Spatial mobility fluctuation induced giant linear magnetoresistance in multilayered graphene foam

Giant, positive, and near-temperature-independent linear magnetoresistance (LMR), as large as 340%, was observed in graphene foam with a three-dimensional flexible network. Careful analysis of the magnetoresistance revealed that Shubnikov–de Haas (SdH) oscillations occurred at low temperatures and decayed with increasing temperature. The average classical mobility ranged from 300 (2 K) to 150 (300 K) $\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, which is much smaller than that required by the observed SdH oscillations. To understand the mechanism behind the observation, we performed the same measurements on the microsized graphene sheets that constitute the graphene foam. Much more pronounced SdH oscillations superimposed on the LMR background were observed in these microscaled samples, which correspond to a quantum mobility as high as $26,500\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. Moreover, the spatial mobility fluctuated significantly from $64,200\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ to $1370\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, accompanied by a variation of magnetoresistance from near 20,000% to less than 20%. The presence of SdH oscillations actually excludes the possibility that the observed LMR originated from the extreme quantum limit, because this would demand all electrons to be in the first Landau level. Instead, we ascribe the large LMR to the second case of the classical Parish and Littlewood model, in which spatial mobility fluctuation dominates electrical transport. This is an experimental confirmation of the Parish and Littlewood model by measuring the local mobility randomly (by measuring the microsized graphene sheets) and finding the spatial mobility fluctuation.

Figure 1

(a) Low-resolution SEM image of graphene foam with a 3D network. The inset shows a typical Raman spectrum of graphene foam. (b) High-resolution SEM image of a graphene foam scaffold; upper and lower insets are planer and cross-sectional HRTEM, respectively, of a multilayered graphene sheet. (c) Field dependence of the MR of macroscopic graphene foam at various temperatures. Inset shows the Hall effect data measured on the same sample. (d) Derivative of MR with respect to magnetic field, $d\text{MR}/dB$, at different temperatures. Inset clearly shows the oscillations in the low-temperature curves of $d\text{MR}/dB$ versus $B$.

Figure 2

(a) Field dependence of MR of a microscaled multilayered graphene sheet separated from the graphene foams measured at low temperatures. The inset is the optical image of the sample with micropatterned electrical contacts, in which the scale bar (white) is 5 μm. MR was measured between electrodes 1 and 2. (b) Plot of $\mathrm{\Delta }R/R_0$ (linear background subtracted) as a function of $B^{-1}$ at different temperatures. (c) Landau level fan diagram for oscillations in $\mathrm{\Delta }R$. An oscillation frequency of $B_{\mathrm{F}}\sim 4.66\mathrm{T}$ was obtained using the slope of the linear fit. (d) Temperature dependence of the SdH oscillation amplitude $\mathrm{\Delta }R/R_0$ at different magnetic fields. The solid lines are the fits to the Lifshitz-Kosevich formula. (e) Magnetic field dependent Landau energy difference $\mathrm{\Delta }{E}_N\left(\mathrm{B}\right)$. The effective mass is obtained from the slope, $m*=0.042m_0$. (f) Dingle plots of ln $[\frac{\mathrm{\Delta }R}{R\left(0\right)}\mathrm{B}sinh\left(\frac{2{\pi }^2{k}_{\mathrm{B}}T}{\mathrm{\Delta }{E}_N}\right)]$ vs $B^{-1}$ at different temperatures.

Figure 3

(a) Plot of crossover field, $H_{\mathrm{C}}$, versus average mobility, ${\langle \mu \rangle }^{-1}$. The inset shows an example of how $H_{\mathrm{C}}$ is determined. (b) The dependence of average mobility, $\langle \mu \rangle$, on MR at different temperatures. The inset shows the temperature-dependent average classical mobility.

Figure 4

(a) Micro-Raman spectra of three graphene sheets from graphene foams. The insets are the optical images of microscaled samples after nanofabrication. The white scale bar in optical images is 5 μm. (b) Magnetic field dependence of MR of three samples (between electrodes 2 and 3) obtained at various temperatures.