† Corresponding author. E-mail:
CrI3 in two-dimensional (2D) forms has been attracting much attention lately due to its novel magnetic properties at atomic large scale. The size and edge tuning of electronic and magnetic properties for 2D materials has been a promising way to broaden or even enhance their utility, as the case with nanoribbons/nanotubes in graphene, black phosphorus, and transition metal dichalcogenides. Here we studied the CrI3 nanoribbon (NR) and nanotube (NT) systematically to seek the possible size and edge control of the electronic and magnetic properties. We find that ferromagnetic ordering is stable in all the NR and NT structures of interest. An enhancement of the Curie temperature TC can be expected when the structure goes to NR or NT from its 2D counterpart. The energy difference between the FM and AFM states can be even improved by up to 3–4 times in a zigzag nanoribbon (ZZNR), largely because of the electronic instability arising from a large density of states of iodine-5p orbitals at EF. In NT structures, shrinking the tube size harvests an enhancement of spin moment by up to 4%, due to the reduced crystal-field gap and the re-balance between the spin majority and minority populations.
Two-dimensional (2D) van der Waals crystals have attracted broad attention due to their novel properties and potential applications in the last two decades.[1] The excellent mechanical,[2] electronic,[1,3–5] optical,[6–8] and especially magnetic properties[9] due to the quantum confinement effect have been widely reported. Isotropic long-range ferromagnetic (FM) order at low dimension has been proved to be thermodynamically unstable in Heisenberg systems from the Mermin–Wagner theorem.[10] However, a number of magnetic 2D-layered structures, such as FePS3,[11] Cr2Ge2Te6,[12–14] and CrI3,[15,16] have recently been demonstrated by experiments to be stable with finite ordering temperature, largely due to the magnetic anisotropy and/or the Ising systems.[17–19] Among them, CrI3 exhibits in-plane FM ordering but interlayer antiferromagnetic ordering (AFM).[15] Interestingly, the layer-dependent magnetic order can be switched by an electrical gating, for example, from an interlayer AFM ordering to ferromagnetic state between the layers in bilayer CrI3 by electron doping.[20,21] Circular polarized photoluminescence has also been reported in CrI3 monolayer.[22] Those findings may promise CrI3 for applications in spintronics and optoelectronics.
Transforming 2D atomic-thick crystals into one-dimensional structures strengthens the quantum size effect in some manner and supplies a new playground for tuning electronic properties.[23–25] Especially, ribbon width and edge configuration in ribbon structures, tube diameter and chirality in nanotubes,[26] decoration style and end-size in nanowires[23] play essential roles on determining the emergent electronic and magnetic properties, as is the case with graphene nanoribbons,[27,28] MoS2 nanoribbons,[29] transition metal chalcogenides nanowires,[30–32] and phosphorene nanoribbons.[33] So it is intriguing to know how different the electronic properties one can achieve or whether it is possible to enhance the magnetic properties through edge structures when bringing CrI3 down from the 2D form to its ribbon or tube counterparts. Reports have barely been found in literature on this topic except for a computation study on the edge-tunable band structure in zigzag CrI3 nanoribbons by Jiang et al.[34] A more systematic and thorough exploration on the size effect on the electronic and magnetic properties of CrI3 nanoribbons and nanotubes is yet to be made.
In this paper, we studied the edge configuration and size dependent electronic and magnetic properties of CrI3 nanoribbons (NRs) and nanotubes (NTs) by using first-principles density functional calculations. Typical zigzag and armchair edge configurations were chosen for both ribbon and tube structures, with ribbon width ranging from 12 Å to 70 Å. Both zigzag (ZZNR) and armchair nanoribbons (ACNR) are reasonably endothermic with respect to their 2D counterparts, with ZZNR slightly more stable than ACNR. Encouragingly, the Curie temperature for both nanoribbons and nanotubes (ACNT and ZZNT), as evaluated from the energy difference between the FM and AFM states, is obviously enhanced from the CrI3 2D crystals. Part contribution is due to the increased spin moment, especially in the case of nanotubes in which the spin moment of Cr is increased by 4%. Iodine edge atoms are also found to contribute to the increased magnetization in the ribbons. Moreover, the band gap Eg of ZZNR increases with increasing ribbon width, while in contrast, the band gap of ACNR and nanotubes (ACNT, ZZNT) decreases with increasing ribbon width and tube diameter unexpectedly. More interestingly, oscillations of band gap size and spin moment of ACNT with ribbon width were found, which may be ascribed to the quantum confinement and the crucial effect of the edges.[27] Polarized optical absorption was also calculated and found to occur in the whole Brillouin zone, due to parallel flat valence and conduction bands, which is promising for optoelectronic applications.
