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Haldane's seminal work established two fundamentally different types of excitation spectra for antiferromagnetic Heisenberg quantum spin chains: gapped excitations in integer-spin chains and gapless excitations in half-integer-spin chains. In finite-length half-integer spin chains, quantization, however, induces a gap in the excitation spectrum, with the upper bound given by the Lieb-Schulz-Mattis (LSM) theorem. Here, we investigate the length-dependent excitations in spin-1/2 Heisenberg chains obtained by covalently linking olympicenes--Olympic rings shaped nanographenes carrying spin-1/2--into one-dimensional chains. The large exchange interaction (J~38 mV) between olympicenes and the negligible magnetic anisotropy in these nanographenes make them an ideal platform for studying quantum spin excitations, which we directly measure using inelastic electron tunneling spectroscopy. We observe a power-law decay of the lowest excitation energy with increasing chain length L, remaining below the LSM boundary. In a long chain with L = 50, a nearly V-shaped excitation continuum is observed, reinforcing the system's gapless nature in the thermodynamic limit. Finally, we visualize the standing wave of a single spinon confined in odd-numbered chains using low-bias current maps. Our results provide compelling evidence for the realization of a one-dimensional analog of a gapless spin liquid., Comment: 5 figures. arXiv admin note: text overlap with arXiv:2402.13590

Understanding and engineering the coupling of spins in nanomaterials is of central importance for designing novel devices. Graphene nanostructures with {\pi}-magnetism offer a chemically tunable platform to explore quantum magnetic interactions. However, realizing spin chains bearing controlled odd-even effects with suitable nanographene systems is challenging. Here, we demonstrate the successful on-surface synthesis of spin-1/2 antiferromagnetic Heisenberg chains with parity-dependent magnetization based on antiaromatic diaza-hexa-peri-hexabenzocoronene (diaza-HBC) units. Using distinct synthetic strategies, two types of spin chains with different terminals were synthesized, both exhibiting a robust odd-even effect on the spin coupling along the chain. Combined investigations using scanning tunneling microscopy, non-contact atomic force microscopy, density functional theory calculations, and quantum spin models confirmed the structures of the diaza-HBC chains and revealed their magnetic properties, which has an S = 1/2 spin per unit through electron donation from the diaza-HBC core to the Au(111) substrate. Gapped excitations were observed in even-numbered chains, while enhanced Kondo resonance emerged in odd-numbered units of odd-numbered chains due to the redistribution of the unpaired spin along the chain. Our findings provide an effective strategy to construct nanographene spin chains and unveil the odd-even effect in their magnetic properties, offering potential applications in nanoscale spintronics.

CrI3 is a layered ferromagnetic insulator that has recently attracted enormous interest as it was the first example of a stand-alone monolayer ferromagnet, paving the way towards the study of two-dimensional magnetic materials and their use as building blocks of hybrid van der Waals layered heterostructures. Here we go one step down in the dimensionality ladder and report the synthesis and characterization of a tubular one-dimensional van der Waals heterostructure where CrI3 nanotubes are encapsulated within multiwall carbon nanotubes, integrating a magnetic insulator and a conductor. By means of the capillary filling of multi-wall carbon nanotubes (MWCNT), we obtained single-wall CrI3 nanotubes with diameters ranging between 2 nm and 10 nm, with an average of 5.3 nm. Using aberration corrected electron microscopy in combination with spectroscopic techniques we confirm the structure and chemical composition of the nanotubes. SQUID measurements, combined with element-specific X-ray magnetic circular dichroism (XMCD) indicate unequivocally that the Cr atoms in encapsulated CrI3 nanotubes are magnetic with a collective state compatible with a radial magnetization state predicted both by first-principles calculations and a model Hamiltonian. Our results represent a step forward in establishing 1D van der Waals heterostructures as a playground for the exploration of non-collinear magnetic states arising from the interplay between magnetic anisotropy and curvature in tubular geometries., Comment: 19 pages with 5 figures

Quantum control techniques play an important role in manipulating and harnessing the properties of different quantum systems, including isolated atoms. Here, we propose to achieve quantum control over a single on-surface atomic spin using Landau-Zener-St\"uckelberg-Majorana (LZSM) interferometry implemented with Scanning Tunneling Microscopy (STM). Specifically, we model how the application of time-dependent, non-resonant AC electric fields across the STM tip-surface gap makes it possible to achieve precise quantum state manipulation in an isolated Fe atom on a MgO/Ag(100) surface. We propose a protocol to combine Landau Zener tunneling with LZSM interferometry that permits one to measure the quantum spin tunneling of an individual Fe atom. The proposed experiments can be implemented with ESR-STM instrumentation, opening a new venue in the research of on-surface single spin control., Comment: 6 pages, 4 figures

