Defective ZrSe2: a promising candidate for spintronics applications

The current study presents the electronic and magnetic properties of monolayer ZrSe2 nanoribbons. The impact of various point defects in the form of Zr or Se vacancies, and their combinations, on the nanoribbon electronic and magnetic properties are investigated using density functional theory calculations in hydrogen-terminated zigzag and armchair ZrSe2 nanoribbons. Although pristine ZrSe2 is non-magnetic, all the defective ZrSe2 structures exhibit ferromagnetic behavior. Our calculated results also show that the Zr and Se vacancy defects alter the total spin magnetic moment with D6Se, leading to a significant amount of 6.34 µB in the zigzag nanoribbon, while the largest magnetic moment of 5.52 µB is induced by D2Se−2 in the armchair structure, with the spin density predominantly distributed around the Zr atoms near the defect sites. Further, the impact of defects on the performance of the ZrSe2 nanoribbon-based devices is investigated. Our carrier transport calculations reveal spin-polarized current-voltage characteristics for both the zigzag and armchair devices, revealing negative differential resistance (NDR) feature. Moreover, the current level in the zigzag-based nanoribbon devices is ∼10 times higher than the armchair devices, while the peak-to-valley ratio is more pronounced in the armchair-based nanoribbon devices. It is also noted that defects increase the current level in the zigzag devices while they lead to multiple NDR peaks with rather negligible change in the current level in the armchair devices. Our results on the defective ZrSe2 structures, as opposed to the pristine ones that are previously studied, provide insight into ZrSe2 material and device properties as a promising nanomaterial for spintronics applications and can be considered as practical guidance to experimental work.

The current study presents the electronic and magnetic properties of monolayer ZrSe 2 nanoribbons.The impact of various point defects in the form of Zr or Se vacancies, and their combinations, on the nanoribbon electronic and magnetic properties are investigated using density functional theory calculations in hydrogen-terminated zigzag and armchair ZrSe 2 nanoribbons.Although pristine ZrSe 2 is non-magnetic, all the defective ZrSe 2 structures exhibit ferromagnetic behavior.Our calculated results also show that the Zr and Se vacancy defects alter the total spin magnetic moment with D 6Se, leading to a significant amount of 6.34 µB in the zigzag nanoribbon, while the largest magnetic moment of 5.52 µB is induced by D 2Se−2 in the armchair structure, with the spin density predominantly distributed around the Zr atoms near the defect sites.Further, the impact of defects on the performance of the ZrSe 2 nanoribbon-based devices is investigated.Our carrier transport calculations reveal spin-polarized current-voltage characteristics for both the zigzag and armchair devices, revealing negative differential resistance (NDR) feature.Moreover, the current level in the zigzag-based nanoribbon devices is ∼10 times higher than the armchair devices, while the peak-to-valley ratio is more pronounced in the armchair-based nanoribbon devices.It is also noted that defects increase the current level in the zigzag devices while they lead to multiple NDR peaks with rather negligible change in the current level in the armchair devices.Our results on the defective ZrSe 2 structures, as opposed to the pristine ones that are previously studied, provide insight into ZrSe 2 material and device properties as a promising nanomaterial for spintronics applications and can be considered as practical guidance to experimental work.
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Zirconium diselenide (ZrSe 2 ), a member of TMDs large family, consists of three layers as X-M-X with strong covalent bonds within the layers and weak van der Waals interlayer bonding [22].Fabrication of monolayer ZrSe 2 is experimentally possible due to such weak interlayer interactions [23][24][25].Bulk ZrSe 2 is shown to be promising for photovoltaics applications due to its bandgap, ranging from infrared to visible spectrum [26,27].Bulk ZrSe 2 has a direct bandgap of 1-07-1.20 eV [28,29]; however, reducing its thickness to a single layer leads to a direct-indirect transition so that the band bap decreases to 0.439 eV [30].Moreover, it has been shown that the physical and chemical properties of 2D ZrSe 2 can be engineered by defects [31,32], doping [33,34], adsorption, electric field, and external strain [35][36][37][38].
Several recent theoretical and experimental studies have investigated the magnetic and electronic properties of ZrSe 2 nanosheets and nanoribbons [26,27,29,39,40].It has been shown that structural vacancy defects have a critical influence on the electronic properties of nanomaterials, revealing unexpected opportunities for new functionalities [32,[41][42][43][44][45][46].In [32], the magnetic properties of bulk ZrSe 2 structure with vacancy defects is studied using density functional theory (DFT) calculations.The results show that the total magnetic moment (M total ) of bulk ZrSe 2 rises by increasing the density of selenium (Se) vacancy.
In this article, the effect of different types of point defects (vacancies) on the magnetic and electronic properties of zigzag and armchair monolayer ZrSe 2 nanoribbons are explored.The nanoribbons are terminated with hydrogen atoms with a specific number of atoms across the width (N = 3).The under-studied structures are denoted as 3ZZSNR-H and 3AZSNR-H in the cases of zigzag and armchair, respectively.We perform our calculations using first-principles methods based on DFT, and the calculated results, i.e. band structure analysis, total and projected density of states (PDOS) analysis, and spin-polarized I-V characteristics, are demonstrated and discussed, followed by the conclusions in the final section.

