Magnetic moment and anisotropy of individual Co atoms on graphene

Photocatalytic Efficiency for CO2 Reduction of Co and Cluster Co2O2 Supported on g-C3N4: A Density Functional Theory and Machine Learning Study

It is well known from experimental results that a single atom of cobalt supported on g-C3N4 is an efficient photocatalyst for the reduction of CO2 to CO, with a better photocatalytic activity than g-C3N4. In this work, we investigate the performance as catalysts for the CO2 reduction of single atoms of cobalt and Co2O2 clusters supported on graphitic carbon nitride (g-C3N4). Employing density functional theory plus Hubbard (DFT + U) calculations, we investigate in detail the reduction mechanisms to CO and HCOOH for the first time. We find that deposition of cobalt on g-C3N4 decreases the work function of g-C3N4 to 6.6 eV and provides a better candidate for the reduction reaction. In addition, we find that the preferred product of CO2 reduction on Co@g-C3N4 is CO, with a rate-determining barrier of 0.97 eV, while on Co2O2@g-C3N4, CO2 reduces to formate with a rate-determining barrier of 0.44 eV. We determine the creation of CO2 from COOH to only take place on Co2O2@g-C3N4, with a (relatively high) barrier of 2.27 eV. In order to obtain more easily the transition state energies of the reactions mentioned above, we applied machine learning methods to search for high-importance descriptors for these quantities, in the case of single transition metal atoms supported on C3N4. Interestingly, our results show that our quantities of interest are closely related to the adsorption energies of products and normalized valence electrons of the products of the elementary reactions as well as those of the metal atoms. The former of these two sets of features can be straightforwardly obtained via DFT, while the latter energies are extensively tabulated. Our results offer guidance for the design of catalysts and photocatalysts for CO2 reduction on single-metal atoms supported on C3N4.

Same effect of biquadratic exchange interaction and Heisenberg linear interaction in a spin spiral

Monolayer (ML) NiCl₂ exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms (B₁), as demonstrated by the spin spiral model in J. Ni et al., Phys. Rev. Lett., 2021, 127, 247204. This interaction is crucial for stabilizing the ferromagnetic collinear order within the ML NiCl₂. However, they neither point out the role of B₁ nor discuss the dispersion relation from spin orbit coupling (SOC) in the spin spiral. As we have done in this work, these parameters might theoretically potentially be derived directly by fitting the calculated spin spiral dispersion relation. Here, we draw attention to the fact that B₁ is equivalent to half of J₃ in Heisenberg linear interactions and that the positive B₁ partially counteracts the negative J₃'s impact on the spin spiral to make the ML NiCl₂ ferromagnetic. The comparatively small J₃ + 1/2B₁ from the spin spiral led us to believe that J₃ could be substituted by B₁, yet it still exists and plays a crucial function in magnetic semiconductors or insulators. The dispersion relation, which we also obtain from SOC, displays weak antiferromagnetic behavior in the spin spiral.

Geometrical and magnetic properties of small titanium and chromium clusters on monolayer hexagonal boron nitride

Magnetic clusters on an insulating substrate are potential candidates for spin-based quantum devices. Here we investigate the geometric, electronic, and magnetic structures of small Ti and Cr clusters, from dimers to pentamers, adsorbed on a single-layer hexagonal boron nitride (h-BN) sheet within the framework of density functional theory. The stable adsorption configurations of the Ti clusters and Cr clusters composed of the same number of atoms are found to be totally different from each other. The difference in their bonding mechanisms has been revealed by the density of states and the charge density difference of the corresponding adsorption systems. While chemical bonds are formed between the Ti atoms and the supporting sheet, the Cr clusters are found in the physisorption state on the substrate. In addition, it is shown that the h-BN sheet is energetically favorable for building three-dimensional Ti clusters. These findings support the use of h-BN as a suitable decoupling substrate for manipulation of quantum spin states in small transition metal (TM) clusters and fabrication of devices based on them.

Correlation anisotropy driven Kosterlitz-Thouless-type quantum phase transition in a Kondo simulator

The precise manipulation of the quantum states of individual atoms/molecules adsorbed on metal surfaces is one of the most exciting frontiers in nanophysics, enabling us to realize novel single molecular logic devices and quantum information processing. Herein, by modeling an iron phthalocyanine molecule adsorbed on the Au(111) surface with a two-impurity Anderson model, we demonstrate that the quantum states of such a system could be adjusted by the uniaxial magnetic anisotropy D_z. For negative D_z, the ground state is dominated by a parallel configuration of the z component of local spins, whereas it turns to be an antiparallel one when D_z becomes positive. Interestingly, we found that these two phases are separated by a Kosterlitz-Thouless-type quantum phase transition, which is confirmed by the critical behaviors of the transmission coefficient and the local magnetic moment. Both phases are associated with spin correlation anisotropy, thus move against the Kondo effect. When the external magnetic field is applied, it first plays a role in compensating for the effect of D_z, and then it contributes significantly to the Zeeman effect for positive D_z, accompanied by the reappearance and the splitting of the Kondo peak, respectively. For fixed negative D_z, only the Zeeman behavior is revealed. Our results provide deep insights into the manipulation of the quantum phase within a single molecular junction.