Unlocking the potential of topological order within many-body spin systems has long been a central pursuit in the realm of quantum materials. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here, we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg (AH) chains[1] with antiferromagnetic couplings $J_1$ and $J_2$ by covalently linking Clar's goblets -- nanographenes each hosting two antiferromagnetically-coupled unpaired electrons[2]. Utilizing scanning tunneling microscopy, we exert atomic-scale control over the spin chain lengths, parities and exchange-coupling terminations, and probe their magnetic response by means of inelastic tunneling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons[3]. Besides, the triplon dispersion relation is successfully extracted from the spatial variation of tunneling spectral amplitudes. Furthermore, depending on the parity and termination of chains, we observe varying numbers of in-gap $S=1/2$ edge spins, enabling the determination of the degeneracy of distinct topological ground states in the thermodynamic limit-either 1, 2, or 4. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our experimental findings, corroborated by theoretical calculations, present a phase-controlled many-body platform, opening promising avenues toward the development of spin-based quantum devices.

The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin-$\frac{1}{2}$ Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin-$\frac{1}{2}$ wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doublon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is bound to be most relevant., Comment: Main text: 4 pages, 3 figures. Supp. Mat.: 10 pages, 9 figures

Electron-spin resonance carried out with scanning tunneling microscopes (ESR-STM) is a recently developed experimental technique that is attracting enormous interest on account of its potential to carry out single-spin on-surface resonance with subatomic resolution. Here we carry out a theoretical study of the role of tip-adatom interactions and provide guidelines for choosing the experimental parameters in order to optimize spin resonance measurements. We consider the case of the Fe adatom on a MgO surface and its interaction with the spin-polarized STM tip. We address three problems: first, how to optimize the tip-sample distance to cancel the effective magnetic field created by the tip on the surface spin, in order to carry out proper magnetic field sensing. Second, how to reduce the voltage dependence of the surface-spin resonant frequency, in order to minimize tip-induced decoherence due to voltage noise. Third, we propose an experimental protocol to infer the detuning angle between the applied field and the tip magnetization, which plays a crucial role in the modeling of the experimental results., Comment: 10 pages, 5 Figures

Coherent control of individual atomic and molecular spins on surfaces has recently been demonstrated by using electron spin resonance (ESR) in a scanning tunneling microscope (STM). Here we present a combined experimental and modeling study of the ESR of a single hydrogenated Ti atom that is exchange-coupled to a Fe adatom located in 0.6-0.8 nm away. Continuous wave and pulsed ESR of the Ti spin showed a Rabi rate with two contributions, one from the tip and the other from the Fe, whose spin interactions with Ti were modulated by the radio-frequency electric field. The Fe contribution is comparable to the tip, as revealed from its dominance when the tip was retracted, and tunable using a vector magnetic field. Our new ESR scheme allows on-surface individual spins to be addressed and coherently controlled without the need for magnetic interaction with a tip. This study establishes a feasible implementation of spin-based multi-qubit systems on surfaces.

Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming interacting spins lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure, and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard-$U$ energy scale, and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of $U$, and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled $S=1/2$ phenalenyl triangulenes, using multi-configurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions., Comment: 14 pages; 10 figures

For the past three decades, nanoscience has widely affected many areas in physics, chemistry, and engineering, and has led to numerous fundamental discoveries as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds a burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this manuscript according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system such as charge, spin, mechanical motion, and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations., Comment: 34 pages, 6 figures, 2 boxes

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect, solitons in one-dimensional conducting polymers and Majorana states in topological superconductors. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk and, remarkably, S = 1/2 edge states at the chain termini, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order. Here, we use on-surface synthesis to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunneling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated quantum spin liquid phases in purely organic materials, with the potential for the realization of measurement-based quantum computation., Comment: 23 pages, 4 main figures and 7 extended data figures; supplementary information containing additional data is included

