Distinguishing Spin Relaxation Mechanisms in Organic Semiconductors

A theory is introduced for spin relaxation and spin diffusion of hopping carriers in a disordered system. For disorder described by a distribution of waiting times between hops (e.g., from multiple traps, site-energy disorder, and/or positional disorder) the dominant spin relaxation mechanisms in organic semiconductors (hyperfine, hopping-induced spin-orbit, and intrasite spin relaxation) each produce different characteristic spin relaxation and spin diffusion dependences on temperature. The resulting unique experimental signatures predicted by the theory for each mechanism in organic semiconductors provide a prescription for determining the dominant spin relaxation mechanism.

Figure 1

(a) Schematic of the time-dependent fields that a single spin experiences from HFI and a constant ($\gamma$) SOC. (b)–(d) $k$, the average hopping rate, is 100, $a=0$ and $\Gamma =0$ so these results are for SOC only. (b) Polarization as a function of time for explicit trap (black line) and biexponential (red dotted line) models. The rate of leaving a trap, $k_0$, for (a), $k_0=10$, and (b), $k_0=0.1$ where each pair is labeled by $k_1$, the rate to be captured by a trap. Spin relaxation decreases as $k_1$ increases (i.e., as trap number increases). The two models are connected through the relations $b=k_1/(k+k_1)$ and $\beta =k_0/k$. Multiexponential model in (c) with varying SOC values and in (d) with different $b$. Slopes of long-time power law dependence are indicated.

Figure 2

Numerical SOC spin relaxation rate (black solid symbols) and HFI spin relaxation rate (red triangles and blue diamonds) as a function of a. SOC calculations use multiple trapping WTD with an exponential density of states while HFI uses the multiexponential WTD. Solid black line is fit using Eq. (10) with one multiplicative fit parameter. Blue diamonds depict the short time-spin relaxation. Red triangles represent the longer-time slower-spin relaxation. Vertical gray line separates regions of algebraic and exponential spin decay. $k_0/a=1000$, $\beta =0.1$, and $\Gamma =0$.