First principles study of magnetism in nanographenes

Magnetism in nanographenes [also known as polycyclic aromatic hydrocarbons (PAHs)] is studied with first principles density functional calculations. We find that an antiferromagnetic (AFM) phase appears as the PAH reaches a certain size. This AFM phase in PAHs has the same origin as the one in infinitely long zigzag-edged graphene nanoribbons, namely, from the localized electronic state at the zigzag edge. The smallest PAH still having an AFM ground state is identified. With increased length of the zigzag edge, PAHs approach an infinitely long ribbon in terms of (1) the energetic ordering and difference among the AFM, ferromagnetic, and nonmagnetic phases and (2) the average local magnetic moment at the zigzag edges. These PAHs serve as ideal targets for chemical synthesis of nanographenes that possess magnetic properties. Moreover, our calculations support the interpretation that experimentally observed magnetism in activated carbon fibers originates from the zigzag edges of the nanographenes.     

Graphene nanodots with intrinsically magnetic protrusions

The three step auf bau of a triangular polyaromatic protrusion attached to a larger parent hexagonal shaped graphene nanodot (GND) is described and the dichotomy between intrinsic protrusion localized magnetism and parent extended zigzag edge magnetism is explored using ab initio density functional theory calculations of spin and charge distributions and geometry. Comparison of a three ring with a ten-ring protrusion-GND establishes a pattern for the magnetization of GNDs with larger protrusions and different morphology. The magnetism of the isolated protrusions arises from the mismatch in numbers of sublattice (alternant hydrocarbon) carbon atoms. In the parent, the sublattices are equivalent providing a singlet ground state and the magnetization appears only on long zigzag edges due to exchange interactions operating in a regime of reduced coulombic interactions. We demonstrate that a small protrusion can quench the magnetism of the edge to which it is attached. Concomitantly, the adjacent edges exhibit a small magnetic enhancement, while the remote edges are unperturbed. With size the protrusion can dominate its edge and exert control over the magnetization of other edges. Different multiplicities of the parent moiety were not found. These calculations provide guidance in understanding how the magnetism changes with system shape and in designing nanodots with a specific magnetization.     

Edge state magnetism of single layer graphene nanostructures

We study edge state magnetism in graphene nanostructures using a mean field theory of the Hubbard model. We investigate how the magnetism of the zigzag edges of graphene is affected by the presence of other types of terminating edges and defects. By a detailed study of both regular shapes, such as polygonal nanodots and nanoribbons, and irregular shapes, we conclude that the magnetism in zigzag edges is very robust. Our calculations show that the zigzag edges that are longer than three to four repeat units are always magnetic, irrespective of other edges, regular or irregular. We, therefore, clearly demonstrate that the edge irregularities and defects of the bounding edges of graphene nanostructures do not destroy the edge state magnetism.     

Spin-spin and spin-orbit interactions in nanographene fragments: a quantum chemistry approach

The relativistic behavior of graphene structures, starting from the fundamental building blocks--the poly-aromatic hydrocarbons (PAHs) along with other PAH nanographenes--is studied to quantify any associated intrinsic magnetism in the triplet (T) state and subsequently in the ground singlet (S) state with account of possible S-T mixture induced by spin-orbit coupling (SOC). We employ a first principle quantum chemical-based approach and density functional theory (DFT) for a systematic treatment of the spin-Hamiltonian by considering both the spin-orbit and spin-spin interactions as dependent on different numbers of benzene rings. We assess these relativistic spin-coupling phenomena in terms of splitting parameters which cause magnetic anisotropy in absence of external perturbations. Possible routes for changes in the couplings in terms of doping and defects are also simulated and discussed. Accounting for the artificial character of the broken-symmetry solutions for strong spin polarization of the so-called "singlet open-shell" ground state in zigzag graphene nanoribbons predicted by spin-unrestricted DFT approaches, we interpolate results from more sophisticated methods for the S-T gaps and spin-orbit coupling (SOC) integrals and find that these spin interactions become weak as function of size and increasing decoupling of electrons at the edges. This leads to reduced electron spin-spin interaction and hence almost negligible intrinsic magnetism in the carbon-based PAHs and carbon nanographene fragments. Our results are in agreement with the fact that direct experimental evidence of edge magnetism in pristine graphene has been reported so far. We support the notion that magnetism in graphene only can be ascribed to structural defects or impurities.     