Adsorption of Transition-Metal Clusters on Graphene and N-Doped Graphene: A DFT Study

Using the dispersion-corrected density functional theory (DFT-D3) method, we systematically studied the adsorption of 15 kinds of transition-metal (TM) clusters on pristine graphene (Gr) and N-doped graphene (N-Gr). It has been found that TM_n (n = 1-4) clusters adsorbed on the N-Gr surface are much stronger than those on the pristine Gr surface, while 3d series clusters present similar geometries on Gr and N-Gr surfaces. The most preferred sites of TMs migrate from hollow to bridge to the top site on the Gr surface along the d series in the periodic table, while the preferred sites of TMs migrate in a much more complex manner on the N-Gr surface. It has also been found that charge transfer decreases along the d series for adsorbed clusters on both surfaces, but adsorbed clusters present less charge transfer on the N-Gr surface than on the Gr surface. What is more interesting is that some TM (Tc, Ru, and Re) clusters change the growth mechanism from the three-dimensional (3D) growth mode on the Gr surface to the two-dimensional (2D) growth mode on the N-Gr surface. At last, it has been found that adsorbed clusters are more dispersed on the N-Gr surface than on the pristine Gr surface due to growth and average aggregation energies.

Visualization of Transition Metal Decoration on h-BN Surface

Functional h-BN (hexagonal boron nitride) has been prepared via the incorporation of transition metal (TM) impurities like nanoparticles and single atoms. Herein, scanning transmission electron microscopy (STEM) combined with density functional theory (DFT) was employed to study Ta-, Co-, Ni-, and Ir-decorated h-BN monolayers to provide an overview of their preferential site occupancies and morphological evolutions on h-BN. Ta, Ni, Ir, and Co single atoms are all positioned on the nitrogen of h-BN; however DFT predicts the occupancy site can vary with their spin state. In terms of microstructural evolution, Co, Ni, and Ir atoms form 3D nanoclusters while Ta atoms are well dispersed and thus the single Ta atom can be decorated on h-BN. This study highlights on TM/h-BN interaction dynamics and presents an avenue for designing nanostructures for electrocatalytic application.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111)

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of MoS_{2} on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer MoS_{2} as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Quantum stochastic resonance of individual Fe atoms

Stochastic resonance, where noise synchronizes a system's response to an external drive, is a wide-reaching phenomenon found in noisy systems spanning from the dynamics of neurons to the periodicity of ice ages. Quantum tunneling can extend stochastic resonance to the quantum realm. We demonstrate quantum stochastic resonance for magnetic transitions in atoms by inelastic electron tunneling with a scanning tunneling microscope. Stochastic resonance is shown deep in the quantum regime, where spin-state fluctuations are driven by tunneling of the magnetization, and in a semiclassical crossover region, where thermally excited electrons drive transitions between ground and excited states. Inducing synchronization by periodically modulating transition rates provides a general mechanism to determine real-time spin dynamics ranging from milliseconds to picoseconds.

Transition-metal adatoms on 2D-GaAs: a route to chiral magnetic 2D materials by design

Using relativistic density-functional calculations, we examine the magneto-crystalline anisotropy and exchange properties of transition-metal atoms adsorbed on 2D-GaAs. We show that single Mn and Mo atom (Co and Os) strongly bind on 2D-GaAs, and induce local out-of-plane (in-plane) magnetic anisotropy. When a pair of TM atoms is adsorbed on 2D-GaAs in a close range from each other, magnetisation properties change (become tunable) with respect to concentrations and ordering of the adatoms. In all cases, we reveal presence of strong Dzyaloshinskii-Moriya interaction. These results indicate novel pathways towards two-dimensional chiral magnetic materials by design, tailored for desired applications in magneto-electronics.

Efficient Ab Initio Multiplet Calculations for Magnetic Adatoms on MgO

Scanning probe microscopy and spectroscopy, and more recently, single-atom electron spin resonance, have allowed the direct observation of electron dynamics at the atomic limit. The interpretation of data is strongly dependent on model Hamiltonians. However, fitting effective spin Hamiltonians to experimental data lacks the ability to explore a vast number of potential systems of interest. By using plane-wave density functional theory as starting point, we build a multiplet Hamiltonian making use of maximally localized Wannier functions. The Hamiltonian contains spin-orbit and electron-electron interactions needed to obtain the relevant spin dynamics. The resulting reduced Hamiltonian is solved by exact diagonalization. We compare three prototypical cases of 3d transition metals Mn (total spin S = 5/2), Fe (S = 2), and Co (S = 3/2) on MgO with experimental data and find that our calculations can accurately predict the spin orientation and anisotropy of the magnetic adatom. Our method does not rely on experimental input and allows us to explore and predict the fundamental magnetic properties of adatoms on surfaces.

