Chemical and Structural Trends in Spin-admixture Parameter of

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Cite This: J. Phys. Chem. C 2019, 123, 19112−19118

Chemical and Structural Trends in the Spin-Admixture Parameter of Organic Semiconductor Molecules Uday Chopra,†,‡ Sergei A. Egorov,†,¶,§ Jairo Sinova,† and Erik R. McNellis*,† †

INSPIRE Group, Johannes Gutenberg University, Staudingerweg 7, D-55128 Mainz, Germany Graduate School Material Science in Mainz, Staudingerweg 9, D-55128 Mainz, Germany ¶ Chemistry Department, University of Virginia, McCormick Road, Charlottesville, Virginia 22901, United States § Leibniz Institute for Polymer Research, Dresden, Hohe Strasse 6, D-01069 Dresden, Germany Downloaded via RUTGERS UNIV on August 8, 2019 at 19:47:48 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: Spin mixing in organic semiconductors is related to spin−orbit coupling (SOC). However, a detailed study analyzing the dependence of the spin-admixture parameter (γ) on structural and material parameters is lacking. We systematically study the effect of increasing the atomic weight in molecules and show that γ does not change as expected from increasing SOC strengths. The spin admixture measures the SOC of the molecular orbital on which the polaron is localized, and therefore common chemical rules of thumb do not necessarily apply. We explore the material parameters influencing γ by evaluating the effect of chemical composition, molecular geometry, and extent of morphological disorder. Finally, we investigate the relation between γ and gyromagnetic coupling tensor shifts, which have also been regarded as a measure of SOC. We show that the assumed linear correlation between the two does not hold in general, and it is due to the absence of the magnetic response term in γ. Our results may serve as a guiding tool for tuning γ with chemical synthesis.

1. INTRODUCTION Organic semiconductors (OS) have attracted significant interest in spintronics1−3 over the last few years. Light-weight chemical composition accompanied by a weak spin−orbit coupling (SOC) gives rise to spin-relaxation lifetimes up to μs4, and spin-diffusion lengths of the order of μm5 have been reported. Organic materials also open up a vast potential of chemical tunability, which can be harvested for required transport properties. These advantages have been collectively utilized in several spintronic phenomenon such as magnetoresistance devices6,7 and the spin Hall effect.8,9 With an increasing interest in the field, modeling spin relaxation has become of primary importance to the community. SOC has been identified as a major factor in several spinrelaxation mechanisms.10−13 References14−16 suggest a phonon-assisted spin-flip mechanism where spin relaxation is driven by coupling between SOC and localized vibrations. Several studies17−20 show that the shift in the electron gyromagnetic coupling (“g”) factor is attributed to SOC in light molecules and can be used as a measure of SOC strength of an organic material. Coupled with an effective hyperfinefield (BHFI), this leads to a local precession with a frequency of ∼(g + Δg)μBBHFI/ℏ. Precession along randomly oriented sites in a disordered morphology leads to spin decay. Within the regime of hopping transport, SOC is realized in the form of the spin-admixture parameter11,21 (γ), which is essentially a spin-flip probability as the charge-hopping events take place during transport within OS. This occurs due to © 2019 American Chemical Society

coupling between opposite spin states at hopping sites. In a recent work,22 we demonstrated a significant advancement over the original technique to calculate γ from first-principles electronic structure theory. This led to both qualitative and quantitative improvements in our calculations, allowing for accurate predictions of spin-diffusion lengths in high-mobility organic polymers.5 The enhanced transferability of our method also allows for treating single-molecule magnets on an equal footing. In this paper, we aim to understand wider trends in γ with respect to chemical structure, substitution, and geometry using our generalized calculation technique. The hopping-assisted spin-flip mechanism is analogous to the Elliott-Yafet theory of spin relaxation23,24 in solid-state systems. However, instead of momentum scattering in a band conductor, the spatial charge hopping between mixed opposite spin states causes the spin decay. The transport is sensitive to the average hopping frequency (ω̅ ), and it was shown by Yu11 2 that T−1 1 ∝ ω̅ γ where T1 is the spin-relaxation time. Therefore, temperature dependence of ω̅ is also reflected in spin relaxation and is one of the major causes of spin relaxation in high-mobility organic materials.25 This approach has been used to describe spin relaxation in several models,26−29 and a similar mechanism of SOC-driven spin flip has been suggested Received: April 11, 2019 Revised: June 26, 2019 Published: July 16, 2019 19112

