scheme was used to respect on-site electron correlation. Herein, the effective Coulomb exchange interaction, U_eff = U − J, where U and J are on-site Coulomb energy and exchange energy parameters, respectively, was set as 3 eV. The veracity of U_eff = 3 eV for 3d transition metal compounds has been confirmed in previous studies.^46,47 Moreover, in this study, the spin-resolved total DOS, atom projected density of states (PDOS) and band structure calculations were performed with a more accurate and reliable Heyd–Scouseria–Ernzerhof (HSE06) scheme.^48,49

Results and discussions

We first performed the structural relaxations, including volume and atom position, for NiX₂ (X = Cl, Br) sheets. A 2 × 2 supercell that contains four Ni atoms and eight X atoms was applied for NiX₂ sheets. The optimized atomic structures of NiX₂ sheets are shown in Fig. 1. NiX₂ sheets show a close resemblance in structure with 1T-MoS₂.⁵⁰ Calculated lattice constants are about 3.50 and 3.70 Å for NiCl₂ and NiBr₂ sheets, respectively, which are comparable to the values of 3.48 and 3.72 Å for NiCl₂ and NiBr₂ in their bulk structures.^51,52 The “thickness” of NiCl₂ and NiBr₂ sheets are found to be about 2.69 and 2.85 Å, respectively, which also are comparable to the values of 2.72 and 2.87 Å for NiCl₂ and NiBr₂ in their bulk structures.^51,52 In addition, we found that the Cl–Ni–Cl bond angle in NiCl₂ sheet is about 92.80°, which is only 1.18° larger than the value of 91.62° found in its bulk structure; the calculated Br–Ni–Br bond angle in NiBr₂ sheet is about 92.17°, which is only 0.07° larger than the value of 92.10° found in its bulk structure.^51,52 Thus, the difference of structural parameters between 2D and their 3D structures is very small, indicating that geometries of NiCl₂ and NiBr₂ sheets obtained from their bulk counterparts are well kept.

Fig. 1 Optimized geometric structures of (a) NiCl₂ and (b) NiBr₂ sheets. The selected 2 × 2 supercell is marked by the dotted lines.

The stabilities of the structures are important for their practical applications. To check whether NiCl₂ and NiBr₂ sheets are stable enough, we performed phonon dispersion curve calculations. During the calculations a 1 × 1 unit cell was used for both cases. Since per unit cell contains three atoms (1Ni atom and 2X atoms), 9 phonon branches (3 acoustic branches and 6 optical branches) were observed in Fig. 2. Clearly, for NiBr₂ sheet, we found that there are no imaginary bands. Thus, NiBr₂ sheet is dynamically stable. As for NiCl₂ sheet, the lowest transverse branch has quite few imaginary frequencies as Γ → 0. Nevertheless, we also conclude that NiCl₂ sheet is dynamically stable for two reasons: (1) the obtained imaginary frequencies might arise from the numerical artifacts because phonon dispersion calculations are highly sensitive to the choices of parameter and supercell and^36,53 (2) the obtained imaginary frequencies might be of acoustic nature because they are derived from a collective vibration mode with a long wavelength.^36,54

Fig. 2 The phonon dispersion curves of (a) NiCl₂ and (b) NiBr₂ sheets.