Ab-initio simulation method
In this research, the simulations are carried out based on DFT implemented in the Quantum Espresso simulation package [47][48][49] by using the generalized gradient approximation and Perdew-Burke-Ernzerhof (PBE) form [50].Moreover, the vacuum space between nanoribbons is set to 15 A • in adjacent supercells, which is suitable to satisfy the Bloch periodic boundary conditions and avoid any interactions.The kinetic cutoff energy is 300 Ry, and also we use 1 × 1 × 7 and 1 × 1 × 8 Monkhorst-Pack k-point mesh as the first Brillouin zone of the supercell in the cases of armchair and zigzag ZrSe 2 nanoribbons, respectively.The optimizations of all atomic structures are performed until the residual force is smaller than 0.01 eV A −1 .In this work, we consider a supercell containing 6 unit cells for the zigzag and 5 unit cells for the armchair structures in order to apply the vacancy defects.

Results and discussions
In this research, we study the effects of different point defects in the form of vacancies on the electronic structure of zigzag and armchair ZrSe 2 nanoribbons (N = 3) with hydrogenpassivated edges.Figure 1 illustrates the zigzag and armchair ZrSe 2 nanoribbon structures after geometry optimization with a variety of possible defects.The unit cell of each nanoribbon is shown in the respective pristine structures.
In this paper, we have considered ten different types of vacancy defects in two 3ZZSNR-H and 3AZSNR-H nanoribbons.The description of the different notations used in this study is summarized in table 1.From the structural point of view, such defects modify the bond lengths between atoms at and near the defect location.For instance, the Zr-Se bond length in the zigzag and armchair pristine structures is 2.72 Å and 2.66 Å, respectively, while depending on the defect type (see table 1), it varies from 2.61 Å to 2.94 Å in the defective zigzag and from 2.52 Å to 2.82 Å in the defective armchair structure.The strongest effect on the Zr-Se bond length is associated with the D 3Se−2 defect type in the zigzag and the D 6Se defect type in the armchair structure.Moreover, we have evaluated the formation energies (E form ) of each vacancy defect using the following equation [51]: where E pristine is the energy of the pristine ZrSe 2 nanoribbon and E defective is the total energy of the supercell of the defective structure.µ Zr and µ Se are the chemical potentials of the Zr and Se atoms; similarly, n and m are the numbers of omitted Zr and Se atoms, respectively.Chemical potential is calculated based on the growth conditions: In Se-rich conditions, µ Se is calculated from the energy of Se in the bulk phase, while for Zrrich conditions, it is derived from µ Se = 1/2 × (µ ZrSe2 − µ Zr ), and µ Zr is the energy of Zr in the bulk phase.Moreover, the As can be seen, the defect formation energy of any Se-vacancy defect type in the armchair nanoribbon is almost equal to the zigzag structure, while the formation energy of Zr-included vacancy defect types in the zigzag structure is significantly larger than the armchair structure.Further, and as expected, the formation energy of chalcogen-vacancy defects is larger (smaller) in the Se-rich (Zr-rich) conditions, while the formation energy of metal vacancy defects is larger (smaller) in the Zr-rich (Se-rich) conditions.For example, in the extreme case of D 6Se , the formation of Se-vacancy in a Se-rich environment has a large formation energy of >22 eV, making such defects very unlikely to form, regardless of the nanoribbon architecture.However, such defect type has a relatively low formation energy in a Zr-rich environment.Figure 2 also shows that the formation energies of Zr and Se vacancy defects are increasing as the number of defects increases.Additionally, the formation energy of single-Se vacancy (D 1Se ) is the lowest energy among all the defect types in both armchair and zigzag nanoribbons in Zr-rich conditions, i.e. 1.09 eV and 1.02 eV, respectively.The total magnetic dipole moment, M total , is calculated by summing all the electron dipole moments for a specific atomic structure [52].The pristine structures of both the zigzag and armchair nanoribbons show zero magnetic moment, while all the defective systems possess magnetic moments (see figure 3).For the double and triple Se-vacancy defects, i.  the largest total magnetic moment of 5.52 µB in the armchair nanoribbon, while in the zigzag structure, the largest value of 6.34 µB is obtained for the D 6Se defect type, which is in good agreement with the results of ZrSe 2 monolayer structure [32].
To study the electronic and magnetic properties of the defective zigzag and armchair ZrSe 2 nanoribbon structures, the band structure analysis is carried out, and the results are illustrated in the supplementary information (SI) section, figure SI1.As shown in this figure, the pristine zigzag and armchair nanoribbons demonstrate non-magnetic semiconducting behavior with a direct bandgap of 0.65 eV and 1.10 eV, respectively, which is in good agreement with the previously reported studies [29,53].Further, figure SI1 shows that defects induce a stronger impact on the band structure of the armchair nanoribbon compared to the zigzag structure.In addition, all Se and Zr vacancies demonstrate asymmetric spinpolarized magnetic properties; in particular, D 6Se in the zigzag and D 2Se−2 in the armchair structures, have the most prominent spin magnetic moments.The total density of states (TDOS) and orbital-resolved PDOS of Se and Zr atoms next to the defect sites are depicted in the SI, figures SI2 and SI3, for the zigzag and armchair structures, respectively.As can be conspicuously seen in the TDOS plots, all the defective structures are magnetic with a significant spin asymmetry in the density of states (DOS), which originates from the vacancy defect.The PDOS shown in figures SI2 and SI3 indicate that p-orbitals of the Se and d-orbitals of the Zr atoms at the vicinity of defects have major contributions to the TDOS.
The spin density of the defective ZrSe 2 nanoribbon structures is illustrated in figure 4. The results indicate that the spin density of the defective structures is primarily distributed on the Zr atoms near the defect sites.This is consistent with the PDOS (figures SI2 and SI3), which indicate the large contribution of Zr atom spin-polarized d-orbitals to the total magnetic moments.
To investigate the impact of the defects on the carrier transport through the ZrSe 2 nanoribbons, electron transmission under each bias condition is calculated self-consistently in the DFT plus non-equilibrium Green's function framework.The presented devices are constructed considering two semiinfinite ZrSe 2 nanoribbons as the left and right leads, and a finite pristine or defective ZrSe 2 nanoribbon as the scattering region (channel).Upon obtaining the electron transmission of the pristine and defective devices, the current-voltage (I-V) characteristic is calculated using the Landauer-Büttiker formula [54] at different bias voltages swept from 0 to 1 V, and shown in figure 5.
The I-V characteristic of the pristine and defective devices show negative differential resistance (NDR) phenomenon [55,56].Comparing the I-V characteristic of the pristine and defective structures, reveals that vacancy defects increase the level of current in both zigzag and armchair architectures.The results also show that the current level in the zigzag devices is much larger (∼10 times) than the armchair devices.The role of defects on the current level is more pronounced in the zigzag device, while defects lead to multi-NDR peaks in the armchair devices.
The NDR characteristic would be very useful for applications such as brain-inspired computing (neuromorphic) with an array of promising memory applications, e.g. the trigger comparators [57], threshold logic devices [58,59], and the emulation of biological neuronal dynamics [60,61].The NDR response is generated from the interaction between the narrow DOS of the doped leads and the discrete states in the scattering region.The resonant tunneling model [62] is a proposed hypothesis for the origin of the NDR behavior.The ratio of the current at the resonant tunneling peak energy to the current at the dip is called the peak-to-valley ratio (PVR).In the ZrSe 2 nanoribbon devices, the PVR of the pristine structures is 1.38 and 7.37 for the zigzag and armchair, respectively.The I-V characteristic of the devices reveal that the NDR feature is only observed in the spin-up current of the D 3Se−2 defect in the zigzag device with a maximum PVR of 1.74.Although possessing a lower current level, the I-V characteristic of the armchair devices exhibit more pronounced PVR values for both the spin-up and down currents, compared to the zigzag devices, with the largest PVR of ∼8.27 for the D 1Zr structure.

