Graphene-based quantum heterospin graphs

TL;DR

The paper develops a three-step ab initio workflow to map graphene-based magnetic building blocks to the bilinear-biquadratic Heisenberg model $H_{BLBQ}$ and compute the low-energy spectrum via exact diagonalization. It predicts ferrimagnetic alternating spin chains with ground-state spin $S$ and degeneracy $g=2S+1$ that grow with chain length, and discovers a symmetry-protected double-$S$ degeneracy in the first excited state of three-leg spin graphs (3-LSGs) linked to $C_{3v}$ swapping symmetry. The degeneracy is robust to magnetic anisotropy but can be lifted by exchange-noise that breaks the symmetry, suggesting feasible experimental observation under moderate perturbations. The results provide a design blueprint for engineering quantum spin graphs with tailored degeneracies using graphene-based MBBs and extend to a broad class of heterospin nanostructures.

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.

Figures (8)

• Figure 1: (a-f) Magnetic dimer systems coupled by bilinear $J$ and biquadratic $\beta$ exchange constants. These dimers are composed of different graphene-based MBBs: S-1T, S-1/2T, and S-1/2O. The dimers are: (a) S-1T and S-1T, (b) S-1/2O and S-1/2O, (c) S-1/2T and S-1/2T, (d) S-1T and S-1/2O, (e) S-1T and S-1/2T, and (f) S-1/2O and S-1/2T.
• Figure 2: (a) shows the two types of ferrimagnetic alternating spin-1 and spin-1/2 chains that can be formed from different graphene MBBs. The top chain is made from S-1T and S-1/2T MBBs, while the bottom chain is made from S-1T and S-1/2O MBBs. Blue (red) arrows represent spin-1 (spin-1/2) sites. (b) shows the energy gap between the GS and the first excited state in blue, and the quantum spin number $S$ for the GS in red, as a function of the chain length $N$. Both calculations were performed using ED over Eq. (\ref{['H_heisenberg_chain']}) taking $\beta$=0.04.
• Figure 3: (a-c) 3-LSGs of lengths $N=7$, 10, and 13 MBBs, respectively. Each blue triangle either represents a spin-1 or spin-1/2 MBB (S-1T or S-1/2T), coupled via isotropic and biquadratic exchange interactions between nearest neighbors (see Table \ref{['table_coupling']}). Site labels are shown in black for the $N=7$, 10, and 13 3-LSGs. For $N=7$, $J_c$ denotes the isotropic exchange coupling between sites 3 and 6.
• Figure 4: (a–d) ED calculations based on the Hamiltonian given by Eq. (\ref{['H_heisenberg']}) for an $N=7$ three-leg spin graph composed of spin-1 MBBs. The exchange coupling $J_c$ connects sites three and six, following the labeling in Fig. \ref{['3legchain1']} (a), thereby coupling two chains: one with $N=2$ and the other with $N=5$. As $J_c$ increases, the two singlet states circled in green - one in the first ES and the other in the second ES - progressively approach each other in energy until they become degenerate at $J_c=J$.
• Figure 5: The construction of the cyclic swapping transformation $\hat{U}^{C^-}_{N}$ for a 3-LSG is illustrated as a subsequent action of the transformation $\hat{U}^{\sigma_3}_N$ and $\hat{U}^{\sigma_1}_N$. Colors indicate the different spin operators associated with the legs.