DOI: 10.1021/acs.jpcc.9b03409 J. Phys. Chem. C 2019, 123, 19112−19118

Article

The Journal of Physical Chemistry C

Figure 1. Chemical structures of the molecules for which calculations are performed. (a) Aromatic hydrocarbons. (b) Heteroatomic π-conjugated molecules and polymers. (c) Single-molecule magnets, metal pthalocyanines, and tetraphynylporphyrins.

in other theories.12,30,31 Spin mixing due to SOC has also been used to describe the spin Hall effect in OS.32 In spite of its critical role in spin transport, its behavior with molecular structure and geometry has not been explored in detail. Our main goal here is to study trends in molecular SOC using γ based on systematic variations in chemical composition and structure of different OS. We begin by questioning whether the conventional rules for SOC apply directly to the spin admixture. As a common rule of thumb, molecular SOC is often assumed proportional to Z4 where Z is the atomic number of constituent elements. This does not necessarily hold for γ. To demonstrate this fact, we focus our discussion on the following different classes of OS, which are considered as potential candidates for spintronic applications. We start with light-weight aromatic hydrocarbons like pentacene and rubrene, which are known for their high mobility and have been used in magnetoresistance devices.33 Fullerenes, exhibiting the same chemical composition but an entirely different geometry, were used in organic spin-valves34 and were found to have large spin-diffusion lengths, up to a few hundred nanometers.35 Complex π-conjugated molecules like tris-(8-hydroxyquinilato)aluminum (Alq3), although possessing a low mobility of 10−5 cm2 V−1 s−1, were one of the first molecules to be used in spintronic devices36,37 and have been widely studied since then.7,38,39 We discuss the effects on spin mixing by substituting Al with its heavier counterparts (Ga and In). Furthermore, we explore chalcogenide molecules like [1]benzothieno[3,2-b][1]-benzothiophene (BTBT) and its derivatives, including substitution with selenium and functionalization with alkyl groups, which were recently studied in detail in refs18 and.19 Polymers like poly[2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene] (pBTTT), poly[3hexylthiophen-2,5-diyl] (p3HT), indacenodithiophene-benzothiadiazole (IDTBT), diketopyrrolopyrrole-benzotriazole (DPPBTZ), poly[benzimidazo-benzophenanthroline] (BBL), and naphthalenediimide-bithiophene (NDIO2-T2), which are known to possess a semicrystalline structure, have also recently instigated research in the field due to their high mobility40−44 and are also of interest to the spintronic community due to their long spin-diffusion length25 and evidence of an inverse spin Hall effect.9 Finally, we hope to bridge the gap between conventional organic and single-molecule magnet (SMM)based spintronics by also including metal complexes with pthalocyanine (Pc) and tetraphynylporphyrin (TPP) ligands.

The list attempts to include representative molecules from all of the different classes of organic semiconductors. We also discuss the role of elemental composition and structural effects on γ for all the molecules described above in Section 3. We conclude by comparing γ to a g-factor shift, which is also considered a measure of molecular SOC, and differentiate between the two quantities.