We study spin excitations and Kondo effect in open-shell nanographenes, motivated by recent scanning tunneling inelastic spectroscopy experiments. Specifically, we consider three systems, the triangulene, the extended triangulene with rocket shape, both with an $S=1$ ground state, and a triangulene dimer with $S=0$ on account of intermolecular exchange. We focus on the consequences of hybridization of the nanographene zero-modes with a conducting substrate on the $dI/dV$ lineshapes associated with spin excitations. The partially filled nanographene zero-modes coupled to the conduction electrons in the substrate constitute multi-orbital Anderson impurity models that we solve in the one-crossing approximation which treats the coupling to the substrate to infinite order. We find that the coupling to the substrate leads to (i) renormalization of the spin flip excitation energies of the bare molecule, (ii) broadening of the spectral features and (iii) the emergence of zero bias Kondo peaks for the $S=1$ ground states. The calculated substrate induced shift of the spin excitation energies is found to be significantly larger than their broadening, which implies that this effect has to be considered when comparing experimental results and theory., Comment: 9 pages, 4 figures; replaced with revised version, accepted in Phys. Rev. B

The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically-motivated ans\"{a}tze on quantum hardware is therefore important to achieve quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller Wave Function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the $U = 0$ limit of the model is prepared. In the second, the non-unitary Gutzwiller projection that selectively removes states with doubly-occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the $|0\rangle$ state confirms the projection was made. Due to its non-deterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength $U/t$. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed., Comment: 5 pages + Supplemental Material

Nanographenes with zigzag edges are predicted to manifest non-trivial pi-magnetism resulting from the interplay of hybridization of localized frontier states and Coulomb repulsion between valence electrons. This provides a chemically tunable platform to explore quantum magnetism at the nanoscale and opens avenues toward organic spintronics. The magnetic stability in nanographenes is thus far limited by the weak magnetic exchange coupling which remains below the room temperature thermal energy. Here, we report the synthesis of large rhombus-shaped nanographenes with zigzag periphery on gold and copper surfaces. Single-molecule scanning probe measurements unveil an emergent magnetic spin-singlet ground state with increasing nanographene size. The magnetic exchange coupling in the largest nanographene, determined by inelastic electron tunneling spectroscopy, exceeds 100 meV or 1160 K, which outclasses most inorganic nanomaterials and remarkably survives on a metal electrode., Comment: 4 figures plus supplementary information

Triangular zigzag nanographenes, such as triangulene and its pi-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 - of immense fundamental and technological relevance. As a first step toward 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 inter-triangulene magnetic coupling., Comment: 4 figures plus supporting information

The emergence of local moments in graphene zigzag edges, grain boundaries, vacancies and sp3 defects has been widely studied theoretically. However, conclusive experimental evidence is scarce. Recent progress in on-surface synthesis has made it possible to create nanographenes, such as triangulenes, with local moments in their ground states, and to probe them using scanning tunnelling microscope (STM) spectroscopy. Here we review the application of the theory of sequential and cotunneling transport to relate the dI/dV spectra with the spin properties of nanographenes probed by STM. This approach permits us to connect the dI/dV with the many-body energies and wavefunctions of the graphene nanostructures. We apply this method describing the electronic states of the nanographenes by means of exact diagonalization of the Hubbard model within a restricted Active Space. This permits us to provide a proper quantum description of the emergence of local moments in graphene and its interplay with transport. We discuss the results of this theory in the case of diradical nanographenes, such as triangulene, rectangular ribbons and the Clar goblet, that have been recently studied experimentally by means of STM spectroscopy. This approach permits us to calculate both the dI/dV spectra, that yields excitation energies, as well as the atomically resolved conductivity maps, that provide information on the wavefunctions of the collective spin modes.

We address the problem of electronic and nuclear spin resonance of an individual atom on a surface driven by a scanning tunnelling microscope. Several mechanisms have been proposed so far, some of them based on the modulation of exchange and crystal field associated to a piezoelectric displacement of the adatom driven by the RF tip electric field. Here we consider a new mechanism, where the piezoelectric displacement modulates the g factor anisotropy, leading both to electronic and nuclear spin flip transitions. We discuss thoroughly the cases of Ti-H (S = 1/2) and Fe (S = 2) on MgO, relevant for recent experiments. We model the system using two approaches. First, an analytical model that includes crystal field, spin orbit coupling and hyperfine interactions. Second, we carry out density functional based calculations. We find that the modulation of the anisotropy of the g tensor due to the piezoelectric displacement of the atom is an additional mechanism for STM based single spin resonance, that would be effective in S = 1/2 adatoms with large spin orbit coupling. In the case of Ti-H on MgO, we predict a modulation spin resonance frequency driven by the DC electric field of the tip., Comment: 15 pages, 7 figures

