Room-Temperature Ordered Spin Structures in ... - ACS Publications

Subscriber access provided by UNIV LIBRE DE BRUXELLES

Article

Room-Temperature Ordered Spin Structures in Cluster-Assembled Single V@Si Sheets 12

Zhifeng Liu J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 29 Dec 2014 Downloaded from http://pubs.acs.org on January 6, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

The Journal of Physical Chemistry

This document is confidential and is proprietary to the American Chemical Society and its authors. Do not copy or disclose without written permission. If you have received this item in error, notify the sender and delete all copies.

Room-Temperature Ordered Spin Structures in ClusterAssembled Single V@Si12 Sheets

Journal: Manuscript ID: Manuscript Type: Date Submitted by the Author: Complete List of Authors:

The Journal of Physical Chemistry jp-2014-08509e.R2 Article 24-Dec-2014 Liu, Zhifeng; Inner Mongolia University, Wang, Xinqiang; Chongqing university, College of physics Cai, Jiangtao; Shaanxi University of Science & Technology, Zhu, Hengjiang; Xinjiang Normal University,

ACS Paragon Plus Environment

Page 1 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Room-Temperature Ordered Spin Structures in Cluster-Assembled Single V@Si12 Sheets Zhifeng Liu*,†,§, Xinqiang Wang†,§, Jiangtao Cai ‡, Hengjiang Zhu║ †School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, P. R. China §College of Physics, Chongqing University, Chongqing 401331, P. R. China ‡School of Science, Shaanxi University Science & Technology, Xi’an 710021, P. R. China ║College of Physics and Electronic Engineering, Xinjiang Normal University, Urumchi 830054, P. R. China. *To whom correspondence should be addressed: [email protected]


1


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 25

ABSTRACT Since most of the existing pristine two-dimensional (2D) materials are either intrinsically nonmagnetic or magnetic with small magnetic moment per unit cell and weak strength of magnetic coupling, introducing transition metal atoms in various nanosheets has been widely used for achieving a desired 2D magnetic material. However, the problem of surface clustering for the doped transition metal atoms is still challenging. Here we demonstrate via first-principles calculations that the recently experimentally characterized endohedral silicon cage V@Si12 clusters can construct two types of single cluster sheets exhibiting hexagonal porous or honeycomb-like framework with regularly and separately distributed V atoms. For the ground state of these two sheets, the preferred magnetic coupling is found to be ferromagnetic due to a free-electrons mediated mechanism. By using external strain, the magnetic moments and strength of magnetic coupling for these two sheets can be deliberately tuned, which would be propitious to their advanced applications. More attractively, our first-principles molecular dynamics simulations show that both the structure and strength of ferromagnetic coupling for the pristine porous sheet are stable enough to survive at room temperature. The insights obtained in this work highlight a new avenue to achieve 2D silicon-based spintronics nanomaterials.

KEYWORDS V@Si12 Cluster, Two-dimensional Material, DFT, FPMD, Ferromagnetism.

1. INTRODUCTION Promoted by the rapid developments of graphene,1-3 2D crystals with atomic thickness have recently attracted extensive interest because of their exotic electronic, optical, mechanical and