The effect of Hubbard-like interaction on molecular magnetism of TM-coronene complex (TM = Fe and Co)

The adsorption of two transition metal adatoms, Fe and Co added to a coronene molecule were studied by means of a full potential local orbital method in the framework of relativistic density functional theory. A sequence of fixed spin moment calculations based on the Hubbard-like interaction (U) were carried out on the basis of the generalized gradient approximation (GGA) of the exchange-correlation functional. We found a transition from low-spin to high-spin state upon increasing the transition metal-coronene distance. Furthermore, the magnetism of both Fe-coronene and Co-coronene complexes revealed sensitivity to the magnitude of the U values. In our GGA+U (U  =  2 eV) calculations, a low-spin ground state was found with in-plane magnetic anisotropy for both Fe-coronene and Co-coronene, whereas the GGA+U (U  =  4 eV) calculations resulted in high-spin state with out-of-plane and in-plane magnetic anisotropy for Fe-coronene and Co-coronene, respectively.

Strain tunable spin reorientation of an individual Fe atom on 2D blue phosphorous

Herein, using first-principles calculations, we predict spin reorientation from in-plane to out-of-plane magnetization of an individual Fe magnet at the monophosphor vacancy in two-dimensional blue phosphorous (2D blue-P) by a few percent of tensile strain. We further reveal that this magnetization reversal is associated with the spin-state transition of Fe 3d ⁵ state from low-spin (1 [Formula: see text]) to high-spin state (5 [Formula: see text]), which occurs at the same tensile strain imposed into 2D blue-P, from the Ligand field theory analyses in the unpaired electron counts. The underlying mechanism for both the spin-state transition and spin-reorientation phenomena is the strain induced changes in the spin-orbit coupled adatomic [Formula: see text] and [Formula: see text] states through the strong hybridization with the P-3p  orbitals. These findings open interesting prospects for exploiting stain engineering of 2D materials to manipulate magnetism and magnetization orientation of single-molecule magnets adsorbed on it.

Size, Composition, and Support-Doping Effects on Oxygen Reduction Activity of Platinum-Alloy and on Non-platinum Metal-Decorated-Graphene Nanocatalysts

Recent investigations reported in the open literature concerning the functionalization of graphene as a support material for transition metal nanoparticle catalysts have examined isolated systems for their potential Oxygen Reduction Reaction (ORR) activity. In this work we present results which characterize the ability to use functionalized graphene (via dopants B, N) to upshift and downshift the adsorption energy of mono-atomic oxygen, O* (the ORR activity descriptor on ORR Volcano Plots), for various compositions of 4-atom, 7-atom, and 19-atom sub-nanometer binary alloy/intermetallic transition metal nanoparticle catalysts on graphene (TMNP-MDG). Our results show several important and interesting features: (1) that the combination of geometric and electronic effects makes development of simple linear mixing rules for size/composition difficult; (2) that the transition from 4- to 7- to 19-atom TMNP on MDG has pronounced effects on ORR activity for all compositions; (3) that the use of B and N as dopants to modulate the graphene-TMNP electronic structure interaction can cause shifts in the oxygen adsorption energy of 0.5 eV or more; (4) that it might be possible to make specific doped-graphene-Ni_xCu_y TMNP systems which fall close to the Volcano Peak for ORR. Our results point to systems which should be investigated experimentally and may improve the viability of future fuel cell or other ORR applications, and provide new paths for future investigations of more detail for TMNP-MDG screening.

Exciting vibrons in both frontier orbitals of a single hydrocarbon molecule on graphene

Vibronic excitations in molecules are key to the fundamental understanding of the interaction between vibrational and electronic degrees of freedom. In order to probe the genuine vibronic properties of a molecule even after its adsorption on a surface appropriate buffer layers are of paramount importance. Here, vibrational progression in both molecular frontier orbitals is observed with submolecular resolution on a graphene-covered metal surface using scanning tunnelling spectroscopy. Accompanying calculations demonstrate that the vibrational modes that cause the orbital replica in the progression share the same symmetry as the electronic states they couple to. In addition, the vibrational progression is more pronounced for separated molecules than for molecules embedded in molecular assemblies. The entire vibronic spectra of these molecular species are moreover rigidly shifted with respect to each other. This work unravels intramolecular changes in the vibronic and electronic structure owing to the efficient reduction of the molecule-metal hybridization by graphene.

Spin-fluctuation and spin-relaxation effects of single adatoms from first principles

Single adatoms offer an exceptional playground for studying magnetism and its associated dynamics at the atomic scale. Here we review recent results on single adatoms deposited on metallic substrates, based on time-dependent density functional theory. First we analyze quantum zero-point spin-fluctuations (ZPSF) as calculated from the fluctuation-dissipation theorem, and show how they affect the magnetic stability by modifying the magnetic anisotropy energy. We also assess the impact of ZPSF in the limit of small hybridization to the substrate characteristic of semi-insulating substrates, connecting to recent experimental investigations where magnetic stability of a single adatom was achieved for the first time. Secondly, we inspect further the dynamics of single adatoms by considering the longitudinal and transverse spin-relaxation processes, whose time-scales are analyzed and related to the underlying electronic structure of both the adatom and the substrate. Thirdly, we analyze spin-fluctuation modes of paramagnetic adatoms, i.e. adatoms where the Stoner criterion for magnetism is almost fulfilled. Interestingly, such modes can develop well-defined peaks in the meV range, their main characteristics being determined by two fundamental electronic properties, namely the Stoner parameter and the density of states at the Fermi level. Furthermore, simulated inelastic scanning tunneling spectroscopy curves reveal that these spin-fluctuation modes can be triggered by tunneling electrons, opening up potential applications also for paramagnetic adatoms. Lastly, an overview of the outstanding issues and future directions is given.