2. THEORY AND COMPUTATIONAL DETAILS Weak SOC in organic molecules allows us to treat the spin− orbit coupling operator (Ĥ soc) as a first-order perturbative correction to the ground state Kohn−Sham Hamiltonian45 with eigenstates |ψkσ⟩ as obtained from a regular DFT calculation. The perturbation on the spin-carrying molecular orbital, |ψ0 ↑ ⟩, leads to the spin-mixed eigenstates, |ψ0 + ⟩. |ψ0 + ⟩ = |ψ0 ↑ ⟩ −

∑ k ≠ 0σ

ψkσ Ĥ soc ψ0 ↑ ⟩ Ek − E 0

ψkσ

(1)

This perturbative treatment is similar to the original formulation by Elliot24 and ref;46 however, in our calculations, instead of assuming the conventional form of Ĥ soc = ∑iξili · si, we define it based on the zeroth order regular approximation (ZORA)47 as expressed in eq 2 and implemented in the quantum chemistry package NWChem.48,49 Ĥ SOC =

c2 s·̂ (∇V × p̂ ) (2c − V )2 2

(2)

Finally, the spin admixture can then be calculated as a change in the norm of eq 1 from the unperturbed state. ⟨ψ0 + ψ0 + ⟩ = ⟨ψ0 ↑ |ψ0 ↑ ⟩ + γ 2 = 1 + γ 2

(3)

Unless otherwise stated in the main text, all calculations were performed with the SARC50 all-electron, minimally augmented, polarized triple-zeta valence basis set recontracted for the zeroth order regular approximation (a.k.a. “MA-ZORADef2-TZVP”). We removed the diffuse (minimal augmentation) functions at the carbon and nitrogen atoms in order to eliminate linear dependencies, but the basis set is otherwise unmodified. We use the hybrid PBE051 exchange-correlation functional for all our calculations. Consequentially, the standard high level of theory used in later sections is our ZORA/UKS generalized γ with PBE0 and the TZVP basis set. 19113


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The Journal of Physical Chemistry C Table 1. Spin Admixtures Calculated for all the Molecules in Figure 1a γ2

molecule aromatic hydrocarbons benzene pentacene rubrene C60 C70 heteroatomic π-conjugated molecules α-NPD triphenylphosphine Alq3 Gaq3 Inq3 BTBT C8-BTBT C8s-BTBT DNTT C8-DNTT C8s-DNTT DATT C8-DATT C8s-DATT *CDTBTBT *C8-CDTBTBT *C8s-CDTBTBT LDTBTBT C8s-LDTBTBT C8-LDTBTBT BSBS *C8-BSBS *C8s-BSBS DNSS C8-DNSS C8s-DNSS

γ2

molecule

2.36 2.69 3.85 5.89 7.81

× × × × ×

10−8 10−8 10−8 10−8 10−8

8.10 5.29 8.49 7.37 3.81 4.39 2.53 4.22 2.03 1.70 1.67 1.35 1.23 1.32 3.53 1.38 2.56 5.09 4.63 6.15 1.11 1.12 1.64 7.28 6.18 6.09

× × × × × × × × × × × × × × × × × × × × × × × × × ×

10−8 10−7 10−5 10−5 10−5 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−6 10−4 10−4 10−4 10−5 10−5 10−5

heteroatomic π-conjugated molecules DASS C8-DASS C8s-DASS *CDSBTBT *C8-CDSBTBT *C8s-CDSBTBT LDSBTBT C8-LDSBTBT C8s-LDSBTBT *CDSBSBS *C8-CDSBSBS *C8s-CDSBSBS LDSBSBS C8-LDSBSBS C8s-LDSBSBS PBTTT P3HT NDI-T2 IDTBT DPPBTz BBL single-molecule magnets AlPc VOPc MnPc CoPc CuPc CuTPP

4.85 4.42 4.74 1.16 9.34 1.22 1.12 1.24 1.15 1.47 1.01 1.09 1.76 1.90 1.62 3.15 3.68 8.73 1.71 5.29 2.44

× × × × × × × × × × × × × × × × × × × × ×

10−5 10−5 10−5 10−4 10−5 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−7 10−7 10−7 10−7 10−7 10−7

9.30 6.20 2.41 5.70 3.72 5.46

× × × × × ×

10−8 10−6 10−2 10−3 10−4 10−4

Molecules marked with * represent outliers in the correlation plot in Figure 4.

a

g-Tensor calculations were performed exactly as reported in ref.18 Our approach is explained in detail in ref.22 Calculations were performed on a wide range of molecules shown in Figure 1. These molecules were selected to emphasize the transferability of our method between systems of interest to both organic and molecular spintronics, including high-mobility polymers and single-molecule magnets. It further demonstrates the potential for high-throughput calculations. All results are presented in Table 1.

