Intrinsic Mobility Limit for Anisotropic Electron Transport in ${\mathrm{Alq}}_3$

Muon spin relaxation has been used to probe the charge carrier motion in the molecular conductor ${\mathrm{Alq}}_3$ (tris[8-hydroxy-quinoline] aluminum). At 290 K, the magnetic field dependence of the muon spin relaxation corresponds to that expected for highly anisotropic intermolecular electron hopping. Intermolecular mobility in the fast hopping direction has been found to be $0.23\pm 0.03{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ in the absence of an electric- field gradient, increasing to $0.32\pm 0.06{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ in an electric field gradient of $1\mathrm{MV}{\mathrm{m}}^{-1}$. These intrinsic mobility values provide an estimate of the upper limit for mobility achievable in bulk material.

Figure 1

The crystal structure of the $\beta$ phase of ${\mathrm{Alq}}_3$ [18], showing the good $\pi -\pi$ orbital overlap between ligands of different molecules along the $c$ axis that is responsible for highly one-dimensional motion of charge carriers.

Figure 2

Positron $F(t)-B(t)$ emission asymmetry for ${\mathrm{Alq}}_3$ taken at $T=290\mathrm{K}$ for a representative number of longitudinal magnetic fields, showing the muon spin relaxation as a function of time. The solid lines are fits to the RK function (1).

Figure 3

The muon spin relaxation parameter as a function of applied field, where a $B^{-1}$ dependence is observed, which is characteristic of 1D diffusion in the RK treatment. At longitudinal fields below $\sim 0.2\mathrm{mT}$, nearby proton nuclear spins are still coupled to the muon. Black: data taken using fly-past mode. Green: data taken using the high-voltage sample holder at 0 V. Inset (top): A Fourier spectrum in an applied transverse field of 250 mT, which allows us to identify two hyperfine coupling constants a and b (see text). Inset (bottom): The fitted LFQ, showing the three different contributions of the different hyperfine parameters (see text), a contribution from diamagnetic muons (TF) and one from unbound muonium (Mu). The bar heights indicate the weight of each contribution.

Figure 4

The muon spin relaxation at 290 K for zero electric field (green) and for an electric field gradient of $1\mathrm{MV}{\mathrm{m}}^{-1}$ (red). Inset (bottom): schematic diagram of the electric field pulse structure relative to the acquisition electronics (denoted by the line color red: $-2\mathrm{kV}$; green: 0 V; gray: vetoed). Inset (top): The muon’s initial asymmetry, the data taken at $-2\mathrm{kV}$ and 0 V. Errors are approximately the point size.