2

Page 3 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


biocompatible properties and potential applications in nanoscale devices.4-9 However, their practical applications in spintronics are being formidably hindered by the difficulty in achieving ordered spin structures at room temperature.10, 11 This stems mainly from the fact that the pristine 2D materials are either nonmagnetic or magnetic with weak exchange interaction. Up to date, although various alternative approaches [e.g., point defects12, non-metal element adsorption13, strain-induce14-16, and introducing transition metal (TM) atoms17-19] of magnetic modulation have been proposed to explore their applications in spin-related devices, the high Curie-Temperature (TC) and the precise control of these modulations for the modified 2D materials still remain challenging. Specifically, the magnetic moments based on the sp states of non-metal element are usually very small and the coupling between them is too weak to realize a room-temperature ferromagnetic ordering. Thus, introducing TM atoms in a 2D system has became a popular choice to enhance the magnetic interactions.18 Unfortunately the introduced TM atoms tend to cluster with each other because of the strong d-d interactions, which results in inhomogeneous distribution of the TM atoms or chemical phase separation into alternating regions with higher and lower concentration of TM cations in the host matrix. In this context, it would be highly desirable to search a more promising 2D magnetic material gathering the multi-advantages: ordered spin, above room-temperature TC, and good compatibility at the same time. Herein, our approach, considering the silicon-based cluster as building blocks to construct 2D crystal structures, should be possible to realize the needed 2D spintronic materials. In nanotechnology, the bottom-up approach, in which the assemblies would be constructed from small molecules or clusters, has been viewed as the most potential strategy to obtain new materials with desired novel properties.20-24 The ideal building blocks and their controllable aggregations would be the prerequisite of one’s goal getting the particular materials, such as the


3


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 25

2D ordered spin structures. With this in mind, scientists have devoted tremendous efforts25-28 to the search of stable silicon building blocks due to the important of silicon in microelectronic industry. While some results revealed that elemental silicon clusters are not suitable for performing as building blocks because of their dangling bonds rendering them chemically reactive, the metal-encapsulated or hydrogenated silicon cage-like clusters were proved as the good building blocks for cluster-assemblies.29-33 Recently, the structure with an encapsulated V atom in a Si12 hexagonal prism cage was obtained by combining experimental infrared multiple photon dissociation spectroscopy with ab initio calculations.34 This means that a new really stable silicon-based building block has been characterized by both experiment and theory, providing a possibility for the design and synthesis of cluster-assembled magnetic materials. More importantly, the approach using such TM-doped clusters V@Si12 as building blocks may bypass the long-standing problem, clustering or disorder of the TM ions during the progress of implantation. For the V@Si12 clusters, however, no study has yet been reported for their assemblies. Of course, it is unclear that whether the identity of cage-like V@Si12 can be preserved in the possible V@Si12-assembled 2D crystals and whether the crystals can survive under experimental temperature. Moreover, because of the emergence of magnetic atoms V, we also wonder if the large magnetic moments can be maintained and hold stable ferromagnetic ordering in the 2D aggregates. Largely motivated by these questions we perform density functional theory (DFT) calculations and first-principles molecular dynamics (FPMD) simulations to explore the possibility of using V@Si12 clusters as building blocks for constructing stable 2D ferromagnetic crystals with a view to achieving the desired 2D spintronic materials. The results show that two stable hexagonal nanosheets (holding porous or honeycomb-like framework) can be constructed


4

Page 5 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


by the V@Si12 clusters without collapsing of their cage-like structure. As is expected, the magnetic V atoms are stably located at the centre of hexagonal prism Si12 and regularly separated in the cluster-assembled sheets with ferromagnetic coupling. The magnetic moment per V atom is approximately 3.65 µB. More interesting, the room temperature ferromagnetic ordering in the porous nanosheet can be detected by our FPMD simulations. 2. COMPUTATIONAL DETAILS The first-principles calculations based on spin-polarized DFT were performed with a planewave basis set as implemented in the VASP code.35 The exchange-correlation potential was treated using the generalized gradient approximation (GGA) functional introduced by Perdew et al.(PBE).36 Ion cores were modeled with projector augmented wave (PAW) potentials.37, 38 The cutoff energy of 400 eV and Monkhorst-Pack grids of special k points, 11×11×1 for the primitive cell of the porous sheet, 9×9×1 for the (2×2) supercell of the honeycomb-like sheet, were chosen to ensure the total energy convergence within 1×10-4 eV. A vaccum region of 18 Å along z direction was applied to avoid interactions between two adjacent images. Ionic relaxation was performed using the standard conjugated gradient algorithm without any symmetric constraint, and the forces tolerance was set at 0.01 eV/Å. As we known, the GGA cannot properly describe the partially filled d-orbitals, so we adopted an orbital-dependent Hubbard U-like term which describes d electrons by Coulomb and exchange corrections. The correlation energy (U = 4 eV) and exchange energy (J = 1 eV) were used for V 3d electrons, which have been broadly tested in previous experimental and theoretical reports.17, 39 Further tests in our work shown that other U values (i.e, 3, 4, 5, and 6 eV) yield the similar results.


