To the editor:

Hu and Wu recently reported tunable magnetoresistance (MR) in organic semiconductors1, claiming that the geometry of multilayer diodes controls the relative influence of (electron–hole) polaron-pair (PP) dissociation and recombination under magnetic fields (B). The underlying hypothesis is B-dependent intersystem crossing (ISC), conversion between spin manifolds of intermolecular exciton precursor PPs or (intramolecular) excitons. Hu and Wu postulate the generation of conductivity-influencing secondary polarons1, so that MR becomes sensitive to the electron–hole balance, determining the exciton–charge ratio1.

ISC is a relaxation process, which Hu and Wu claim to be controlled by external and internal Zeeman splitting, and singlet–triplet splitting1. These are effects usually described by the B-dependent Zeeman term and spin–spin interaction (spin–dipolar and exchange coupling). We agree that B may control the singlet–triplet content of electron–hole pairs2; the relevance to relaxation processes (for example, ISC) is not obvious. Spin–spin interactions of a spin–pair Hamiltonian do not determine relaxation directly. ISC must instead be described by spin-relaxation theory3, adding a fluctuation Hamiltonian Hf to a pair Hamiltonian H0. Hf determines statistical addends to the Liouville equation (the Redfield matrix4) for the spin ensemble, and accounts for hyperfine interactions from randomly polarized and spatially distributed H-atoms. Hu and Wu do not explain how these interactions and thus ISC are influenced by B. Can B even change the PP singlet–triplet content to account for MR?

We could not infer values quoted for the internal Zeeman effect (“a range of 1–10μeV”1) from ref. 26, which states zero-field splitting parameters E and D as 1 μeV and 10 μeV, respectively, for naphthalene crystals. Suffice to note that the zero-field parameters in most organic materials are not determined by spin–orbital coupling as claimed by Hu and Wu, but by spin–dipolar coupling4 within the PPs. Although measurements of the dipolar coupling for poly(phenylenevinylene)5 (D ≈ 72 mT, E < 10 mT) suggest that the material used by Hu and Wu, poly[2-methoxy-5-(2´-ethylhexyloxy)-1,4-phenylenevinylene], has similar parameters to naphthalene, it is unclear why the magnetic field should change spin-dependent PP recombination and dissociation rates. Following Hu and Wu, we consider PPs responsible for MR in terms of a two-spin system (s = ½) with Landé-factors ga and gb (2 due to weak spin–orbit coupling), a mutual exchange coupling J, and a dipolar coupling determined by the zero-field matrix related to the zero-field parameters4. At low fields (μΒB ≈ E < D, with μΒ Bohr's magneton), B/E controls mixing of the two triplet states |T+〉 = |↑↑〉, |T〉 = |↓↓〉; B does not modify spin-dependent transition rates4. For μΒBD the spin–dipolar interaction is expressed in the high-field approximation6, revealing a magnetic-field-induced decoupling of the pair partners with the four PP eigenstates |1〉 = |↑↑〉, |2〉 = cosφ|↑↓〉 + sinφ|↓↑〉, |3〉 = −sinφ|↑↓〉 +cosφ|↓↑〉 and |4〉 = |T〉 = |↓↓〉; |2〉 and |3〉 are linear combinations of the product states (|↑↓〉 and |↓↑〉), determined by the B-induced tilt angle

with d = 1/3D(3cos2Θ−1) describing the dipolar coupling's2 dependence on the spin-pair's main axis angle Θ relative to the orientation of B. The angle φ depends on η = μΒB(gagb)/(2J + d), the ratio of the difference of polaron Zeeman energies to the spin–spin coupling strengths. Contradicting Hu and Wu1, the PP singlet–triplet ratio cannot change as the Zeeman splitting exceeds J and d. Given this tiny value (μΒB(gagb)<200 neV at B = 328 mT; ref. 5), the crossover (η≈1)) occurs at B 3 T, far exceeding Hu and Wu's fields1. This B-limit is a lower estimate as it is likely that |J| >> |D| (ref. 5). Although equation (1) explains a B-dependence of an individual PP's singlet content, it cannot apply directly to disordered PP ensembles where all four eigenstates are generated equally. The singlet character of |2〉 increases with increasing B, that of |3〉 decreases; why should spin-dependent PP dissociation rates (which determine conductivity) then depend on B?

Testing for B-dependent singlet–triplet exciton formation requires simultaneous probing of singlet and triplet densities in organic light-emitting diodes. This is achieved by monitoring sensitizzed intrinsic phosphorescence7 (note that phosphorescent acceptor dopants modify triplet generation and B-dependencies8, as do field-dependent bimolecular reactions9). Despite MR, strong fields (8 T) do not alter the singlet–triplet balance7, in agreement with triplet absorption spectroscopy10. Even at low fields (hyperfine field11) where MR is largest12, no change occurs. Although hyperfine interactions may be causally linked to MR (ref. 12), electron–nuclear spin coupling does not modify PP spin configurations. A viable alternative to Hu and Wu's excitonic picture1 (and to earlier hyperfine field-mixing models of field-dependent photoconductivity11) lies in the assumption of spin-dependent bipolaronic transport, providing a minimalistic parametric framework to describe positive and negative MR12.