Hyperfine interactions in open-shell planar $s{p}^2$-carbon nanostructures

Abstract

We investigate hyperfine interaction (HFI) using density-functional theory for several open-shell planar $s{p}^2$-carbon nanostructures displaying $\pi$ magnetism. Our prototype structures include both benzenoid ([$n$]triangulenes and a graphene nanoribbon) as well as non-benzenoid (indene, fluorene, and indene[2,1-b]fluorene) molecules. Our results obtained with ORCA indicate that isotropic Fermi contact and anisotropic dipolar terms contribute in comparable strength, rendering the HFI markedly anisotropic. We find that the magnitude of HFI in these molecules can reach more than 100 MHz, thereby opening up the possibility of experimental detection via methods such as electron spin resonance-scanning tunneling microscopy (ESR-STM). Using these results, we obtain empirical models based on $\pi$-spin polarizations at carbon sites. These are defined by generic $s{p}^2$ HFI fit parameters which are derived by matching the computed HFI couplings to $\pi$-spin polarizations computed with methods such as ORCA, SIESTA, or mean-field Hubbard (MFH) models. This approach successfully describes the Fermi contact and dipolar contributions for ${}^{13}$C and ${}^1$H nuclei. These fit parameters allow to obtain hyperfine tensors for large systems where existing methodology is not suitable or computationally too expensive. As an example, we show how HFI scales with system size in [$n$]triangulenes for large $n$ using MFH. We also discuss some implications of HFI for electron-spin decoherence and for coherent nuclear dynamics.

22 pages, 9 figures; version published Phys.Rev.B

References in corpus (20)

• Graphene Spintronics
• Emergence of magnetism in graphene materials and nanostructures
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin qubits in graphene quantum dots
• Spin-orbit gap of graphene: First-principles calculations
• Magnetism in graphene nano-islands
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Improvements on non-equilibrium and transport Green function techniques: the next-generation transiesta
• Dissipative Phase Transition in Central Spin Systems
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Ab initio supercell calculations on nitrogen-vacancy center in diamond: its electronic structure and hyperfine tensors
• Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
• First principles study of magnetism in nanographenes
• Quantum-Coherent Nanoscience
• Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots
• Hyperfine Interactions in Graphene and Related Carbon Nanostructures
• Direct observation of the magnetic ground state of the two smallest triangular nanographenes
• Non-benzenoid high-spin polycyclic hydrocarbons generated by atom manipulation
• First-principles hyperfine tensors for electrons and holes in GaAs and silicon
• Magnetic frustration and fractionalization in oligo(indenoindenes)

Cited by in corpus (1)

• High mobility transport in isotopically-enriched ${}^{12}$C and ${}^{13}$C exfoliated graphene