5


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 25

3. RESULTS AND DISCUSSION Before examining the 2D V@Si12-assembled nanosheets, we first investigated the structure, stability and magnetic properties of the isolated cationic and neutral V@Si12 clusters (see Supporting Information, Figures S1-S4). The results suggest that both the cationic and neutral V@Si12 have almost the same lowest-energy geometry (a distorted hexagonal prism cage with a V atom located at the center) which has been characterized by previous theoretical calculations40, 41

and recently experimental study34. The novel stability of this structure can be understood by its

compact geometrical shape and the saturated dangling bonds of Si12 with the endohedral V atom. Although the V-Si interactions can stabilize the cluster, the resulting magnetic moments of the V atom are almost completely quenched (0 μB for V@Si12+ and 1μB for V@Si12) because the formation of V-Si bond enhances the electronic kinetic energy over the exchange energy favoring parallel spins. Interestingly, however, Khanna et al.42 recently proposed that the formation of new Si-Si bonds may reduce the coupling between Si and the endohedral metal atom and recovers the spin moment of the magnetic metal atom. On the basis of these, it would be reasonable to assume that the V@Si12 cluster could serve as a potential building block to establish an ordered 2D structure with high magnetism. By comparison with C, Si atom prefers the formation of σ bonds through sp3 hybridization. In the isolated V@Si12, each Si atom is bonded to three Si neighbors, and therefore it remains a dangling bond which is finally saturated by the central V atom. When the V@Si12 building blocks aggregate together, the Si dangling bonds of a building block may be saturated by the Si atoms of its nearest-neighbor building blocks, resulting in a stable structure and a recovery of magnetic moment of the V atom. With this in mind, we tried every possible means to design the potential 2D crystals by keeping the following two regulations. First, a periodic framework can


6

Page 7 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Atomic structures of the fully optimized V@Si12-assembled sheets. (a) A top and (b) a side view of the hexagonal porous sheet (P6/mmm); (c) a top and (d) a side view of the honeycomb-like sheet (P6/mmm). Dashed rhombus with Bravais lattice vectors a and b (|a|=|b|) marks the primitive unit cell for the corresponding sheet.

be established by the periodic transitions of V@Si12 in two different directions. Second, each Si atom in the designed structure has four Si neighbors forming a 4-fold coordinated sp3-like hybridization environment. Under the consideration of spin polarization, all the obtained initial structures were fully optimized without any symmetry constraint. Then, two nanosheets were finally characterized, in which the endohedral cage of V@Si12 can survive without structural collapse. Figure 1 presents the atomic structures of these two V@Si12-assembled nanosheets, i.e., a hexagonal porous sheet (Figures 1a and 1b) and a honeycomb-like sheet (Figures 1c and 1d). It is found that in the porous sheet every V@Si12 building block is linked by three neighboring ones via square Si4 faces forming inter-cluster cubic linkages. The primitive cell of this sheet contains two building blocks with lattice constant being of 11.49 Å. The diameter of pore (twelvemembered ring) surrounded by six building blocks is 9.33 Å. Such porous characteristic may