In addition to simply distinguishing molecular SOC strength wrt elemental composition, we also report variations based on structure and geometry for these molecules. In polymers, we observe that γ2 is similar for all planar conformations (∼10−7). However, the distributions of individual sites in a morphology vary vastly from each other. We categorize these trends according to chemical composition and geometry, and discuss them in detail in the following sections. 3.1. Chemical Composition. Relativistic effects become dominant with increasing nuclear mass. Therefore, a molecule with heavier atoms would generally have a larger SOC compared to one with a light-weight chemical composition. In agreement with this, aromatic hydrocarbons were found to have the smallest γ. Following the increasing order of atomic weights of the constituent elements, heteroatomic πconjugated molecules have γ in the order of nitrogen-based followed by sulfur-based and finally selenium-based molecules. We also explore substitution effects in chalcogenidecontaining molecules. We find that the difference between γ of both single and multiple-substituted Se molecules is very small compared to that of their S counterparts. For example, DTBTBT has γ2 ≈ 10−6, whereas DSBTBT and DSBSBS have γ2 ≈ 10−4. Therefore, spin mixing is generally governed by the heaviest atom in the molecule. For the molecules mentioned above, although we see that the spin admixture and hence the SOC increase with heavier

3. RESULTS AND DISCUSSION We categorize the molecules for which we performed spinadmixture calculations into the following groups: (a) aromatic hydrocarbons, (b) heteroatomic π-conjugated systems, and (c) metal complexes. Generally, γ obeys an ascending order with respect to (wrt) atomic weights of the heaviest atoms in the molecules, with aromatic hydrocarbons having the smallest γ followed by other heteroatomic π-conjugated molecules and metal-centered molecular magnets. This appears to be consistent with SOC scaling with atomic weights; however, we find several exceptions to this order. For instance, Xq3 molecules do not show any variation with substitution of the metal center (X) with its heavier counterparts. Furthermore, the transition-metal complexes show a variation within six orders of magnitude, and the scaling is inconsistent wrt atomic numbers. 19114


