Mechanism of length-induced magnetism in polyacene molecules

Within the celebrated Su-Schrieffer-Heeger model including electron-lattice and electron-electron interactions, the electronic ground state of polyacene ($n$-acene) is studied as a function of molecular length $n$. The results demonstrate that the ground state exhibits a phase transition from a nonmagnetic state to an antiferromagnetic state at a critical length of $n=7$. The magnetism is explained by calculating the lattice distortion and the related average hopping rate of the π electrons. It is revealed that in polyacenes, there exist two competing mechanisms that minimize the molecular energy, namely the lattice dimerization and the formation of an antiferromagnetic spin density. Since the dimerization is restricted to the regions near the ends of the molecules the former mechanism is dominant for short molecules, which therefore assume a nonmagnetic state. When the length is increased beyond the critical value, the lattice dimerization in the middle of the molecule is reduced and a rapid drop of the average hopping rate occurs. This makes the second mechanism dominant and the associated antiferromagnetic state is stabilized. The effect of different interaction strengths and values of hopping integrals on the critical length is discussed. The results are confirmed by first-principles calculations. Suggestions for the design of organic antiferromagnets with a similar ladder structure are also given.

Figure 1

Simplified structure of polyacene molecules.

Figure 2

Relative total energy $\mathrm{\Delta }{E}_{\mathrm{total}}=E_{ms}-E_{\mathrm{NM}}$ of the molecule as a function of length. $ms$ can be taken as NM, AFM, and FM states, respectively.

Figure 3

Spin density on the upper and lower chains from $n=5$ to $n=8$ in the ground state.

Figure 4

Total spin on one chain $\left(M_j\right)$ and average spin per ring $\left(m_j\right)$ on one chain as functions of length.

Figure 5

Probability density of the spin-up and spin-down HOMOs in the ground state for $n=6$ and 7.

Figure 6

Lattice distortion from $n=5$ to $n=11$ in the ground state.

Figure 7

Average hopping rate $T_n$ along one chain with $n$ from 4 to 11. The inset shows the difference $\mathrm{\Delta }{T}_n=T_n-T_{n-1}$.

Figure 8

Energy gap of the molecule as a function of length for the NM, AFM, and FM states.

Figure 9

(a) Spin density in one chain for $n=4$ with and without e-l coupling α. (b) Critical length $n_c$ of the NM-AFM transition as a function of α.

Figure 10

Critical length $n_c$ of the NM-AFM transition as a function of the value of (a) $t_{\perp }$ and (b) u.

Figure 11

(a) First-principles results for the relative total energy as a function of length for the NM, AFM, and FM states. (b) Spin density and bond lengths for $n=6$ and 7. Insets: spin density for $n=6$ and 7. The pink color denotes positive values and the blue color negative values.