Triplet states of zigzag edged hexagonal graphene molecules C(6m∗∗2)H(6m) (m = 1, 2, 3, ..., 10) and carbon based magnetism

The geometry and magnetization (spin distribution) of the series of flat hexagonal zigzag edged molecules C(6m??2)H(6m) (m = 1,2, ..., 10) in their lowest triplet state (S(z) = 1) has been calculated using density functional theory and a connection established from the known benzene (m = 1) triplets to the triplets and singlet ground state of the largest molecules (m = 9, 10). The triplet state potential energy surface has two minima corresponding to distortions from the ground state geometry, such that CC bonds bisected by a C(2)" rotation axis are either longer or shorter. For both geometries, the spin on the carbon atoms forms a pattern that peaks at the middle of an edge and for large index (m) values is the same (apart from sign) as the edge pattern of the hexagonally sectored singlet radical ground state of the largest member C(600)H(60). This similarity suggests that the singlet ground state of the larger (m = 9, 10) zigzag edged hexangulenes is possibly a hex-radical, in some ways analogous to the di- and higher multiradical ground state of the linear acenes C(4m + 2)H(2m + 4) starting around m ≥ 8 and 9. The spin patterns provide guidance in interpreting the multiradical nature of ground and low lying excited states of large hexangulenes and how magnetism evolves with size in molecules with graphene cores.     

Con(n=2～10)团簇的结构和磁性

采用密度泛函理论中的局域自旋密度近似(LSDA)和广义梯度近似(GGA)对Con(n=2～10)团簇的几何构型进行优化，并对能量、频率和磁性进行了计算,两种方法确定的基态构型完全一致,并从平均键长、平均配位数和对称性对磁性的影响进行了理论探讨.研究表明, Con(n=2～10)基态团簇的磁性在n=2～4时主要受平均键长的影响,在n=5～9时主要受平均配位数的影响,在n=10时受原子间距和平均配位数的相互影响,最终导致与Co8基态团簇具有相同的磁性.基态团簇在Co5和Co9出现了磁性局域最小点.     

Magnetism in Nonplanar Zigzag Edge Termini of Graphene Nanoribbons

Graphene nanoribbons (GNRs) and nanographenes synthesized by on-surface reactions using tailor-made molecular precursors offer an ideal playground for a study of magnetism towards nano-spintronics. Although the zigzag edge of GNRs has been known to host magnetism, the underlying metal substrates usually veil the edge-induced Kondo effect. Here, we report the on-surface synthesis of unprecedented, π-extended 7-armchair GNRs using 7-bromo-12-(10-bromoanthracen-9-yl)tetraphene as the precursor. Characterization by scanning tunneling microscopy/spectroscopy revealed unique rearrangement reactions leading to pentagon- or pentagon/heptagon-incorporated, nonplanar zigzag termini, which demonstrated Kondo resonances even on bare Au(111). Density functional theory calculations indicate that the nonplanar structure significantly reduces the interaction between the zigzag terminus and the Au(111) surface, leading to a recovery of the spin localization of the zigzag edge. Such a distortion of planar GNR structures offers a degree of freedom to control the magnetism on metal substrates.     

(CoMn)n(n=1～5)合金团簇的结构和磁性

All geometry structures of (CoMn)n (n=1-5) clusters were optimized, and the energy, frequence and magnetism of (CoMn)n (n=1-5) clusters were calculated by using the local spin density approximation and generalized gradient approximation of density functional theory. The same ground state structures of CoMn alloy clusters were confirmed in two methods, and magnetism of CoMn alloy ground state clusters was studied systemically. In order to understand structure and magnetism of CoMn alloy clusters better, Co2n (n=1-5) and Mn2n (n=1-5) clusters were calculated by the same method as alloy clusters, whose ground state structure and magnetism were confirmed. Moreover, the ground state structure and magnetism of clusters with the corresponding CoMn alloy clusters was compared. Results indicated that for (CoMn)n (n=1-4) clusters, geometry structures of CoMn alloy clusters are the same as the corresponding pure clusters still, (CoMn)3 and (CoMn)4 exhibit magnetic bistability, show ferromagnetic and anti-ferromagnetic coupling, local magnetic moment of Co, Mn atoms in CoMn alloy clusters almost preserves magnetism of pure clusters still.     

Ground state, growth, and electronic properties of small lanthanum clusters

The DMol cluster method based on density-functional theory has been employed to study the structural stability and electronic structure of La(n) (n=2-14) clusters. The ground states have been found out for lanthanum clusters. The Jahn-Teller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd-even alternation and that 7- and 13-atom clusters are magic. Further, the HOMO-LUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.     

Magnetic and electronic properties of α-graphyne nanoribbons

Based on the first-principles calculations, we investigate the magnetic and electronic properties of α-graphyne nanoribbons (NRs). We show that all the armchair α-graphyne NRs are nonmagnetic semiconductors with band gaps as a function of ribbon widths. The zigzag α-graphyne NRs are found to have magnetic semiconducting ground state with ferromagnetic ordering at each edge and opposite spin orientation between the two edges. Under the application of transverse electric field, we further predict the existence of half-metallicity in the zigzag NRs which strongly depends on the width of the ribbon.     