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lighter-weight elements and therefore gives the smallest γ in the series. In our previous work,22 we discuss this variation in detail and showed that the spin admixtures for MPc’s correlate well with the spin-relaxation times reported in ref.52 As discussed above, γ is dependent on the spin-carrying MO; therefore, a heavy element may not necessarily imply a higher γ unless the MO has contribution from a higher-angularmomentum atomic orbital of the heavy element. Using the correct MO for the perturbation, which can be easily obtained from first-principles calculations, also circumvents the use of complex analytical methods used in ref11 to calculate γ and hence makes our approach more general and transferable to a wider range of molecules. 3.2. Molecular Structure and Geometry. In the preceding sections, we showed that the spin admixture is susceptible to changes in the electronic structure, which in turn is sensitive to molecular geometry. Here, we focus our discussion on polymer systems, which can exist in different conformations due to rotation about dihedral angles between monomers and explore the effects on spin mixing by investigating its behavior in the crystalline and disordered morphology. The relation between γ and the dihedral angle (θ) between two adjacent π orbitals was studied before in the context of a biphenyl molecule,11 and a similar dependence was also shown for transpolyacetylene.10 This variation was derived as γ2 = γ20[1 + tan2(θ)] where γ20 is the spin admixture for a planar biphenyl. This is attributed to the effect of the angular momentum operator, which gives a zero expectation value when the adjacent π orbitals are parallel; however, with increased torsion angles, the overlaps between opposite-spin orbitals also increase. We extrapolate this effect to polymers where the charge is delocalized over several monomers, which may appear in different conformations wrt each other. We have calculated spin admixtures for both crystalline (planar) and amorphous (disordered) geometries of three polymer systems, pBTTT, IDTBT, and NDIO2-T2, which are known to occur in semicrystalline structures. As the spin admixture is defined for a particular electronic state, a disordered polymer morphology consists of a distribution of such states in the form of a network of segments where the charge(s) undergo(es) hopping transport. We have calculated the spin admixtures for each of these segments present in morphologies obtained from molecular dynamics simulations. This distribution of γ2 is presented in Figure 3. We observe that crystalline geometries tend to have smaller values compared to disordered segments due to the absence of any dihedral angles in the former. We also find that the crystalline geometries for different polymers have a similar measure of γ2 ≈ 2−8 × 10−7 because of a similar chemical composition. This is especially true in the case of p3HT and pBTTT, which only differ by fused and disjoint thiophene rings. For the amorphous geometries, we report vastly different spin-admixture values due to the presence of a larger degree of freedom withing the torsion angles, for example, between IDT and BT units and the bulky NDIO2 and T2 units attributed to steric hindrance between units in the corresponding polymers. From Figure 3, we also infer that while the distributions tend to peak around similar values of γ, the width of the distribution is different for each polymer. This may have implications in spin transport because the charge may experience different spin-relaxation rates at each site, for example, frequently visited

elements, Xq3 and metal complexes do not follow this order. The γ2 for all Xq3 molecules lies within a range of ∼10−5 and does not show any variation on substitution with heavier elements. Also, for transition metal compounds, it varies within six orders of magnitude, ranging between 10−8 for AlPc and 10−2 for MnPc, which cannot be simply explained by variation in atomic numbers. The entire discussion has been summarized in Figure 2 where the molecules are grouped by the atomic number of the heaviest element present.

Figure 2. Variation of γ with the heaviest atomic number. Molecules that do not follow the order: metal trishydroxiquinolates, tetraphenylporphyrins, and pthalocyanines indicated by orange points. The fit (blue) corresponds to Z8 because γ 2 ∝ HSOC2 .

Trends described in the preceding text can be rationalized by considering the nature of the perturbed molecular orbital (MO), |ψ0⟩, in eq 1, which carries the spin. For most OS, |ψ0⟩ is usually the frontier orbital, with the exception of metal complexes, which may possess spin polarization even in a neutral state due to the presence of unpaired electrons in the d shell. For most π-conjugated molecules, the spin density is uniformly delocalized over the entire molecule. Therefore, |ψ0⟩ has contribution from atomic orbitals of all constituent atoms. Hence, the presence of a heavier element consequently leads to a larger spin-admixture parameter, and we see the expected variation. Terminal substitution with C-8 alkyl chains barely affect the spin-density distribution on the conjugated unit; therefore, we do not observe a significant difference in γ on comparing with corresponding nonalkylated molecules. The reasoning can also be extended to molecules that are exceptions to the trend in Figure 1. In the case of Xq3’s, the |ψ0⟩ comprises of π orbitals of the 8-hydroxyquinoline ligands on which the charge is delocalized. Therefore, substitution of the central metal atom with a heavier one has a negligible effect on the spin admixture, and therefore no variation is observed. Our observations are in agreement with low-temperature measurements by Nuccio et al.14 where substitution led to a negligible effect on spin relaxation. The high-temperature effects, however, are driven by a vibrational spin relaxation and are beyond the scope of this article. In molecular magnets like MPc’s, |ψ0⟩ usually has a large contribution from the d orbitals of the metal center, which has a different symmetry in each case. Therefore, the variation in γ is sensitive to the nature of the orbital rather than simply the atomic number of the element. Similarly, for CuPc and CuTPP, the spin MO is dx2 − y2 in both cases; hence, the γ has a similar magnitude. Finally, the lack of d orbitals in AlPc causes the unpaired electron to be delocalized on the Pc ligand, which comprises of 19115


