Effect of electron localization on the edge-state spins in a disordered network of nanographene sheets

The magnetism and its dynamical behavior is investigated in relation to electron-localization effect for the edge-state spins of three-dimensional randomly networked nanographene sheets which interact weakly with each other. The electron transport is governed by Coulomb-gap variable-range hopping between nanographene sheets. At high temperatures, the electron spin resonance (ESR) signal with a feature of homogeneous spin system reveals the bottleneck effect in the spin relaxation to the lattice for a strongly coupled system of edge-state spins and conduction $\pi$ electrons, in a given nanographene sheet. Below 20 K, a discontinuous ESR line broadening accompanied by hole-burning proves the formation of an inhomogeneous spin state, indicating a static spatial distribution of on-resonance fields. This inhomogeneity originates from a distribution of the strengths of the ferrimagnetic moments on the individual nanographene sheets, taking into account that the constituent nanographene sheets with their shapes randomly varying have different strengths of ferrimagnetic moments. Strong electron localization below 20 K in the internanographene electron hopping is responsible for the crossover from the homogeneous spin state to the inhomogeneous one, in the latter of which ferrimagnetic short-range ordering is evident in the edge-state spin system.

Figure 1

Model structure of an arbitrary-shaped nanographene sheet, which consists of a combination of zigzag and armchair edges, the former of which has localized spins of edge-state ferromagnetically arranged. $J_0$ and $J_1$ are the intrazigzag-edge ferromagnetic and interzigzag-edge ferromagnetic/antiferromagnetic exchange interactions, respectively.

Figure 2

(a) Temperature dependence of ESR intensity in vacuum, at $1\mu \text{W}$ (▲) and $10\mu \text{W}$ (△) microwave power. (b) The corresponding peak-to-peak widths $\Delta H_{\text{PP}}$ of the ESR signal obtained after fitting the Lorentzian function. Insets of (a) and (b): zoomed-in curves in the range 4–35 K for $1\mu \text{W}$. (c) Inverse static susceptibility as a function of temperature in vacuum (◼) and the linear fit (solid line), measured at $H=1\text{T}$.

Figure 3

Microwave-power dependence of ESR intensity in vacuum, at 30 K (◼) and 10 K (◻). The blown-up view of low-power region is given in the inset. The solid lines are straight-line fit to the low-power region and dashed lines are guide to the eyes.

Figure 4

The ESR signals in vacuum at 10, 15, 20, and 25 K measured with 16 mW.

Figure 5

(a) Temperature dependence of ESR peak-to-peak widths in vacuum (◼) and oxygen pressures of 0.1 Pa (◻), 1 Pa (⊞), 5 Pa (▲), 10 Pa (●), and 20 Pa ($\ast$). Oxygen was introduced at room temperature, before cooling. (b) and (c) The corresponding normalized signal intensities.

Figure 6

(a) Temperature dependence of dc conductivity in vacuum. (b) Resistivity vs temperature plot corresponding to (a) and linear fit (dotted line). The arrow marks correspond to 57 and 8 K.