Next, we carried out spin-polarized calculations to study the magnetic properties of NiX₂ sheets. In order to decide the most favorable state, a 2 × 2 supercell consisting of four Ni and eight X atoms was used. Three different coupling structures, including FM, AFM and nonmagnetic (NM) structures, were considered as shown in Fig. 3(a). Our calculations showed that for both structures, NM coupling is the least stable coupling, and FM coupling is somewhat more stable than AFM coupling. Calculated energy differences between AFM and FM couplings, ΔE = E_AFM − E_FM, are about 63 and 71 meV for NiCl₂ and NiBr₂ sheets, respectively. Calculated net magnetic moment for NiCl₂ unit cell is about 1.91 μ_B, in which each Ni atom contributes 1.57 μ_B and each Cl atom contributes 0.16 μ_B; calculated net magnetic moment for NiBr₂ unit cell is about 1.88 μ_B, in which each Ni atom contributes 1.50 μ_B and each Br atom contributes 0.18 μ_B. Corresponding spin charge distributions for NiCl₂ and NiBr₂ sheets with FM coupling are shown in Fig. 3(b). Long-range magnetic ordering observed here makes NiCl₂ and NiBr₂ sheets promising candidates for spin applications. In order to estimate the robustness of FM coupling, we calculated the values of the exchange parameter J and Curie temperature T_c. The value of J was obtained from the Ising model with the expression H = −J∑m_im_j, where H is the Hamiltonian in the absence of external magnetic field, J is the exchange parameter for two nearest neighbor Ni atoms located at sites i and j, and m_i and m_j are the magnetic moments of Ni atoms at sites i and j, respectively.¹⁴ For NiCl₂ and NiBr₂ sheets, J can be represented as J = ΔE/16m².^14,55 Calculated values of J are about 1.59 and 1.94 meV for NiCl₂ and NiBr₂ sheets, respectively. The positive sign of the constants confirm that Ni atoms in both cases prefer to be formed as FM coupling instead of AFM coupling. Furthermore, comparing with the values of other dihalides, such as 0.63 meV in CrCl₃ sheet and 0.81 meV in CrBr₃ sheet,³⁰ we believe the J values obtained here are large enough. The value of T_c was further evaluated based on a classical Heisenberg model with the formula T_c = 2/3(ΔE/k_β),⁵⁶ where k_β is the Boltzmann constant. Calculated values of T_c are about 121 and 136 K for NiCl₂ and NiBr₂ sheets, respectively. Comparing with the values of 66 K reported in CrCl₃ sheet and 86 K reported in CrBr₃ sheet,³⁰ the obtained values of T_c here are also somewhat higher.

Fig. 3 (a) Ferromagnetic, antiferromagnetic, nonmagnetic configurations for NiCl₂ and NiBr₂ sheets. (b) The spin density distributions for ferromagnetic NiCl₂ and NiBr₂ sheets.

Finally, we explored the electronic properties of NiCl₂ and NiBr₂ sheets. Spin-polarized band structures based on HSE06 functional are shown in Fig. 4. Two important features were observed for NiCl₂ and NiBr₂ sheets. First, both sheets present a semiconducting property. Calculated band gaps are about 5.0 and 4.0 eV for NiCl₂ and NiBr₂ sheets, respectively. For both structures, the valence band maximum (VBM) and conduction band minimum (CBM) are contributed by spin-up and spin-down channels, respectively. In order to understand the origin of VBM and CBM, PDOS of Ni and Cl atoms in NiCl₂ sheet and Ni and Br atoms in NiBr₂ sheet were calculated, as shown in Fig. 5. It can be seen that for NiCl₂ sheet, the VBM mainly comes from the Cl atom and the CBM mainly comes from the Ni atom, and for NiBr₂ sheet, VBM mainly comes from the Br atom and the CBM mainly comes from the Ni atom. Further studies showed that VBM and CBM in NiCl₂ sheet are caused by the Cl-3p and Ni-3d orbitals, respectively, and VBM and CBM in NiBr₂ sheet are caused by the Br-4p and Ni-3d orbitals, respectively. In addition, we also calculated the band structures of NiCl₂ and NiBr₂ sheets with different U_eff, shown in Fig. 1S in the ESI.† Clearly, the change of band structure for both structures is very small with the increase of U_eff, indicating that the semiconducting property with large band gap found in NiCl₂ and NiBr₂ sheets is rather strong. Second, as shown in Fig. 4, a distinct asymmetry between the spin-up and spin-down channels was observed for NiCl₂ and NiBr₂ sheets. The asymmetry of spin channels mainly comes from the bands located at the energy region from −8.0 to 0 eV for both sheets. As shown in Fig. 5, we found that Ni atoms have a dominant contribution in the introduction of asymmetry of spin channels, and the contributions of Cl/Br atoms are small. Thus, for both sheets, the moment was caused mainly by Ni atoms, in accord with the moment calculations mentioned above. Further examination reveals that all d orbitals including d_xy, d_yz, d_z², d_xz and d_x²−y² orbitals contribute to the magnetism for both sheets. As a result, the solid semiconductor and remarkable magnetism show great potential for the application of NiCl₂ and NiBr₂ sheets in the spin field.

