arXiv subjects

Ricardo Ortiz

Publications and source records attributed to Ricardo Ortiz.

15 recordsLinked to original sources

arXiv2026

Topological Engineering of a Frustrated Antiferromagnetic Triradical in Aza-Triangulene Architectures

Open-shell nanographenes provide a versatile platform to host unconventional magnetic states within their π-conjugated networks. Particularly appealing are graphene architectures that incorporate spatially separated radicals and tunable interactions, offering a scalable route toward spin-based quantum architectures. Triangulenes are ideal for this purpose, as their radical count scales with size, although strong hybridization prevents individual spin control. Here, we realize a radical reconfiguration strategy that transforms a single-radical aza-triangulene into three topologically protected spin states by covalently extending it with armchair anthene moieties of increasing length. Scanning tunnelling spectroscopy reveals emergent correlated spins forming a frustrated spin trimer whose interaction weakens with anthene length. This trend is captured by multi-reference electronic-structure calculations, which trace a progressive rise in polyradical character driven by the progressive reorganization of the correlated frontier orbitals into three edge-localized natural orbitals. Consequently, the initial single-radical doublet reorganizes into non-interacting edge spins, a molecular analog of a three-qubit quantum register.

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arXiv2025

Topological edge states in a double isomeric Class-II oligo(indenoindene)

I report the theoretical prediction of non-trivial physics in a one dimensional multiradical system consisting in fused six and five membered $π$-conjugated carbon rings, known as oligo(indenoindene) (OInIn). Topologically protected electronic states may emerge in fermionic chains if there is an alternation in the coupling of adjacent unpaired electrons, being described effectively by the Su-Schrieffer-Heeger (SSH) model. Class-II OInIn isomers act as tight-binding chains in the non-interacting regime, thus we can expect the emergence of SSH physics in an OInIn produced by the combination of two isomers that belong to this class. That is the case of the system studied in this manuscript, whose calculated non-interacting band structure shows a gap opening compared to the gapless pure isomeric forms, hosting ingap localized states at the chain termini depending on the termination, and a non-zero Zak phase that confirms the non-trivial topology. These results were consistent with spin unrestricted mean-field Hubbard and density functional theory calculations, showing antiferromagnetic unquenched local magnetic moments at the pentagons, and strong edge localization depending on the termination. This work advances in the understanding of the physics of non-alternant multiradical $π$-conjugated hydrocarbons.

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arXiv2025

Organic altermagnets based in two-dimensional nanographene frameworks

Altermagnetism stands as a third type of collinear magnetic order, whose band structure combines a net zero magnetization with a non-relativistic spin-splitting caused by a broken time reversal symmetry. So far, the strategy to design platforms displaying altermagnetism has relied mostly on inorganic crystals with d-metals as spin centers, where a representative example is the two-dimensional square lattice with antiparallel D2h magnetic blocks related by a pi/2 rotation. Despite the fact that there is no strong requirement for the magnetic atoms to be metals, the construction of an altermagnetic framework with light elements like carbon is challenging due to symmetric constrictions. We show how it is possible to overcome this by including non-alternant rings in pi-conjugated nanographenes. More specifically, dibenzo[ef,kl]heptalene, an S = 1 pi-conjugated hydrocarbon consisting of a graph of two fused heptagons and hexagons, represents a suitable building block for an altermagnetic 2D crystal. In this work, we confirm this hypothesis with DFT calculations of the spin polarized band structure, presenting a spin compensated ground state with broken time reversal symmetry, and a d-wave symmetry of the first valence and conduction bands. Consistent results are obtained for covalent organic frameworks based on dibenzo[ef,kl]heptalene units connected by linkers, paving the way for the realization of organic altermagnetic materials.

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arXiv2025

On-surface Synthesis of a Ferromagnetic Molecular Spin Trimer

Triangulenes are prototypical examples of open-shell nanographenes. Their magnetic properties, arising from the presence of unpaired $π$ electrons, can be extensively tuned by modifying their size and shape or by introducing heteroatoms. Different triangulene derivatives have been designed and synthesized in recent years, thanks to the development of on-surface synthesis strategies. Triangulene-based nanostructures with polyradical character, hosting several interacting spin units, can be challenging to fabricate but are particularly interesting for potential applications in carbon-based spintronics. Here, we combine pristine and N-doped triangulenes into a more complex nanographene, \textbf{TTAT}, predicted to possess three unpaired $π$ electrons delocalized along the zigzag periphery. We generate the molecule on an Au(111) surface and detect direct fingerprints of multi-radical coupling and high-spin state using scanning tunneling microscopy and spectroscopy. With the support of theoretical calculations, we show that its three radical units are localized at distinct parts of the molecule and couple via symmetric ferromagnetic interactions, which result in a $S=3/2$ ground state, thus demonstrating the realization of a molecular ferromagnetic Heisenberg-like spin trimer

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arXiv2024

A Route Toward the On-Surface Synthesis of Organic Ferromagnetic Quantum Spin Chains

