Tuning the effective spin-orbit coupling in molecular semiconductors

Abstract

The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects has proven difficult due to competing relaxation mechanisms. Here we present a systematic study of the g-tensor shift in molecular semiconductors and link it directly to the SOC strength in a series of high-mobility molecular semiconductors with strong potential for future devices. The results demonstrate a rich variability of the molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We correlate the above g-shifts to spin-lattice relaxation times over four orders of magnitude, from 200 to 0.15 μs, for isolated molecules in solution and relate our findings for isolated molecules in solution to the spin relaxation mechanisms that are likely to be relevant in solid state systems.

Figure 1. ESR and optical spectra of doped molecules.

(a) Optical absorption spectra of a 0.5 × 10⁻³ mol l⁻¹ solution of rubrene in dichloromethane with increasing amounts of AlCl₃ (traces 1–3). We observe the expected bleaching of the transition between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) together with the emergence of charge induced transitions in the sub band gap regime from the HOMO to the singly occupied molecular orbital (SOMO). The grey arrows emphasize the increase of charge induced absorption and the decrease of the neutral molecule absorption peaks with higher doping levels. (b) A schematic of energy levels with possible optical transitions for a neutral and positively charged molecule. The shifts of the HOMO and LUMO energy levels reflects the reorganization of the molecular geometry to accommodate the charge. (c,d) Derivative ESR spectra of BTBT and C8-BTBT with best fits including (solid line) or excluding (dashed line) HFI from the first two hydrogens on the side chains.

Figure 2. Relationship between g-shift and atomic spin densities.

(a) Spin isodensity contours of cationic (left) BSBS and C8-BSBS, and (right) L-DTBTBT and C-DTBTBT radicals. The C8-BSBS molecule shown has alkyl chains at the outer bonding site. Spin maxima and minima are shown in blue and red, respectively. The shifted bonding site at the phenyl rings has been labelled, and the observed spin depletion at heavy atoms highlighted. Note that only part of the alkyl chains in C8-BSBS are shown. (b) Correlation plot of Δg^OZ/SOC-terms calculated using DFT versus fitted on the form of equation 3. The outliers identified in the text are shown as light blue triangles, with the other numbers represented by dark blue circles. The magenta line y=x represents a perfect fit. For brevity Δg^OZ/SOC has here been relabelled Δg. (c) Plot of changes in Δg^OZ/SOC terms as a function of change of effective heavy atom spin upon alkylation of molecules (see text). Red and green lines represent linear fits to the sulfur- and selenium-based molecules, respectively.

Figure 3. Power-saturation measurement of spin lifetimes.

(a) Schematic of the Bruker ER 4122SHQE cavity with microwave magnetic and electric fields in-plane and out-of-plane, respectively. Plot insets show the magnetic field strength across the cavity. We account for the vertical distribution of B₁ and minimize horizontal variations by confining our samples to a diameter of 1 mm. (b) Power saturation of the integrated ESR absorption spectra for the series of molecules with fitted curves to extract T₁ and T₂. (c) Evolution of derivative ESR spectrum with increasing microwave powers for the example of L-C12-DTBTBT.

Figure 4. Dependance of spin relaxation times on the effective SOC.

(a) Spin lattice relaxation time versus Δg for all measured molecules. Error bars represent 95% confidence intervals. Dashed line shows the expected proportionality T₁∝(Δg)⁻² for relaxation via SOC fields. (b) Spin coherence time versus Δg for all measured molecules. Error bars show the 95% confidence intervals. (c) Dependence of T₁ and T₂ on the correlation time τ_C of field fluctuations from the Redfield theory. Model values of ω_L/2π=9.4 GHz and were used for the plot. (d) Correlation times τ_C as estimated from the Redfield theory and plotted against rotational correlation times obtained from DOSY NMR diffusion constants (when available). Error bars from 95% confidence intervals of T₁ and T₂ and error propagation.