(CoCr)n (n=1-5)合金团簇的结构和磁性

采用密度泛函理论中的广义梯度近似(GGA)对(CoCr)n (n=1-5)团簇的几何结构、电子结构和磁性进行了系统的研究, 确定了团簇的基态和亚稳态. 结果表明, CoCr二元合金团簇的基态几何构型呈对称有序排列, 其磁性均呈反铁磁性耦合; 团簇键长和配位数的大小对原子局域磁性有很明显的影响; 受Cr原子的影响, 在(CoCr)4团簇中, 非相邻的Co原子之间呈现反铁磁性耦合.     

Quenching of local magnetic moment in oxygen adsorbed graphene nanoribbons

The electronic and magnetic properties of oxidized zigzag and armchair graphene nanoribbons, with hydrogen passivated edges, have been investigated from ab initio pseudopotential calculations within the density functional scheme. The oxygen molecule in its triplet state is adsorbed most stably at the edge of a zigzag nanoribbon. The Stoner metallic behavior of the ferromagnetic nanoribbons and the Slater insulating (ground state) behavior of the antiferromagnetic nanoribbons remain intact upon oxygen adsorption. The formation of a spin-paired C-O bond drastically reduces the local atomic magnetic moment of carbon at the edge of the ferromagnetic zigzag ribbon.     

Collective All‐Carbon Magnetism in Triangulene Dimers

Triangular zigzag nanographenes, such as triangulene and its π‐extended homologues, have received widespread attention as organic nanomagnets for molecular spintronics, and may serve as building blocks for high‐spin networks with long‐range magnetic order, which are of immense fundamental and technological relevance. As a first step towards these lines, we present the on‐surface synthesis and a proof‐of‐principle experimental study of magnetism in covalently bonded triangulene dimers. On‐surface reactions of rationally designed precursor molecules on Au(111) lead to the selective formation of triangulene dimers in which the triangulene units are either directly connected through their minority sublattice atoms, or are separated via a 1,4‐phenylene spacer. The chemical structures of the dimers have been characterized by bond‐resolved scanning tunneling microscopy. Scanning tunneling spectroscopy and inelastic electron tunneling spectroscopy measurements reveal collective singlet–triplet spin excitations in the dimers, demonstrating efficient intertriangulene magnetic coupling.     

Electronic and magnetic properties of armchair and zigzag graphene nanoribbons

The electronic properties, band gap, and ionization potential of zigzag and armchair graphene nanoribbons are calculated as a function of the number of carbon atoms in the ribbon employing density functional theory at the B3LYP6-31G* level. In armchair ribbons, the ionization potential and band gap show a gradual decrease with length. For zigzag ribbons, the dependence of the band gap and ionization potential on ribbon length is different depending on whether the ribbon has an unpaired electron or not. It is also found that boron and nitrogen zigzag and armchair doped graphene nanoribbons have a triplet ground state and could be ferromagnetic.     

Impact of Tube Curvature on the Ground‐State Magnetism of Axially Confined Single‐Walled Carbon Nanotubes of the Zigzag‐Type

The magnetic properties of axially confined, hydrogenated single‐walled carbon nanotubes (SWCNTs) of the (n,0)‐type with n=5–24 are systematically explored by density functional theory. Emphasis is placed on the relation between the ground‐state magnetic moments of SWCNTs and zigzag graphene nanoribbons (ZGNRs). Comparison between the SWCNTs considered here and ZGNRs of equal length gives rise to two basic questions: 1) how does the nanotube curvature affect the antiferromagnetic order known to prevail for ZGNRs, and 2) to what extent do the magnetic moments localized at the SWCNT edges deviate from the zero‐curvature limit of n/3 μ_B? In response to these questions, it is found that systems with n≥7 display preference for antiferromagnetic order at any length investigated, whereas for n=5, 6 the magnetic phase varies with tube length. Furthermore, elementary patterns are identified that describe the progression of the magnitude of the magnetic moment with n for the longest tubes explored in this work. The spin densities of the considered SWCNTs are analyzed as a function of the tube length L, with L ranging from 3 to 11 transpolyene rings for n≥7 and from 3 to 30 rings for n=5 and 6.     