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interdigitation or bulky groups adjacent to each other can lead to steric hinderance, which also distorts the backbone polymer chain, leading to a larger spin-mixing. This behavior of spin admixture can be used to tune spin transport via molecular design in these materials. 3.3. Comparison with Δg. As discussed in the theory section, spin−orbit correction changes the ground-state wave function obtained from a nonrelativistic Hamiltonian. These corrections also affect the HF couplings54 as it depends on electron density at the nucleus. In addition to this, SOC in molecules also leads to a deviation in the gyromagnetic factor from the free electron value, which in turn scales the effective HF precession frequency experienced by the spin during its dwell time on the molecule. This deviation (Δg) can be directly estimated using electron paramagnetic resonance (EPR). Spin−orbit and the orbital Zeeman corrections also have dominant contributions to the total Δg.55 It has also been demonstrated by Yu11 that Δg is also analogous to γ, and the two quantities are proportional as both scale with spin−orbit coupling constants, ξ. This relation was recently discussed in detail in ref19 where T1 was shown to be proportional to Δg−2. Here, we evaluate this argument in detail, whether both can be interchangeably used as a measure of SOC. We investigated the same set of molecules as in ref18 and try to establish the correlation between Δg and γ. From Figure 4,

Figure 3. Distribution of γ2 for segments obtained from MD morphologies of PBTTT, IDTBT, and NDIO2-T2. Dashed lines indicate the γ2 for a crystal optimized segment of the corresponding polymer.

sites with large distortions along the backbone and hence larger γ could lead to a faster spin relaxation. This, of course, requires in-depth analysis of occupation probabilities of the sites with charge-transport simulations, which is beyond the scope of this paper. Our argument suggested by these results is in agreement with observations from Miller and co-workers53 where they observed a faster relaxation for glassy (amorphous) polyfluorene films compared to that of an ordered one (β phase), and we reason that this is due to larger average spin-mixing in the former morphology. Large distortions along the backbone in the amorphous phase may also cause the charge being localized over a smaller unit. This also affects the spin-mixing. We further investigate the effects of polaron delocalization on spin mixing by varying the number of monomers in the polymer chain for IDTBT, as summarized in Table 2. Since the value does not change Table 2. Variation in γ2 wrt the Number of Monomers of IDTBT no. of monomers 1 2 3 4

IDTBT 3.50 1.71 1.51 1.37

× × × ×

10−7 10−7 10−7 10−7

Figure 4. Correlation between γ and Δg with and without the outliers (magenta-colored points). Depletion of spin-density in C-DXBXBX compared with BXBX and L-DXBXBX affects the magnetic response term, and therefore these type of molecules do not show correlation with γ.

beyond 4 units so as to affect the distribution in Figure 3, we do not use a larger unit. We report a slightly larger spin-mixing for a more localized polaron. We observe the same in chalcogenide molecules where increasing the size of the conjugated segment, for instance, in BXBX, DNXX, and DAXX, results in a corresponding decrease in γ. This effect has also been reported in ref.10 This implies dependence of crystallite size on spin-relaxation rates in the polymer. A wellordered morphology with a larger crystallite size might have the polaron delocalized to a larger unit, which might lead to a smaller spin-mixing. However, the average charge-transfer rates might also be higher in such a morphology. Therefore, modeling spin transport requires an intricate balance to be maintained between these two parameters to obtain required properties. Therefore, for ordered polymers prepared using annealing, which gives rise to larger crystallite sizes, the spin-mixing would be smaller compared to that of disordered structures due to a large torsional degree of freedom between conjugated units, such as p3HT. Moderation of the alkyl chains to reduce

it is evident that the two quantities correlate with an r2 = 0.562 when all the molecules are included. However, on excluding certain outliers, the correlation increases with an r2 = 0.935. We found that all the outliers correspond to C-type isomers of the BXBX class of molecules. To understand this behavior, we compare the expressions for Δg(OZ/SOC) with γ. (OZ/SOC) gμν =