Emergence of Kondo Resonance in Graphene Intercalated with Cerium

The interaction between a magnetic impurity, such as cerium (Ce) atom, and surrounding electrons has been one of the core problems in understanding many-body interaction in solid and its relation to magnetism. Kondo effect, the formation of a new resonant ground state with quenched magnetic moment, provides a general framework to describe many-body interaction in the presence of magnetic impurity. In this Letter, a combined study of angle-resolved photoemission (ARPES) and dynamic mean-field theory (DMFT) on Ce-intercalated graphene shows that Ce-induced localized states near Fermi energy, E_F, hybridized with the graphene π-band, exhibit gradual increase in spectral weight upon decreasing temperature. The observed temperature dependence follows the expectations from the Kondo picture in the weak coupling limit. Our results provide a novel insight how Kondo physics emerges in the sea of two-dimensional Dirac electrons.

Stability and local magnetic moment of bilayer graphene by intercalation: first principles study

The migration and magnetic properties of the bilayer graphene with intercalation compounds (BGICs) with magnetic elements are theoretically investigated based on first principles study. Firstly, we find that BGICs with transition metals (Sc-Zn) generate distinct magnetic properties. The intercalation with most of the transition metal atoms (TMAs) gives rise to large magnetic moments from 1.0 to 4.0 μ B, which is valuable for the spintronics. Moreover, graphene can protect the intrinsic properties of the intercalated TMAs, which can be important for applications in catalysis. These phenomena can be explained by theory of spd hybridization definitely. Secondly, weak coupling between TMAs and the surroundings indicates the possibility of implementing quantum information processing and generating controlled entanglements. For the possibility of using these materials in ultrafast electronic transistors, spintronics, catalysis, spin qubit and important applications for the extensions of graphene, we believe that BGICs can provide a significant path to synthesize novel materials.

Giant perpendicular magnetic anisotropy in Fe/III-V nitride thin films

Large perpendicular magnetic anisotropy (PMA) in transition metal thin films provides a pathway for enabling the intriguing physics of nanomagnetism and developing broad spintronics applications. After decades of searches for promising materials, the energy scale of PMA of transition metal thin films, unfortunately, remains only about 1 meV. This limitation has become a major bottleneck in the development of ultradense storage and memory devices. We discovered unprecedented PMA in Fe thin-film growth on the [Formula: see text] N-terminated surface of III-V nitrides from first-principles calculations. PMA ranges from 24.1 meV/u.c. in Fe/BN to 53.7 meV/u.c. in Fe/InN. Symmetry-protected degeneracy between x² - y² and xy orbitals and its lift by the spin-orbit coupling play a dominant role. As a consequence, PMA in Fe/III-V nitride thin films is dominated by first-order perturbation of the spin-orbit coupling, instead of second-order in conventional transition metal/oxide thin films. This game-changing scenario would also open a new field of magnetism on transition metal/nitride interfaces.

First-principles study of enhanced magnetic anisotropies in transition-metal atoms doped WS2 monolayer

Considerable progress in contemporary spintronics has been made in recent years for developing nanoscale data memory and quantum information processing. It is, however, still a great challenge to achieve the ultimate limit of storage bit. 2D materials, fortunately, provide an alternative solution for designing materials with the expected miniaturizing scale, chemical stability as well as giant magnetic anisotropy energy. By performing first-principles calculations, we have examined two possible doping sites on a WS₂ monolayer using three kinds of transition metal (TM) atoms (Mn, Fe and Co). It is found that the TM atoms prefer to stay on the W atom site. Additionally, differently from the case of Mn, doping Co and Fe atoms on the W vacancy can achieve perpendicular magnetic anisotropy with a much larger magnitude, which provides a bright prospect for generating atomic-scale magnets of storage devices.

Interatomic Spin Coupling in Manganese Clusters Registered on Graphene

Different interatomic spin interactions in graphene-regulated Mn atomic clusters are investigated by low-temperature scanning tunneling microscopy and magnetic-field-dependent inelastic spin excitation spectroscopy. All dimers observed exhibit an antiferromagnetic (AFM) singlet ground state and spin transition from the singlet to triplet states, but their AFM coupling strength shows a unique dependence on their site registration on the graphene. Intriguing spin coupling can be found in the graphene-mediated Mn trimers, which manifest multilevel spin excitations. In combination with Heisenberg spin modeling and first-principles numerical simulation, an exclusive noncollinear spin configuration of the Mn trimer regulated by the graphene template can be determined, and our observed experimental exchange energies cannot be understood by a direct spin exchange mechanism, but suggest a nonlocal Ruderman-Kittel-Kasuya-Yosida indirect spin exchange mechanism through substrate modulation, which has not yet been achieved in graphene so far.