Conclusion
In conclusion, we have studied the electronic and magnetic properties of pristine and defective zigzag and armchair monolayer ZrSe 2 nanoribbons using first-principles calculations based on DFT.From the calculated results, the single and double Zr vacancy and Se vacancy defects strongly affect the total spin magnetic moment, leading to the total magnetic moments of up to 5.52 µB and 6.34 µB in the armchair and zigzag nanoribbons, respectively.Our quantum transport calculations reveal that the I-V characteristic of the nanoribbon-based devices with defects is spin-polarized; an interesting feature promising for spintronic logic devices.Further, the observed spin-dependent NDR behavior and the impact of defect type on the PVR demonstrate the critical role of vacancies in such devices.Our study highlights the importance of considering the realistic properties of TMDs, including vacancies commonly observed in 2D materials, in understanding the physics governing the device behavior and in designing device architectures for applications such as spintronics.The results are expected to provide more effective guidance for experiments.

Figure 2 .
Figure 2. Formation energy of different defect types in the ZrSe 2 zigzag (blue) and armchair (red) nanoribbons.Solid and patterned represent Se-rich and Zr-rich conditions, respectively.

Figure 5 .
Figure 5. Spin-polarized I-V characteristic of (left) zigzag, and (right) armchair ZrSe 2 nanoribbon based devices, demonstrating the role of point defects on the device features.

Table 1 .
Definition of the defects in ZrSe 2 nanoribbons and their associated Zr-Se bond length.