石墨烯条带的电子结构与性质:电场及长度效应

在密度泛函理论(DFT)和含时密度泛函理论(TDDFT)的基础上对宽度上含有8个zigzag链的石墨烯条带(8-ZGNR)的基态和激发态的性质进行了理论研究,着重考察了条带长度及电场的影响.B3LYP杂化泛函的计算结果显示:在基态上,8-ZGNR的最低能量态并不具有磁性,随着长度的增加,才会显示出反铁磁的性质.静电场的加入使8-ZGNR显示出反铁磁性和半金属性.在激发态上,诱导电子会随着外激光脉冲的变化而发生移动和变化,但是相比而言,α自旋电子更容易被激发而产生较明显的诱导电子密度,而β自旋电子则更容易脱离外激光场的控制而产生非绝热现象.     

Carbogenic Nanodots: Photoluminescence and Room‐Temperature Ferromagnetism

Herein, blue fluorescent carbogenic nanodots (CNDs) with room‐temperature ferromagnetism were synthesized by thermal decomposition of organic precursors at different temperatures. Photoluminescence (PL) studies show excitation‐wavelength‐dependent emission properties and PL excitation (PLE) studies confirm the triplet ground state of carbene at the zigzag edge as the fluorescent center. Room‐temperature magnetic studies reveal the ferromagnetic nature of CNDs and temperature‐dependent studies show the presence of an antiferromagnetic phase along with a ferromagnetic phase below 50 K. EPR studies reveal the presence of conduction electrons and localized spins with different g factors. Localized spins at zigzag edges are the origin of the unconventional magnetic behavior, whereas exchange coupling between conduction and localized spins are responsible for long‐range magnetic ordering.     

Spin exchange interaction through phenylene-ethynylene bridge in diradicals based on iminonitroxide and nitronylnitroxide radical derivatives. 1. Experimental investigation of the through-bond spin exchange coupling

A series of bis-iminonitroxide diradical derivatives of different lengths and geometry have been prepared that incorporate a conjugated phenylene-ethynylene bridge as a rigid spacer. This paper describes the synthesis of these new components and their main characterizations. An unexpected singlet ground state and substituent effects on the singlet-triplet gap have been found for substituted "m-phenylene"-based diradicals. The effects of the pi-conjugation on the intramolecular through-bond spin coupling have been investigated by changing the length of the spacer within linear derivatives. The EPR studies demonstrate the intramolecular magnetic coupling between the radical spins within all compounds. This result is very attractive and unusual, given the large distance between the radicals from 15 A in the dimer to 36 A in the pentamer.     

Localized Gaussian type orbital-periodic boundary condition-density functional theory study of infinite-length single-walled carbon nanotubes with various tubular diameters

The detailed geometrical structures of zigzag and armchair type single-walled carbon nanotubes (SWCNTs) with infinite tubular length were investigated using localized Gaussian type orbital-periodic boundary condition-density functional theory (LGTO-PBC-DFT) method. The structures of (n, 0) zigzag SWCNTs were optimized for n = 5-21, (n, n) armchair SWCNTs for n = 3-12. For comparison, the optimized geometry of a two-dimensional graphite sheet was also calculated. It was found that the optimized structures of the SWCNTs showed two C-C bond lengths that decrease with an increase in the tubular diameter. More specifically, the two bond lengths converged with those found in the two-dimensional graphite sheet. We also found a degeneracy in the highest occupied crystal orbitals if identical bond lengths were employed for the zigzag SWCNTs and the two-dimensional graphite sheet. This implies that the two different bond lengths found in the zigzag SWCNTs and the two-dimensional graphite sheet are probably due to the Jahn-Teller effect. The armchair SWCNTs show two slightly different bond lengths if the diameter is less than 12 A; otherwise they are almost identical, approaching the longer bond length of the two-dimensional graphite sheet. This can be due to the fact that the armchair SWCNTs do not have degeneracy in occupied crystal orbitals for identical C-C bond lengths. The crossing point of the conducting and valence bands of each armchair SWCNT were also calculated and show a diameter dependence in which the deviation from 2pi/3a decreases as diameter increases.     

One-dimensional Intrinsic Ferromagnetic Semiconductor CuCl_2: a First-principles Study

One-dimensional nanowires with robust magnetism are desirable for spintronic applications. Herein, on the basis of the first-principles calculations, systematic investigations on the electronic and magnetic properties of the CuCl2 nanowire were performed, which can be potentially tailored from its bulk form. The CuCl2 nanowire exhibits a ferromagnetic ground state. The band structures indicate that the CuCl2 nanowire is a ferromagnetic semiconductor. The spin flip gap is large enough for avoiding spin flip. Phonon dispersion and Born-Oppenheimer molecular dynamics simulation manifest that the CuCl2 nanowire is stable. In addition, distinct magnetic properties of the CuCl2 nanowires inside two types of carbon nanotubes were obtained. The study broadens the family of the existing one-dimensional materials with promising applications for spintronics.