∑ k ,l

∂Pklα − β ⟨ϕk |hνSOC|ϕl⟩ ∂Bμ

(4)

The above equation represents the orbital Zeeman and SOC contributions to the total g-tensor. The first term represents the response on the spin density (Pα − β) to the μth component of the magnetic field. In the absence of any external field, this corresponds to the local hyperfine fields. The second term includes SOC matrix elements expanded in basis functions |ϕk⟩ , as apparent in eq 1. Therefore, the spin-admixture and gtensor terms differ only by a response term. To justify this, we compare the spin-density of C- and L-type isomers in Figure 4. 19116


The Journal of Physical Chemistry C We find that the absence of spin density from the chalcogenide atoms implies a negligible response term and therefore leads to a small Δg; however, since γ is independent of the response, it remains unaffected with variation in spin density. Finally, we argue that both quantities can describe SOC effects however in the context of different mechanisms and experimental conditions. The experiments in ref19 measures a local spin relaxation, which depends on HFI and SOC and involves a magnetic response; therefore, the g-factor shifts fit well to relaxation times. γ, on the other hand, is a measure of SOC of the orbital on which the charge is localized and crucial for understanding spin relaxation where SOC is the active mechanism.

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ACKNOWLEDGMENTS

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REFERENCES

Funding was from the Alexander von Humboldt Foundation, the ERC Synergy Grant SC2 (no. 610115), the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X, EU FET Open RIA grant no. 766566, and Grant Agency of the Czech Republic grant no. 14-37427G. U.C. is a recipient of a DFG-funded position through the Excellence Initiative by the Graduate School Materials Science in Mainz (no. GSC 266). S.A.E. acknowledges the Alexander von Humboldt Foundation for financial support.

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4. CONCLUSIONS In this paper, we presented a comprehensive study on different trends in the spin-admixture parameter using highly accurate first-principles calculations on different classes of organic semiconductors. We found that, rather than a simple function of the atomic number, the spin admixture and hence the SOC are properties of the spin-carrying MO. We concluded this based on trends in γ of metal complexes where γ varies depending on whether the polaron is localized on a π orbital of the ligand or on a d orbital of the metal. We also discussed several structural factors that affect γ and consequently the spin transport in organic materials. Spin mixing can be chemically tuned by varying the torsion angles in extended conjugated systems such as polymers. Planar molecules like pBTTT, BBL, and DPPBTz have a smaller spin-admixture compared to that of ones with a larger degree of freedom in the dihedral angle, such as p3HT and NDIO2T2. Furthermore, localizing the charge on segments of different sizes also influences SOC. Our observations are also shown to be consistent with previous experiments in the literature.53 Finally, we explored the relation between g-factor shifts and γ, and contrary to ref,11 the linear relationship suggested based on a simplistic approximation is not strictly valid. Although both Δg and γ can represent SOC, they do not correlate with each other because of molecules where the spin density is absent from the heavy elements that contribute to SOC. γ is not known to be measured via experiments; however, its effect on spin transport can be observed in terms of spinrelaxation times. Our calculations of spin admixture correspond with spin lifetimes of molecules where SOC is a major cause of relaxation. This demonstrates the potential and utility of our first-principles approach, which can incorporate the effects of SOC on electronic structure. Our first-principles method to calculate γ is a useful tool that could be used to further the understanding of spin transport in organics beyond simplistic approximations to harvest tunability of organic materials. We hope that our discussions can supplement effective material design for spintronic applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Uday Chopra: 0000-0002-0395-1456 Erik R. McNellis: 0000-0002-2745-3320 Notes

The authors declare no competing financial interest. 19117


Article

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Chemical and Structural Trends in Spin-admixture Parameter of

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