Chemically Engineering Magnetic Anisotropy of 2D Metalloporphyrin

Continuous miniaturization of magnetic units in spintronics devices inspires efforts to search for novel 2D magnetic materials with giant magnetic anisotropy energy (MAE). Through systematic first-principles calculations, large MAE of 24 meV in W or Re embedded 2D polyporphyrin frameworks is found. Interestingly, the MAE can be enhanced up to 60 meV, through replacing the hydrogen atoms on the edges of the Re based 2D polyporphyrin framework by hydroxyl and amino radicals. Analysis of the electronic structures reveals that the enhancement of MAE is mainly attributed to charge redistributions and energy shifts of Re 5d orbitals induced by the functional radicals. The findings pave a new and feasible way for tailoring the magnetic properties of magnetic organic materials to fulfill the criteria for applications in spintronics devices at high temperature.

Unconventional magnetic anisotropy in one-dimensional Rashba system realized by adsorbing Gd atom on zigzag graphene nanoribbons

The Rashba effect, a spin splitting in electronic band structures, attracts much attention for potential applications in spintronics with no requirement of an external magnetic field. Realizing a one-dimensional (1D) Rashba system is a big challenge due to the difficulties of growing high-quality heavy-metal nanowires or introducing strong spin-orbit coupling (SOC) and broken inversion symmetry in flexible materials. Here, based on first-principles calculations, we propose a pathway to realize the Rashba spin-split by adsorbing Gd atom on zigzag graphene nanoribbons (Gd-ZGNR) and further investigate the magnetic anisotropy energy (MAE). Perpendicular MAE and unconventional MAE contributions in k-space are found in the self-assembled Gd-ZGNR system, which presents a remarkable Rashba effect (the estimated strength is 1.89 eV Å) due to the strong SOC (∼65.6 meV) and the asymmetric adsorption sites at the nanoribbon edge. Moreover, first-order MAE is connected to the intrinsic Rashba effect beyond the traditional second-order MAE, which is confirmed based on the analysis of electronic structures perturbed with SOC in comparison with metastable Gd-ZGNR at the central symmetric adsorption site. The dependence on the ribbon width of the first-order MAE and the Rashba effect on Gd-ZGNRs are also examined. This work not only opens a new gate for designing the 1D Rashba system but also provides insight into the unconventional MAE due to the intrinsic Rashba effect, which would be of great significance for searching Majorana fermions and promoting potential applications in spintronics.

Giant magnetic anisotropy of rare-earth adatoms and dimers adsorbed by graphene oxide

The rare-earth dimers adsorbed onto graphene oxide possess huge magnetic anisotropy which can be effectively tuned by electric field.

Superlattice of Single Atom Magnets on Graphene

Regular arrays of single atoms with stable magnetization represent the ultimate limit of ultrahigh density storage media. Here we report a self-assembled superlattice of individual and noninteracting Dy atoms on graphene grown on Ir(111), with magnetic hysteresis up to 5.6 T and spin lifetime of 1000 s at 2.5 K. The observed magnetic stability is a consequence of the intrinsic low electron and phonon densities of graphene and the 6-fold symmetry of the adsorption site. Our array of single atom magnets has a density of 115 Tbit/inch², defined by the periodicity of the graphene moiré pattern.

Size-Dependent Ligand Quenching of Ferromagnetism in Co3(benzene)n+ Clusters Studied with X-ray Magnetic Circular Dichroism Spectroscopy

Cobalt-benzene cluster ions of the form Co₃(bz)_n⁺ (n = 0-3) were produced in the gas phase, mass-selected, and cooled in a cryogenic ion trap held at 3-4 K. To explore ligand effects on cluster magnetic moments, these species were investigated with X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) spectroscopy. XMCD spectra yield both the spin and orbital angular momenta of these clusters. Co₃⁺ has a spin magnetic moment of μ_S = 6 μ_B and an orbital magnetic moment of μ_L = 3 μ_B. Co₃(bz)⁺ and Co₃(bz)₂⁺ complexes were found to have spin and orbital magnetic moments identical to the values for ligand-free Co₃⁺. However, coordination of the third benzene to form Co₃(bz)₃⁺ completely quenches the high spin state of the system. Density functional theory calculations elucidate the spin states of the Co₃(bz)_n⁺ species as a function of the number of attached benzene ligands, explaining the transition from septet to singlet for n = 0 → 3.

High-coverage stable structures of 3d transition metal intercalated bilayer graphene

Alkali-metal intercalated graphite and graphene have been intensively studied for decades, where alkali-metal atoms are found to form ordered structures at the hollow sites of hexagonal carbon rings. Using first-principles calculations, we have predicted various stable structures of high-coverage 3d transition metal (TM) intercalated bilayer graphene (BLG) stabilized by the strain. Specifically, with reference to the bulk metal, Sc and Ti can form stable TM-intercalated BLG without strain, while the stabilization of Fe, Co, and Ni intercalated BLG requires the biaxial strain of over 7%. Under the biaxial strain ranging from 0% to 10%, there are four ordered sandwich structures for Sc with the coverage of 0.25, 0.571, 0.684, and 0.75, in which the Sc atoms are all distributed homogenously instead of locating at the hollow sites. According to the phase diagram, a homogenous configuration of C8Ti3C8 with the coverage of 0.75 and another inhomogeneous structure with the coverage of 0.692 were found. The electronic and magnetic properties as a function of strain were also analyzed to indicate that the strain was important for the stabilities of the high-coverage TM-intercalated BLG.