A variety of planar {\pi}-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states, as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

Shrinking spintronic devices to the nanoscale ultimately requires localized control of individual atomic magnetic moments. At these length scales, the exchange interaction plays important roles, such as in the stabilization of spin-quantization axes, the production of spin frustration, and creation of magnetic ordering. Here, we demonstrate the precise control of the exchange bias experienced by a single atom on a surface, covering an energy range of four orders of magnitude. The exchange interaction is continuously tunable from milli-eV to micro-eV by adjusting the separation between a spin-1/2 atom on a surface and the magnetic tip of a scanning tunneling microscope (STM). We seamlessly combine inelastic electron tunneling spectroscopy (IETS) and electron spin resonance (ESR) to map out the different energy scales. This control of exchange bias over a wide span of energies provides versatile control of spin states, with applications ranging from precise tuning of quantum state properties, to strong exchange bias for local spin doping. In addition we show that a time-varying exchange interaction generates a localized AC magnetic field that resonantly drives the surface spin. The static and dynamic control of the exchange interaction at the atomic-scale provides a new tool to tune the quantum states of coupled-spin systems.

Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises ultrathin insulating multiferroics, spin liquids, and ferromagnets, but new characterization methods are required to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and inter-layer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95%, 300%, and 550% for bilayer, trilayer, and tetralayer CrI3 barriers, respectively. We further measure inelastic tunneling spectra for our junctions, unveiling a rich spectrum of collective magnetic excitations (magnons) in CrI3. Our results establish vertical tunneling as a versatile probe of magnetism in atomically thin insulators.

Quantum spin networks having engineered geometries and interactions are eagerly pursued for quantum simulation and access to emergent quantum phenomena such as spin liquids. Spin-1/2 centers are particularly desirable because they readily manifest coherent quantum fluctuations. Here we introduce a controllable spin-1/2 architecture consisting of titanium atoms on a magnesium oxide surface. We tailor the spin interactions by atomic-precision positioning using a scanning tunneling microscope (STM), and subsequently perform electron spin resonance (ESR) on individual atoms to drive transitions into and out of quantum eigenstates of the coupled-spin system. Interactions between the atoms are mapped over a range of distances extending from highly anisotropic dipole coupling, to strong exchange coupling. The local magnetic field of the magnetic STM tip serves to precisely tune the superposition states of a pair of spins. The precise control of the spin-spin interactions and ability to probe the states of the coupled-spin network by addressing individual spins will enable exploration of quantum many-body systems based on networks of spin-1/2 atoms on surfaces.

Two-dimensional semiconducting materials are particularly appealing for many applications. Although theory predicts a large number of two-dimensional materials, experimentally only a few of these materials have been identified and characterized comprehensively in the ultrathin limit. Lead iodide, which belongs to the transition metal halides family and has a direct bandgap in the visible spectrum, has been known for a long time and has been well characterized in its bulk form. Nevertheless, studies of this material in the nanometer thickness regime are rather scarce. In this article we demonstrate an easy way to synthesize ultrathin, highly crystalline flakes of PbI2 by precipitation from a solution in water. We thoroughly characterize the produced thin flakes with different techniques ranging from optical and Raman spectros-copy to temperature-dependent photoluminescence and electron microscopy. We compare the results to ab initio calculations of the band structure of the material. Finally, we fabricate photodetectors based on PbI2 and study their optoelectronic properties., Comment: main text 20 pages + 10 figures, supporting information 16 pages + 17 figures

The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of the tight-binding model, however not many experimental approaches exist that allow to tailor artificial crystal lattices using a bottom-up approach. The ability to engineer and study atomically crafted designer materials by scanning tunnelling microscopy and spectroscopy (STM/STS) helps to understand the emergence of material properties. Here, we use atom manipulation of individual vacancies in a chlorine monolayer on Cu(100) to construct one- and two-dimensional structures of various densities and sizes. Local STS measurements reveal the emergence of quasiparticle bands, evidenced by standing Bloch waves, with tuneable dispersion. The experimental data are understood in terms of a tight-binding model combined with an additional broadening term that allows an estimation of the coupling to the underlying substrate., Comment: 7 figures, 12 pages, main text and supplementary material