Fig. 4 Spin-polarized HSE06 + U band structures of NiCl₂ and NiBr₂ sheets. The red and blue solid lines correspond to the spin-up and spin-down states.

Fig. 5 Spin-polarized partial density of states of Ni and Cl atoms in NiCl₂ sheet and Ni and Br atoms in NiBr₂ sheet.

It has been proven that the magnetic property of materials can be tuned by strain.⁵⁷ Thus, we also investigated the strain effect on the magnetic properties of NiCl₂ and NiBr₂ sheets by varying the biaxial strain from −12–12%. As shown in Fig. 6(a), total energies of NiCl₂ and NiBr₂ sheets increase continuously with the increase of tensile strain or compression strain, indicating that fracture process will not happen when NiCl₂ and NiBr₂ sheets are deformed. Variations of the spin moment and the energy difference between AFM and FM states, ΔE, as a function of strain are shown in Fig. 6(b). One can see that the responses of ΔE against the strain for NiCl₂ and NiBr₂ sheets are somewhat different. For NiCl₂ sheet, the ΔE first increases and then decreases with the increase of strain, and for NiBr₂ sheet, the ΔE presents a tendency towards monotonic increase. Nevertheless, except for 12% compression strain applied in NiBr₂ sheet, ΔE is always positive for both cases, indicating that FM coupling is more stable than AFM coupling for different deformed structures. Moreover, for both cases, the moment increases almost linearly as we increase the strain. For NiCl₂ sheet, the moment increases from 1.49 to 1.61 μ_B when the strain increased from −12–12%, and, for NiBr₂ sheet, the moment increases from 1.42 to 1.54 μ_B when the strain increased from −12–12%. In addition, we also calculated their band structures with different strains, as shown in Fig. 2S in the ESI.† The change of band structure is very small with the increase of strain for both structures. Tunable magnetism and stable FM coupling and the semiconducting property indicate great potential applications of NiCl₂ and NiBr₂ in flexible spin nanoelectronics.

Fig. 6 (a) Change of total energies of ferromagnetic and antiferromagnetic NiCl₂ and NiBr₂ sheets with strain. (b) The changes of energy difference between AFM and FM couplings and magnetic moment of Ni atom with strain for NiCl₂ and NiBr₂ sheets.

Conclusions

In conclusion, using DFT, we constructed NiX₂ (X = Cl, Br) sheets and studied their geometrical structures, stabilities, electronic and magnetic properties. Both sheets show a tri-layered structure in which the central layer is formed by Ni atoms and the top and bottom layers are formed by X atoms. The phonon dispersion calculations show that ultrathin NiX₂ structures are dynamically stable. Spin polarized calculations revealed that FM coupling is the ground state for NiX₂ sheets. Calculated energy differences between AFM and FM couplings are about 63 and 71 meV for NiCl₂ and NiBr₂ sheets, respectively. The spin-polarized DOS and band structure calculations based on HSE06 functional revealed that both sheets are solid semiconductors with remarkable magnetisms. In addition, strain effect calculations show that FM coupling is always more stable than AFM coupling for NiCl₂ and NiBr₂ sheets, and the moments of NiCl₂ and NiBr₂ sheets can be effectively tuned by applying biaxial strain. These results open the possibility for two new promising 2D structures in the application of spin devices.

Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 11504044), the Fundamental Research Funds for the Central Universities (No. ZYGX2015KYQD012) and the New Academic Researcher Award (No. Y03111023901014002).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ra02218b

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