Magnetic remanence in single atoms

A permanent magnet retains a substantial fraction of its saturation magnetization in the absence of an external magnetic field. Realizing magnetic remanence in a single atom allows for storing and processing information in the smallest unit of matter. We show that individual holmium (Ho) atoms adsorbed on ultrathin MgO(100) layers on Ag(100) exhibit magnetic remanence up to a temperature of 30 kelvin and a relaxation time of 1500 seconds at 10 kelvin. This extraordinary stability is achieved by the realization of a symmetry-protected magnetic ground state and by decoupling the Ho spin from the underlying metal by a tunnel barrier.

Unconventional magnetisation texture in graphene/cobalt hybrids

Magnetic domain structure and spin-dependent reflectivity measurements on cobalt thin films intercalated at the graphene/Ir(111) interface are investigated using spin-polarised low-energy electron microscopy. We find that graphene-covered cobalt films have surprising magnetic properties. Vectorial imaging of magnetic domains reveals an unusually gradual thickness-dependent spin reorientation transition, in which magnetisation rotates from out-of-the-film plane to the in-plane direction by less than 10° per cobalt monolayer. During this transition, cobalt films have a meandering spin texture, characterised by a complex, three-dimensional, wavy magnetisation pattern. In addition, spectroscopy measurements suggest that the electronic band structure of the unoccupied states is essentially spin-independent already a few electron-Volts above the vacuum level. These properties strikingly differ from those of pristine cobalt films and could open new prospects in surface magnetism.

Depopulation of Single-Phthalocyanine Molecular Orbitals upon Pyrrolic-Hydrogen Abstraction on Graphene

Single-molecule chemistry with a scanning tunneling microscope has preponderantly been performed on metal surfaces. The molecule-metal hybridization, however, is often detrimental to genuine molecular properties and obscures their changes upon chemical reactions. We used graphene on Ir(111) to reduce the coupling between Ir(111) and adsorbed phthalocyanine molecules. By local electron injection from the tip of a scanning tunneling microscope the two pyrrolic H atoms were removed from single phthalocyanines. The detachment of the H atom pair induced a strong modification of the molecular electronic structure, albeit with no change in the adsorption geometry. Spectra and maps of the differential conductance combined with density functional calculations unveiled the entire depopulation of the highest occupied molecular orbital upon H abstraction. Occupied π states of intact molecules are proposed to be emptied via intramolecular electron transfer to dangling σ states of H-free N atoms.

Complex Magnetic Exchange Coupling between Co Nanostructures and Ni(111) across Epitaxial Graphene

We report on the magnetic coupling between isolated Co atoms as well as small Co islands and Ni(111) mediated by an epitaxial graphene layer. X-ray magnetic circular dichroism and scanning tunneling microscopy combined with density functional theory calculations reveal that Co atoms occupy two distinct adsorption sites, with different magnetic coupling to the underlying Ni(111) surface. We further report a transition from an antiferromagnetic to a ferromagnetic coupling with increasing Co cluster size. Our results highlight the extreme sensitivity of the exchange interaction mediated by graphene to the adsorption site and to the in-plane coordination of the magnetic atoms.

Growth mode and structures of magnetic Mn clusters on graphene

Lowest-energy geometries of Mn clusters on graphene. Blue and pink balls represent Mn atoms with negative and positive magnetic moments.

Giant Magnetic Anisotropy of Co, Ru, and Os Adatoms on MgO (001) Surface

Large magnetic anisotropy energy (MAE) is desirable and critical for nanoscale magnetic devices. Here, using ligand-field level diagrams and density functional calculations, we well explain the very recent discovery [I. G. Rau et al., Science 344, 988 (2014)] that an individual Co adatom on a MgO (001) surface has a large MAE of more than 60 meV. More importantly, we predict that a giant MAE up to 110 meV could be realized for Ru adatoms on MgO (001), and even more for the Os adatoms (208 meV). This is a joint effect of the special ligand field, orbital multiplet, and significant spin-orbit interaction, in the intermediate-spin state of the Ru or Os adatoms on top of the surface oxygens. The giant MAE could provide a route to atomic scale memory.

Origin of Perpendicular Magnetic Anisotropy and Large Orbital Moment in Fe Atoms on MgO

We report on the magnetic properties of individual Fe atoms deposited on MgO(100) thin films probed by x-ray magnetic circular dichroism and scanning tunneling spectroscopy. We show that the Fe atoms have strong perpendicular magnetic anisotropy with a zero-field splitting of 14.0±0.3  meV/atom. This is a factor of 10 larger than the interface anisotropy of epitaxial Fe layers on MgO and the largest value reported for Fe atoms adsorbed on surfaces. The interplay between the ligand field at the O adsorption sites and spin-orbit coupling is analyzed by density functional theory and multiplet calculations, providing a comprehensive model of the magnetic properties of Fe atoms in a low-symmetry bonding environment.