We used ab initio density functional theory with the exchange–correlation functional of Perdew, Burke, and Ernzerhof (PBE) flavor[35] as implemented in the Vienna ab initio simulation package (VASP).[36] The cut-off energy for the plane-wave basis set was set to be 350 eV. The Monkhorst–Pack scheme[37] was used to sample the Brillouin zone (BZ) over a 16×1 ×1 k-mesh. The energy difference threshold for electronic self-consistency was set to be 10−7 eV. We used the plus U method with U = 2.65 eV for the Cr atom.[38] All the structures were fully relaxed with the method of conjugate gradients[39] until the atomic force was less than 0.02 eV/Å. The van der Waals interaction was taken into account for all the structures. The vacuum space between two neighboring slabs was set to be 15 Å to avoid the artificial inter-slab interactions.
To evaluate the optical absorption, the electron-photon matrix element
![]() |
![](cpb_28_7_077301/cpb_28_7_077301_ieqn2.gif)
![]() |
![](cpb_28_7_077301/cpb_28_7_077301_ieqn3.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn4.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn5.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn6.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn7.gif)
In the following, we shall discuss the size dependence of the electronic and magnetic properties of CrI3 nanoribbons and nanotubes.
Let us firstly define the ribbon structures for CrI3. Two typical structures of ZZNR and ACNR are defined according to the sublattice of Cr atoms (blue), similar to the definition of graphene nanoribbon type, as shown in Fig.
![]() |
![]() |
![](cpb_28_7_077301/cpb_28_7_077301_ieqn9.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn10.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn11.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn12.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn13.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn14.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn15.gif)
![](cpb_28_7_077301/cpb_28_7_077301_ieqn16.gif)
As evident by the negative formation enthalpy given in Fig.
Firstly we studied the electronic properties of ZZNR, specifically the electronic band structure, magnetic properties, and relative stability between FM and AFM states, as shown in Fig.
To have more insight into the magnetic property, we calculated the electronic band structure and density of states (DOS), as showed in Fig.
Helicity dependence of photoluminescence was reported in 2D CrI3 monolayer and bilayer.[22] It is worth checking whether it exists in the one-dimensional ribbon structure. We show the wave-vector, laser-energy, and (linearly and circularly) polarization dependence of optical absorption in Fig.
The edge type has been seen to significantly change the electronic and magnetic properties of NRs such as carbon NRs,[27] phosphorene NRs,[33] and MoS2 NRs.[29] Besides the zigzag edge in honeycomb lattices, the armchair edge is another typical structure. Now let us shift from ZZNR to ACNR to see the edge structure effect on the electronic properties of nanoribbons. The spin configurations for both AFM and FM states are given in Fig.
Compared to ribbon structures with dangling bonds at the edge, tubular structures without edges should be more advantageous for many applications. But how about the magnetic properties in the tubular structures? Here we studied CrI3 nanotubes with two typical chiralities, ZZNT(n, 0) and ACNT(n, n). Figure
More interestingly, the spin moment of Cr atoms mCr is sensitive to the tube diameter D, as shown in Fig.
In summary, we have studied the structural stability, electronic properties, and magnetic properties of low-dimensional nanoribbons and nanotubes of CrI3 by ab initio density functional calculations. Ferromagnetic ordering is found to be stable in all the NR and NT structures of interest. An enhancement of the Curie temperature TC can be expected when CrI3 structure goes from 2D to NR/NT. The energy difference between the FM and AFM states can be improved by even up to 3 to 4 times in ZZNR, largely because of the electronic instability arising from a large DOS of I-5p orbitals at EF. In NT structures, shrinking the tube size can reduce the crystal-field gap and drive a re-balance between spin majority and minority populations to harvest an enhancement of spin moment by up to 4%. Our theoretical results may give a guidance to the size and edge control of electronic and magnetic properties in low-dimensional magnetic devices.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] | |
[40] | |
[41] | |
[42] | |
[43] | |
[44] |