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arXiv:2507.23360 · Physical review. B./Physical review. B

Graphene-based quantum heterospin graphs

Gabriel Martínez‐Carracedo, Amador García‐Fuente, László Oroszlány, László Szunyogh, Jaime Ferrer

Published Nov 24, 2025• 0 citations
arXivHTMLPDF

Abstract

We investigate from first principles a variety of low-dimensional open quantum spin systems based on magnetic nanographene structures that contain spin-1/2 and spin-1 triangulenes and/or olympicenes. These graphene nanostructures behave as localized spins and can be effectively described by a quantum bilinear-biquadratic Heisenberg Hamiltonian, for which we will compute the energy spectrum and the quantum numbers associated with the low-energy eigenstates. We propose the experimental realization of antiferromagnetic alternating spin chains using these graphene nanostructures, which result in ferrimagnetic systems whose ground state spin and degeneracy depend on the length of the chain. We identify a double degeneracy in the total spin quantum number $S$ of the first excited state in three-leg spin graphs (3-LSGs) and other heterospin nanostructures, which depends on both the number of sites and the spin species, and originates from the swapping transformation symmetry of the Hamiltonian. Numerical simulations indicate that this degeneracy remains largely robust for $N=7$ spin-1 3-LSGs under realistic perturbations present in experimental conditions.

DOI
10.1103/v3fm-lvsh

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We investigate from first principles a variety of low-dimensional open quantum spin systems based on magnetic nanographene structures that contain spin-1/2 and spin-1 triangulenes and/or olympicenes. These graphene nanostructures behave as localized spins and can be effectively described by a quantum bilinear-biquadratic Heisenberg Hamiltonian, for which we will compute the energy spectrum and the quantum numbers associated with the low-energy eigenstates. We propose the experimental realization of antiferromagnetic alternating spin chains using these graphene nanostructures, which result in ferrimagnetic systems whose ground state spin and degeneracy depend on the length of the chain. We identify a double degeneracy in the total spin quantum number SSS of the first excited state in three-leg spin graphs (3-LSGs) and other heterospin nanostructures, which depends on both the number of sites and the spin species, and originates from the swapping transformation symmetry of the Hamiltonian. Numerical simulations indicate that this degeneracy remains largely robust for N=7N=7N=7 spin-1 3-LSGs under realistic perturbations present in experimental conditions.
Magnetic nanographenes are emerging as versatile building blocks for artificial spin lattices, enabling the exploration of flagship one-dimensional quantum-magnetism models with unprecedented control. The spin-1 Heisenberg model, including bilinear and biquadratic exchange, was first realized using [3]-triangulenes, revealing the Haldane phase. More recently, Clar’s goblets enabled the spin-1/2 Heisenberg model with exchange alternation, uncovering additional topological phases. Here we show that spin-1 nanographenes can be used to explore bond-alternating chains both in the Haldane phase and beyond it, in a dimerized phase with emergent edge spin-1. We use density matrix renormalization group (DMRG) to analyze how biquadratic exchange, which is known to be large in spin-1 nanographenes, determines the phase transition boundary. Combining multiconfigurational and first-principles calculations, we identify two realistic candidates to realize these two different phases: the recently synthesized extended Clar’s goblet and a passivated [4]-triangulene. We demonstrate how to distinguish these phases experimentally using inelastic electron tunneling spectroscopy, paving the way for their observation.
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The low-energy structures of the quantum ferrimagnetic Heisenberg chain consisting of (5/2, 1/2, 1/2) trimers are investigated theoretically. The results of the linear spin-wave theory are compared with those from the numerical exact diagonalization calculation and the matrix product method for the lowest optical mode. The temperature behaviour of thermodynamical properties such as magnetic susceptibility, specific heat and entropy are analysed in the framework of the modified spin-wave theory. The results of the calculations are used to explain the experimental data obtained for the molecule-based heterospin magnets [Mn(hfac) 2 BNO R ] (R = H, F, Cl, Br) with one-dimensional chain structure.
The manifestations of topological effects in finite antiferromagnetic Heisenberg chains are examined by density-matrix renormalization-group techniques. We find that the difference between integer and half-integer spin chains shows up in ground-state energy per site when the length of the spin chain is longer than \ensuremath{\sim}\ensuremath{\xi}, where $\ensuremath{\xi}\ensuremath{\sim}\mathrm{exp}(\ensuremath{\pi}S)$ is a spin-spin correlation length, for spin magnitudes S up to 5/2.5/2.5/2. For open chains with spin magnitudes S=5/2S=5/2S=5/2 to S=5,S=5,S=5, we verify that end states with fractional spin quantum numbers ${S}^{\ensuremath{'}}$ exist and are visible in the structure of the low-energy excitation spectrum even when the chain length is much smaller than the correlation length \ensuremath{\xi}. The robustness of end states points to the possibility of the existence of general hidden topological order in quantum spin chains with spin magnitudes S> 1.S>~1.S> 1.
Inferring microscopic Hamiltonians from experimental data is a central challenge in quantum materials and quantum simulation. In low-dimensional spin systems, exchange interactions are often assumed to be spatially uniform, despite structural and environmental inhomogeneities that can locally modify the coupling. Here, we leverage a local, length-independent machine learning methodology to reconstruct spatially modulated exchange interactions directly from inelastic scanning tunneling spectroscopy maps. We demonstrate this approach with nanographene spin chains, identifying both near-uniform and inhomogeneous regimes across the synthesized magnets. The reconstructed models quantitatively reproduce the experimental spectra and recover the correct scaling of the excitation gap with system size. Our results establish a general strategy to bridge local spectroscopic measurements with effective many-body Hamiltonians.