Quantum engineering of spin and anisotropy in magnetic molecular junctions

Single molecule magnets and single spin centres can be individually addressed when coupled to contacts forming an electrical junction. To control and engineer the magnetism of quantum devices, it is necessary to quantify how the structural and chemical environment of the junction affects the spin centre. Metrics such as coordination number or symmetry provide a simple method to quantify the local environment, but neglect the many-body interactions of an impurity spin coupled to contacts. Here, we utilize a highly corrugated hexagonal boron nitride monolayer to mediate the coupling between a cobalt spin in CoH_x (x=1,2) complexes and the metal contact. While hydrogen controls the total effective spin, the corrugation smoothly tunes the Kondo exchange interaction between the spin and the underlying metal. Using scanning tunnelling microscopy and spectroscopy together with numerical simulations, we quantitatively demonstrate how the Kondo exchange interaction mimics chemical tailoring and changes the magnetic anisotropy.

The spins of single molecules and defect centres possess properties which can be strongly influenced by their material contacts in electrical junctions. Here, the authors study the coupling between cobalt hydride complexes and a Rh(111) contact, mediated through a hexagonal boron nitride layer.

Transient dynamics of magnetic Co-graphene systems

We report the investigation of response time of spin resolved electron traversing through a magnetic Co-graphene nano-device. For this purpose, we calculate the transient current under a step-like upward pulse for this system from first principles using non-equilibrium Green's function (NEGF) formalism within the framework of density functional theory (DFT). In the absence of dephasing mechanisms, transient current shows a damped oscillatory behavior. The turn-on time of the magnetic Co-graphene nano-device was found to be around 5-20 femtoseconds, while the relaxation time can reach several picoseconds due to the damped oscillation of transient current for both majority spin and minority spin. The response time was determined by the resonant states below the Fermi level, but does not depend on the chirality of graphene and the amplitude of pulse bias. Each resonant state contributes to the damped oscillation of transient current with the same frequency and different decay rates. The frequency of the oscillation is half the pulse bias and the decay rate equals the lifetime of the corresponding resonant state. When inelastic phase-relaxing scattering is considered, the long duration oscillatory behavior of the transient current is suppressed and the relaxation time is reduced to hundreds of femtoseconds.

Graphene-Induced Magnetic Anisotropy of a Two-Dimensional Iron Phthalocyanine Network

A single layer of flat-lying iron phthalocyanine (FePc) molecules assembled on graphene grown on Ir(111) preserves the magnetic moment, as deduced by X-ray magnetic circular dichroism from the Fe L2,3 edges. Furthermore, the FePc molecules in contact with the graphene buffer layer exhibit an enhancement of the magnetic anisotropy, with emergence of an in-plane easy magnetic axis, reflected by an increased orbital moment of the FePc molecules in contact with the C atoms in the graphene sheet. The origin of the increased magnetic anisotropy is discussed, considering the absence of electronic state hybridization, and the breaking of symmetry upon FePc adsorption on graphene.

Enhanced magnetic anisotropies of single transition-metal adatoms on a defective MoS2 monolayer

Single magnetic atoms absorbed on an atomically thin layer represent the ultimate limit of bit miniaturization for data storage. To approach the limit, a critical step is to find an appropriate material system with high chemical stability and large magnetic anisotropic energy. Here, on the basis of first-principles calculations and the spin-orbit coupling theory, it is elucidated that the transition-metal Mn and Fe atoms absorbed on disulfur vacancies of MoS₂ monolayers are very promising candidates. It is analysed that these absorption systems are of not only high chemical stabilities but also much enhanced magnetic anisotropies and particularly the easy magnetization axis is changed from the in-plane one for Mn to the out-of-plane one for Fe by a symmetry-lowering Jahn-Teller distortion. The results point out a promising direction to achieve the ultimate goal of single adatomic magnets with utilizing the defective atomically thin layers.

Controlling the spin of co atoms on pt(111) by hydrogen adsorption

We investigate the effect of H adsorption on the magnetic properties of individual Co atoms on Pt(111) with scanning tunneling microscopy. For pristine Co atoms, we detect no inelastic features in the tunnel spectra. Conversely, CoH and CoH2 show a number of low-energy vibrational features in their differential conductance identified by isotope substitution. Only the fcc-adsorbed species present conductance steps of magnetic origin, with a field splitting identifying their effective spin as Seff=2 for CoH and 3/2 for CoH2. The exposure to H2 and desorption through tunnel electrons allow the reversible control of the spin in half-integer steps. Because of the presence of the surface, the hydrogen-induced spin increase is opposite to the spin sequence of CoHn molecules in the gas phase.

Chern half metals: a new class of topological materials to realize the quantum anomalous Hall effect

New topological insulators that demonstrate the quantum anomalous Hall effect (QAHE) are a cutting-edge research topic in condensed matter physics and materials science. So far, the QAHE has been observed only in Cr-doped (Bi,Sb)2Te3 at extremely low temperature. Therefore, it is important to find new materials with large topological band gap and high thermal stability for the realization of the QAHE. On the basis of first-principles and tight-binding model calculations, we discovered a new class of topological phase, Chern half metal, which manifests the QAHE in one spin channel while is metallic in the other spin channel, in Co or Rh deposited graphene. The QAHE is robust in these sytems for the adatom coverage ranging from 2% to 6%. Meanwhile, these systems have large perpendicular magnetic anisotropy energies of 5.3 and 11.5 meV, necessary for the observation of the QAHE at reasonably high temperature.