We study a graphene Hall probe located on top of a magnetic surface as a detector of skyrmions, using as working principle the anomalous Hall effect produced by the exchange interaction of the graphene electrons with the non-coplanar magnetization of the skyrmion. We study the magnitude of the effect as a function of the exchange interaction, skyrmion size and device dimensions. Our calculations for multiterminal graphene nanodevices, working in the ballistic regime, indicate that for realistic exchange interactions a single skyrmion would give Hall voltages well within reach of the experimental state of the art. The proposed device could act as an electrical transducer that marks the presence of a single skyrmion in a nanoscale region, paving the way towards the integration of skyrmion-based spintronics and graphene electronics., Comment: 8 pages, 6 figures

To push commercial electronics beyond its current size limits, atomic-scale communication channels and logic units need to be designed, making the use of quantum entities an imperative. In this regime, quantum fluctuations naturally become prominent, and are generally considered to be detrimental. Here we show that for spin-based information processing, these fluctuations can be uniquely exploited to gate the flow of classical binary information across a magnetic chain. Moreover, this information flow can be controlled with a modest external magnetic field that drives the system through different many-body quantum phases in which the orientation of the final spin does or does not reflect the orientation of the initial input. Our results are general for a wide class of anisotropic spin chains that act as magnetic cellular automata, and suggest that quantum fluctuations may play a unique role in driving classical information flow at the atomic scale., Comment: 5+7 pages, 4+5 figures

We report on the large-scale synthesis of highly oriented ultrathin MoO3 layers using a simple and low-cost atmospheric pressure by van der Waals epitaxy growth on muscovite mica substrates. By this method we are able to synthetize high quality centimeter-scale MoO3 crystals with thicknesses ranging from 1.4 nm (two layers) up to a few nanometers. The crystals can be easily transferred to an arbitrary substrate (such as SiO2) by a deterministic transfer method and extensively characterized to demonstrate the high quality of the resulting crystal. We also study the electronic band structure of the material by density functional theory calculations. Interestingly, the calculations demonstrate that bulk MoO3 has a rather weak electronic interlayer interaction and thus it presents a monolayer-like band structure. Finally, we demonstrate the potential of this synthesis method for optoelectronic applications by fabricating large-area field-effect devices (10 micrometers by 110 micrometers in lateral dimensions), finding responsivities of 30 mA/W for a laser power density of 13 mW/cm2 in the UV region of the spectrum and also as an electron acceptor in a MoS2-based field-effect transistor., Comment: Main text (11 figures) and supporting information (11 figures)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co and Ni) deposited on a Cu$_2$N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent Nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent Nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal., Comment: 12 pages, 14 figures, regular article

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non- magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In a first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized-gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effect of spin-orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both, the undistorted and Jahn-Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed., Comment: 10 pages, 7 Figures

The properties of quantum systems interacting with their environment, commonly called open quantum systems, can be strongly affected by this interaction. While this can lead to unwanted consequences, such as causing decoherence in qubits used for quantum computation, it can also be exploited as a probe of the environment. For example, magnetic resonance imaging is based on the dependence of the spin relaxation times of protons in water molecules in a host's tissue. Here we show that the excitation energy of a single spin, which is determined by magnetocrystalline anisotropy and controls its stability and suitability for use in magnetic data storage devices, can be modified by varying the exchange coupling of the spin to a nearby conductive electrode. Using scanning tunnelling microscopy and spectroscopy, we observe variations up to a factor of two of the spin excitation energies of individual atoms as the strength of the spin's coupling to the surrounding electronic bath changes. These observations, combined with calculations, show that exchange coupling can strongly modify the magnetic anisotropy. This system is thus one of the few open quantum systems in which the energy levels, and not just the excited-state lifetimes, can be controllably renormalized. Furthermore, we demonstrate that the magnetocrystalline anisotropy, a property normally determined by the local structure around a spin, can be electronically tuned. These effects may play a significant role in the development of spintronic devices5 in which an individual magnetic atom or molecule is coupled to conducting leads., Comment: 15 pages, 3 figures, Nature Nanotechnology 9, 64 (2014)

We study the electronic structure of a heterojunction made of two monolayers of MoS2 and WS2. Our first-principles density functional calculations show that, unlike in the homogeneous bilayers, the heterojunction has an optically active band-gap, smaller than the ones of MoS2 and WS2 single layers. We find that that the optically active states of the maximum valence and minimum conduction bands are localized on opposite monolayers, and thus the lowest energy electron-holes pairs are spatially separated. Our findings portrait the MoS2-WS2 bilayer as a prototypical example for band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.