7


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 25

make it a promising multifunctional atom/molecular sieve membrane. In the honeycomb-like sheet, each building block is linked by six neighboring ones via linear Si-Si edges forming intercluster square linkages. The optimized lattice constant is 7.26 Å. In both of these two sheets, as is assumed, the V atoms are separately and regularly distributed into an intermediate layer which is sandwiched between two layers of Si atoms, giving a hexagonal arrangement (see the red atoms in Figure1). The stability of these two suggested V@Si12-sheets can first be tested by analyzing their binding energies compared to n individual V@Si12 clusters. The calculated results are 2.04 eV and 3.09 eV per V@Si12 for the porous and honeycomb-like sheet, respectively, which indicates that both of these two sheets are more stable than a collection of individual V@Si12 clusters. Namely, the actual syntheses of such systems are possible. Since the building block V@Si12 has been obtained experimentally, we believe that the two assembled sheets will be the promising synthetic targets. To further provide a rigorous test for the stability of these two sheets, we have computed their phonon density of states. The results show that in the whole Brillouin zone the frequencies of all phonon modes are positive. (Figure S5, as an example, presents the case of porous sheet). This proves that the two sheets are kinetically stable. To understand the formation mechanism of these two stable cluster-assembled 2D materials, a detailed analysis of the bonding characteristics for the inter-cluster Si-Si bonds has been carried out. The electron density difference with respect to the sum of atomic densities43, as shown in Figure 2, shows that all the inter-cluster Si-Si bonds are mainly covalent, the same as Si-Si bonds in the building block V@Si12. Taking more detailed examination, it can be found that charge accumulation in the middle of the inter-cluster Si-Si bond for the honeycomb-like sheet is slightly larger than that for the porous sheet, which results in the stronger covalent binding (3.09


8

Page 9 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Isosurface plots (0.08 e/Å) of electron density difference with respect to the sum of atomic densities. (a) The case of the porous sheet in its inter-cluster cubic linkage region. (b) The case of the honeycomb-like sheet in its inter-cluster square linkage region. eV with respect to 2.04 eV per V@Si12 for the binding energies) and the shorter bond length (2.39 Å with respect to 2.45 Å). As mentioned in our previous design regulations, each Si atom in the sheets is connected with four neighboring Si atoms forming a 4-fold coordinated covalent environment (see the left column in Figure 2). Compared with the 4-fold coordinated sp3 hybridization environment of Si atom in diamond silicon (holding the bond angle of 109°28'), such covalent environment has some distortion in bond angles (changing from 109°28' to 90°, 120°or 150°) because of the influence of the central V atom (i.e., Vd-Sisp hybridization, more detailed discussion will be presented in the following subsection). As a matter of fact, the formation of the assembled 2D framework is just from these distorted bond angles. Therefore, we can conclude that “V-modified sp3 hybridization of the Si atoms in the inter-cluster linkage” is the assembled mechanism of the stable 2D materials. In order to explore the preferred magnetic coupling between separated V atoms, we calculated the energies of ferromagnetic, antiferromagnetic, and nonmagnetic states of the two sheets. For the magnetic states, the initial value of the magnetic moment of each encapsulated V


9


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 25

atom was set to that of the individual V atom. During the spin-polarized optimization, the magnetic moment was allowed to relax, while the spin direction of each V atom was manually fixed to keep the sheet in the ferromagnetic or antiferromagnetic state. The non-spin-polarized optimization was performed as a nonmagnetic state. In Figure 3, we present the equilibrium configurations, the local magnetic arrangements, and the relative energies in different spin states for the two sheets. Clearly, the ferromagnetic state is found to be the most energetically stable, with energy 0.207 and 0.026 eV lower than that of the antiferromagnetic state for porous and honeycomb-like sheet, respectively, indicating that the two sheets are both 2D ferromagnetic materials. It should be noted that, as our expectation, the magnetic moments of the endohedral V

Figure 3. Different magnetic couplings between the encapsulated V atoms in the two proposed sheets. The arrows represent spin directions of the encapsulated V atoms. (a) Ferromagnetic coupling FM, (b) antiferromagnetic coupling AFM and (c) nonmagnetic state NM for the porous sheet. The corresponding state is presented in (d), (e) and (f), respectively, for the honeycomblike sheet. The relative energies (E) and magnetic moments (m) for (1×1) unit cell of the porous sheet and (2×2) supercell of the honeycomb-like sheet in different magnetic state are also displayed.