Three-dimensional mapping of single-atom magnetic anisotropy

Magnetic anisotropy plays a key role in the magnetic stability and spin-related quantum phenomena of surface adatoms. It manifests as angular variations of the atom's magnetic properties. We measure the spin excitations of individual Fe atoms on a copper nitride surface with inelastic electron tunneling spectroscopy. Using a three-axis vector magnet we rotate the magnetic field and map out the resulting variations of the spin excitations. We quantitatively determine the three-dimensional distribution of the magnetic anisotropy of single Fe atoms by fitting the spin excitation spectra with a spin Hamiltonian. This experiment demonstrates the feasibility of fully mapping the vector magnetic properties of individual spins and characterizing complex three-dimensional magnetic systems.

Magnetism of Ho and Er atoms on close-packed metal surfaces

We investigated the magnetic properties of individual Ho atoms adsorbed on the (111) surface of Pt, which have been recently claimed to display single ion magnetic behavior. By combining x-ray absorption spectroscopy and magnetic dichroism measurements with ligand field multiplet calculations, we reveal a ground state which is incompatible with long spin relaxation times, in disagreement with former findings. A comparative study of the ground state and magnetic anisotropy of Ho and Er on Pt(111) and Cu(111) emphasizes the different interaction of the 4f orbitals with localized and delocalized substrate states. In particular, we find a striking rotation of the magnetization easy axis for Er, which changes from out of plane on Pt(111) to in plane on Cu(111).

Stability, energetics, and magnetic states of cobalt adatoms on graphene

We investigate the stability and electronic properties of single Co atoms on graphene with near-exact many-body calculations. A frozen-orbital embedding scheme was combined with auxiliary-field quantum Monte Carlo calculations to increase the reach in system sizes. Several energy minima are found as a function of the distance h between Co and graphene. Energetics only permit the Co atom to occupy the top site at h=2.2  Å in a high-spin 3d(8)4s(1) state, and the van der Waals region at h=3.3  Å in a high-spin 3d(7)4s(2) state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.

Tailoring the magnetism of Co atoms on graphene through substrate hybridization

We determine the magnetic properties of individual Co atoms adsorbed on graphene (G) with x-ray absorption spectroscopy and magnetic circular dichroism. The magnetic ground state of Co adatoms strongly depends on the choice of the metal substrate on which graphene is grown. Cobalt atoms on G/Ru(0001) feature exceptionally large orbital and spin moments, as well as an out-of-plane easy axis with large magnetic anisotropy. Conversely, the magnetic moments are strongly reduced for Co/G/Ir(111), and the magnetization is of the easy-plane type. We demonstrate how the Co magnetic properties, which ultimately depend on the degree of hybridization between the Co 3d orbitals and graphene π bands, can be tailored through the strength of the graphene-substrate coupling.

Resonant-enhanced spectroscopy of molecular rotations with a scanning tunneling microscope

We use rotational excitation spectroscopy with a scanning tunneling microscope to investigate the rotational properties of molecular hydrogen and its isotopes physisorbed on the surfaces of graphene and hexagonal boron nitride (h-BN), grown on Ni(111), Ru(0001), and Rh(111). The rotational excitation energies are in good agreement with ΔJ = 2 transitions of freely spinning p-H2 and o-D2 molecules. The variations of the spectral line shapes for H2 among the different surfaces can be traced back to a molecular resonance-mediated tunneling mechanism. Our data for H2/h-BN/Rh(111) suggest a local intrinsic gating on this surface due to lateral static dipoles. Spectra on a mixed monolayer of H2, HD, and D2 display all three J = 0 → 2 rotational transitions, irrespective of tip position, thus pointing to a multimolecule excitation, or molecular mobility in the physisorbed close-packed layer.

Kondo effect of cobalt adatoms on a graphene monolayer controlled by substrate-induced ripples

The Kondo effect, a widely studied phenomenon in which the scattering of conduction electrons by magnetic impurities increases as the temperature T is lowered, depends strongly on the density of states at the Fermi energy. It has been predicted by theory that magnetic impurities on free-standing monolayer graphene exhibit the Kondo effect and that control of the density of states at the Fermi level by external means can be used to switch the effect on and off. However, though transport data for Co adatoms on graphene monolayers on several substrates have been reported, there exists no evidence for a Kondo effect. Here we probe the role of the substrate on the Kondo effect of Co on graphene by combining low-temperature scanning tunneling microscopy and spectroscopy measurements with density functional theory calculations. We use a Ru(0001) substrate that is known to cause graphene to ripple, yielding a moiré superlattice. The experimental data show a sharp Kondo resonance peak near the Fermi energy from only Co adatoms at the edge of atop regions of the moiré pattern. The theoretical results show that the variation of the distance from the graphene to the Ru substrate, which controls the spin polarization and local density of states at the Fermi energy, is the key factor for the appearance of the Kondo resonance. The results suggest that rippling of graphene by suitable substrates is an additional lever for tuning and selectively switching the appearance of the Kondo effect.