Engineering sublattice imbalance is an intuitive way to induce high-spin ground states in bipartite polycyclic conjugated hydrocarbons (PCHs). Such high-spin molecules can be employed as building blocks of quantum spin chains, which are outstanding platforms to study many-body physics and fundamental models in quantum magnetism. Recent reports on the bottom-up synthesis of antiferromagnetic molecular spin chains provided insights into paradigmatic quantum phenomena such as fractionalization. In contrast to antiferromagnetism, demonstration of ferromagnetic coupling between PCHs has been scarce. Previous attempts in this direction were limited by the formation of non-benzenoid rings leading to spin quenching, or the use of spacer motifs that considerably weaken the magnitude of ferromagnetic exchange. Here, we demonstrate the on-surface synthesis of short ferromagnetic spin chains based on dibenzotriangulene (DBT), a PCH with a triplet ground state. Our synthetic strategy centers on achieving a direct (that is, without a spacer motif) majority-minority sublattice coupling between adjacent units. This leads to a global sublattice imbalance in spin chains scaling with the chain length, and therefore a ferromagnetic ground state with a strong intermolecular ferromagnetic exchange. By means of scanning probe measurements and multiconfigurational quantum chemistry calculations, we analyze the electronic and magnetic properties of ferromagnetic dimers and trimers of DBT, and confirm their quintet and septet ground states, respectively, with an intermolecular ferromagnetic exchange of 7 meV. Furthermore, we elucidate the role of sublattice coupling on magnetism through complementary experiments on antiferromagnetic DBT dimers with majority-majority and minority-minority couplings. We expect our proof-of-principle study to provide impetus for the design of purely organic ferromagnetic materials.

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arXiv2024

Tuning the Spin Interaction in Non-planar Organic Diradicals Through Mechanical Manipulation

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of $π$ character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with anti-parallel spins coupled through a conformational dependent interaction. The 2-OS molecule is a protected derivative of the Chichibabin's diradical, featuring a non-planar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule's magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs for a new class of all-carbon spin-crossover materials.

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arXiv2023

Bistability between $π$-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in non-linear optics and photovoltaics. Here, we report the generation of unsubstituted indeno[1,2-a]fluorene, the final and yet unreported parent indenofluorene isomer, on various surfaces by cleavage of two C-H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunneling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, while it exhibits charge bistability between neutral and anionic states on the lower work function surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits either of two ground states: an open-shell pi-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. Switching between open- and closed-shell states of a single molecule is observed by changing its adsorption site on NaCl.

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arXiv2023

Olympicene radicals as building blocks of two-dimensional anisotropic networks

I propose monoradical nanographenes without C3 symmetry as building blocks to design two-dimensional (2D) carbon crystals. As representative examples I study the honeycomb and Kagome lattices, showing that by replacing the sites with olympicene radicals the band dispersion near the Fermi energy corresponds, respectively, to that of Kekulé/anti-Kekulé graphene and breathing Kagome tight-binding models. As a consequence, finite islands of these new crystals present corner states close to the Fermi energy, just like the parent models. In the case of Kekulé/anti-Kekulé graphene, such states are topologically protected, standing as examples of second-order topological insulators with a non-zero Z2- or Z6-Berry phase. Differently, those of the breathing Kagome lattice are of trivial nature, but the ground state has been predicted to be a spin liquid in the antiferromagnetic Heisenberg model. Hence, 2D systems made of low-symmetric nanographenes may be convenient platforms to explore exotic physics in carbon materials.

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arXiv2022

Magnetic frustration and fractionalization in oligo(indenoindenes)

Poly(indenoindenes) are π-conjugated ladder carbon polymers with alternating hexagons and pentagons hosting one unpaired electron for each five-membered ring in the open-shell limit. Here we study the main magnetic interactions that are present in finite oligo(indenoindenes) (OInIn), classifying the six possible isomers in two different classes of three isomers each. One class can be rationalized by frustrated S = 1/2 Heisenberg chains, with ferromagnetic interactions between neighbour sites and antiferromagnetic interactions between the next neighbours. The other class is characterized by the more trivial antiferromagnetic order. Employing several levels of theory we further show that the ground state of one of the isomers is a valence-bond solid (VBS) of ferromagnetic dimers (S = 1). This is topologically similar to that of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is known to show fractional S = 1/2 states at the edges.

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arXiv2021

Renormalization of spin excitations and Kondo effect in open shell nanographenes

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.

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arXiv2021

Observation of fractional edge excitations in nanographene spin chains

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.

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arXiv2020

Giant magnetic exchange coupling in rhombus-shaped nanographenes with zigzag periphery

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.

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arXiv2020

Collective All-Carbon Magnetism in Triangulene Dimers

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.

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arXiv2020

Probing local moments in nanographenes with electron tunneling spectroscopy

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.

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arXiv2019

Exchange rules for diradical π-conjugated hydrocarbons

A variety of planar π-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.

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