10

Page 11 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


atoms are recovered to a certain extent (3.5µB and 3.8 µB per V@Si12 for the porous and honeycomb-like sheet, respectively). This can be understood by the fact that the formation of SiSi bonds between building blocks weakens the Si-V coupling (More details will be provided in the following discussion). Since the GGA functionals are deficient in describing high spin states, the hybrid functionals developed by Heyd, Scuseria, and Ernzerhop (HSE06)44 were employed to further examine whether the ground spin state is really ferromagnetic. Delightedly, the HSE06 results also approve that the ferromagnetic sate is more stable than the other states for both of the two sheets. The energy difference between ferromagnetic state and antiferromagnetic state (i.e., exchange energy Eex=EAFM-EFM) is 0.059 eV per V@Si12 for the porous sheet, and 0.011 eV for the honeycomb-like sheet. Like the results of GGA-PBE, these values also show that the porous sheet possesses a stronger ferromagnetic coupling. Having studied the magnetic ground state of the two characterized nanosheets, it is important to investigate their detailed electronic structures. Since the strong magnetic coupling will lead to a high Curie Temperature TC and may meet the demand of practical application, here we focus our attention just on the case of the porous sheet in which the exchange energy per V@Si12 is up to 104 meV (59 meV from HSE06). Figure 4 presents the band structure and spinresolved total density of state (TDOS) of the porous sheet. Remarkably, unlike the free-standing zero-bandgap silicene,45 the porous sheet appears metallic feature as the case of silicene on a hydrogenated C-terminated SiC(0001) surface.46 The spin-resolved TDOS reveals that the charge transport will be mainly dominated by the spin-up electron. Specifically, the measured spin polarization [P=((N↑-N↓)/(N↑+N↓))×100%] at the Fermi level is as large as 18.25%. To further understand the physical origin of such spin splitting in this framework, we carried out a detailed


11


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 25

Figure 4. Band structures and spin-resolved total density of state (DOS) for the ferromagnetic state of the porous sheet. The short dotted line marks the Fermi level.

Figure 5. Projected DOS on the s, p, and d orbitals of different atoms for the (1×1) ferromagnetic porous sheet. (a) s and p orbitals of Si atom; (b) s, p, and d orbitals of V atom; (c) spin density (ρ↑-ρ↓) for the (2×2) ferromagnetic porous sheet; (d) d sub-orbitals of V atom in the (1×1) ferromagnetic porous sheet. analysis of orbital-resolved DOS. Figures 5a and 5b present the sp orbitals of Si and spd orbitals of V, respectively. Clearly, the magnetic moments are mainly attributed to the 3d orbitals of V atoms. Additionally, close examination of the Si-p orbitals indicates that they also receive a few


12

Page 13 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


contributions from planar Si-px orbital. More direct evidence for these results is displayed in the net magnetic charge density (i.e., spin density ρ↑-ρ↓, see Figure 5c). It is known that in a D6h symmetry (Si12) crystal-field environment, the 3d orbitals will split into three states: a single A1d (dz ) state and two doubly degenerate states, i.e., E1d (dxz+dyz) and E2d (dxy+dx -y ). As is shown in 2

