Exact diagonalization study for nanographene: Modulation of charge and spin, magnetic phase diagram, and thermodynamics

We investigate the many-body-instability-driven electronic, magnetic, and thermodynamic properties of graphene nanoflakes described by an extended Hubbard model using exact diagonalization. Our exact results lead to a complete magnetic phase diagram in $n-V$ space, where $n$ is the filling and $V$ is the nonlocal Coulomb interaction. The phase diagram is found to consist of reentrant phases with net magnetic moment, separated by those with zero magnetic moment. The interplay of local and nonlocal Coulomb interaction, geometry, and filling gives rise to complex magnetic phases with coexisting antiferromagnetic and ferromagnetic correlations, of both short-range and long-range nature. A small change in temperature or in the strength of the nonlocal Coulomb interaction is found to drive the change in the magnetic state. The low-temperature thermodynamic behavior, driven by the crossover of eigenstates of contrasting magnetic characters, is signaled by a sharp peak in the specific heat.

Figure 1

Geometries of 13-site (left panel) and 14-site (right panel) nanographenes, constructed by linking three benzene rings. The C atoms have been numbered for the sake of identification of atoms. For easy identification, the atoms belonging to groups A, B, C, and D, are marked as closed circles, closed squares, open circles, and open squares, respectively. Refer to Table 1 and the text for details.

Figure 2

Magnetic phase diagram for NF13 (top panel) and NF14 (bottom panel) obtained by varying $V$ and $n$. The solutions with net and zero magnetic moment are colored red (dark gray) and yellow (white), respectively, while those with near degeneracy (energy difference $\le 0.001t)$ between the two solutions are shown as hatched areas.

Figure 3

The charge and magnetic moments at different sites for NF13. The red (dark gray), white, and cyan (light gray) spheres represent sites with depleted charge, accumulated charge, and average charge, respectively. Top panel: Filling of $13e^{-}$ and $V$ values of 0, $0.57t$, $1.00t$, $1.57t$, and $2.00t$. Bottom panel: Fillings of $17e^{-},18e^{-}$, and $19e^{-}$ for fixed $V$ value of $1.57t$. See text for details.

Figure 4

Spin-spin correlation functions (bottom panel) for NF13, for $17e^{-}$ filling and various different values of $V$. The corresponding charge distributions are shown in the upper panel. The antiferromagnetic and ferromagnetic correlations are shown by white and red (dark gray) bonds, respectively. See text for details.

Figure 5

Spin-spin correlation (bottom panel) for NF13 for $V=0.57t$ and different values of $e^{-}$ filling. The corresponding charge distributions are shown in the upper panel. The conventions adopted are the same as in Fig. 4.

Figure 6

Charge distribution (top panel) and spin-spin correlations (bottom panel) for NF14, for $V=1.0t$, and different values of $e^{-}$ filling. The color convention is the same as in Figs. 4 and 5.

Figure 7

Eigenvalue spectrum (top panel), magnetization (middle panel), and specific heat (bottom panel) for NF13, for filling of $8e^{-}$ and $V=1.00t$. In the eigenvalue spectrum, the magnetic (zero-moment) solutions are shown as black, solid (gray, dashed) lines.