2

2

Figure 5d, the localized dz , dxz, and dyz states (A1d and E1d) are occupied only by spin-up 2

electrons at the Fermi energy, which generates most of the magnetic moments (3.5 µB) of the building block. Compared with the isolated cluster [1 µB from Vd (↑↓ ↑↓ ↑↓ ↑↓ ↑), see the SI, Figure S4], the magnetism of the building blocks in the sheet is greatly recovered. This is consistent with the assumption mentioned above that the formation of inter-cluster Si-Si bonds reduces the orbital hybridization between Si-sp and V-d (comparing the Figure S4a with Figure S6), thus remaining the atomic-like unpaired spins of V atoms. Since the minimum distance between separated V atoms is up to 6.6 Å, it is almost impossible to form a ferromagnetic ordering among the localized moments by direct exchange interaction. To understand the physical mechanism of the ferromagnetism, we may be able to adopt a nearly-free-electron gas mode like in the TMSi12 clusters.41 Supposing that each Si atom in the sheet framework contributes one electron to the “free-electron gas”, then these freeelectrons (i.e., Si 2p, see Figure 5a) will provide the needed medium to realize the ferromagnetic coupling between the separately distributed V atoms. Therefore, we can conclude that freeelectrons mediated mechanism is responsible for the long-range ferromagnetic coupling in the porous sheet. Moreover, on the basis of this we can also understand why the 2D porous sheet is metallic. Although the characterized porous sheet possesses the desirable properties, it is very important to examine whether such framework is thermally stable and whether its ferromagnetic


13


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 25

state can survive at room temperature. To explore this aspect, we built a large supercell containing 104 atoms and performed spin-polarized GGA+U FPMD simulation with a NoseHoover thermostat at 300 K. Figure 6 shows the fluctuations in temperature, potential energy, and magnetic moment as a function of the simulation time (8000 fs). Except for some thermal fluctuations, we find no structure destruction of the sheet during the whole time. And interestingly, the endohedral cage structure of building block is well preserved. These results indicate that the integrity of V@Si12 and the Si-Si bonds between neighboring building blocks are thermally stable up to at least 300 K. In Figure 6c, it is found that at room temperature the supercell of the porous sheet can remain magnetism with an average magnetic moment of around 21 µB, implying that the magnetism of the porous sheet is robust against thermal turbulence under experimental environment. While the 300 K is not a magnetic critical temperature because

Figure 6. The fluctuations of temperature (a), potential energy (b), and magnetic moment (c) as a function of the molecular dynamic simulation step at 300 K


14

Page 15 of 25

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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


our FPMD simulation does not include spin-dynamics, we can conclude that the critical temperature TC of the porous sheet must be larger than room temperature. According to the Heisenberg model, we estimated the TC using the mean-field value with KBTC = (2/3) ΔE,47 where the ΔE is the energy difference EAFM-EFM per unit cell. The calculation value of TC is 803 K (456 K from HSE06), which is larger than room temperature, further approving our above conclusion.

Figure 7. Magnetic moment and exchange energy (EAFM-EFM) under different external strain ɛ for the (1×1) porous sheet (a) and (2×2) honeycomb-like sheet (b).

In generally, for the promising 2D spintronic materials, their advanced applications often require them to hold the novel magnetic properties which can be deliberately tuned by external control parameters such as elastic stress. Thus, one of the critical issues determining the practical applications is whether the magnetic state and magnetic moment of our predicted V@Si12assembled sheets can be precisely modulated by external strain. To answer this question, we


15


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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 25

Figure 8. Schematic diagrams of the exchange mechanisms. (a) Si-V ferromagnetic coupling through p-d hybridization due to covalency of Si-V bonds under compress strain, (b) V-V antiferromagnetic coupling through super-exchange interaction due to ionicity of Si-V bonds under tensile strain.

carefully investigated the magnetic properties of the two proposed sheets under biaxial strain ɛ along the basic vectors a and b directions. Figure 7 presents the changes in the magnetic moment and exchange energy Eex for the (1×1) porous and (2×2) honeycomb-like sheet under the strain from -10% to 10%. From the changes of Eex, we can find that under the compress strain (ɛ0). Under the tensile strain (ɛ>0), however, they prefer to an antiferromagnetic state (Eex

Room-Temperature Ordered Spin Structures in ... - ACS Publications

Recommend Documents