(PP) rrap3ht/c 61 PCBM (Fig. 2e) MEHPPV/C 61 PCBM (Fig. 2f) Supplementary Table (1) device/figure a HF (mt) J (mt) (CTE) 4 2 >1 0.

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1 Supplementary Table (1) device/figure a HF (mt) J (mt) (CTE) S / T (PP) (PP) rrp3ht/pcbm (Fig. b) rrp3ht/pcbm (Fig. c) PBT7/C 71 PCBM (Fig. d) 4 > > >1 0.7 rrap3ht/c 61 PCBM (Fig. e) 4 <1 0.6 MEHPPV/C 61 PCBM (Fig. f) 4 <1 0.6 Table caption: The parameters used for the simulations shown in Fig.. a HF is the HFI strength for both PP and CTE. J is the exchange interaction strength for CTE. S / T is the ratio of the singlet to triplet decay rates for the PP. is the dispersive parameter for the g mechanism associated with the PP.

2 Supplementary Discussion The g mechanism for calculating the MPC response. The equation of the spin Hamiltonian model for the g mechanism is given in Eq. (1) in the text. At B=0 the four spin eigen-states are divided into a singlet (S, at E S =J/) and a three-fold degenerate triplet states (T 0, T 1, T -1 at E T =-J/). In the S-T basis, SS z >= S, T 0, T 1, T -1 >, the Zeeman term (for B 0) is non-diagonal and the Hamiltonian Eq. (1) reads, H J p p J J J, (1) where p = B gb/ħ and = B g 1 +g )B/ħ. From Eq. (1) it is evident that only the S and T 0 states mix at finite B. Within the x S-T 0 manifold, the solution for the -level system is very well documented 1 as written in the text. Thus, at finite field the eigen-states are not the pure S and T 0 states, and therefore starting at t=0 with the system in the S state, the population oscillates between the two levels. Having the wave functions and energies, we can write the time dependent density matrix matrix elements are iht / ih t/ 0 () t e e whose i mn ( t) ( ) e t 0, () where the meaning of the various symbols is explained in the text. Taking into account the levels finite decay times we multiply Eq. () by the level dependent decay factor: exp(-t/ ); see Eq. (3). The fraction of PP or CTE in the =S,T 0 configuration decays in time and is the given by mn ( t) Tr( P ) P ( ) e e i mn 0 t t (3) Assuming spin dependent dissociation rates k DS, k DT, for the PP or CTE we obtain for the steady state density of free carriers

3 S, T ( ) i k P e t e t dt D mn 0 * S kd ( P ) mn( P ) S, T n, m 1 ( ) 0 1 (4) where we have assumed 0 =P S as in Eq. (3) in the text. Dispersive relaxation. First order decay kinetics in which the photoexcitations density reduces exponentially in time, N exp( t/ ), gives rise to a Lorentzian line shape in 1 the frequency domain, N (1 ). Distribution of relaxation times have been widely used to describe relaxation processes in amorphous and glassy materials,3. The description of the complex relaxation processes in these materials required the use of special distribution functions. Experimental data in these materials have been widely interpreted in terms of the Kohlrausch Williams Watts function, the so-called stretched exponential decay,3. In the frequency domain, the stretched exponential relaxation is closely related to a broader family of dispersive relaxation processes, such as Cole Cole 4 in which the response depends on a fractional power of the frequency 3. In this case, the 1 density profile in frequency takes the form N Re[1 ( i ) ] where 1 is the dispersive parameter 5,6. We use this dispersive profile for fitting the MPC(B) response Magnetic field induced spin polarization. The contribution of spin polarization in high magnetic fields ( spin statistics ) was considered recently by Wang et. al. 7 for explaining the magneto-electroluminescence (MEL(B)) response in organic light emitting diodes (OLED), and magneto-conductance (MC(B)) response in bias driven organic photovoltaic cells at low temperatures and high fields. Here we consider a pair of S=½ species as in Equation (1) above. For the sake of simplicity we disregard the small S-T 0 Zeeman splitting, g B B, (relative to the S-T ±1 splitting, ±g B B) since its effect on spin polarization is negligible because g B B<<k B T.

4 In complete thermal equilibrium (see below for its definition) the fraction of pairs in the singlet configuration is e 1 (1 e ) 1 e e 4 4(1 e ) b b thermal S b b b P (5) where bg B B/k B T (for J<<g B B) is the polarizing parameter, and k B is the Boltzmann constant. Clearly, P S =¼ for B=0. Starting from any given configuration, the system evolves toward thermal equilibrium exponentially, with a time constant that is the spin relaxation time, s. For species with decay time,, the average singlet fraction is therefore thermal 1 thermal PS PS ( PS ) e 4 1 (1 e ) 4 4(1 e ) b (1 e ) b (6) and the average triplet fraction is 3 (1 e ) P P e 4 4(1 e ) b T 1 S (1 ) b (7) Each of the singlet and triplet population is magnetic field dependent, but the total population ((P S +P T )) is not. In order to have finite MPC the PP dissociation into free carriers needs be spin-dependent. Let us denote by the ratio of singlet to triplet dissociation rates. Clearly, when =1 PP singlet and triplet contribute equally to the photoconductivity, and thus PC does not depend on the magnetic field. The contribution of the PP dissociation to the conductivity (or PC) may be written as ( B) ( P P ) whereas MC (MPC) is given by S T ( B) 1 (1 e ) MC (0) 3 (1 e ) b 1 (1 e ) b (8) At the temperatures relevant to this work, b<<1; consequently by expanding Eq. (8) up to b we obtain Eq. (5) in the main text.

5 Supplementary Methods Data simulation. For the actual calculations of the MPC(B) response in the entire field range from B=0 to B=9 Tesla, we added to the Hamiltonian H (Eq. (1) above ) an isotropic HFI term: H a I S (9) HF HF j j j where a HF is the HFI strength, S j =½ is the polaron spin and I j is the nuclear spin associated with the polaron. For the donor-polaron we take as a HFI representative value a HF / B =4 mt; this is a typical value for the proton HFI in polymers such as P3HT. For the acceptor-polaron we take a HF / B =50 T, since in PCBM the polaron wave function resides mostly within the C 60 structure that is composed of ~99% spinless 1 C nuclei. For the high field simulations shown in Figs. 1c, 1f, the particular values of the exchange (J) and the HF (a HF ) are not relevant since their effect is already saturated. For the low and intermediate field range ( B <0.4 Tesla, Figs. b-f) it is important to include both J and a HF. As discussed in the text, the HFI is responsible for the narrow feature MPC N observed in Figs. 1 and. The exchange interaction determines the shape of the response caused by spin mixing due to the g mechanism. As discussed above, the S and T 0 states are separated by an amount J (in the absence of the HFI and at B=0); therefore the g mechanism cannot be operative up to B~J/g B, forming a flat MPC(B) response at small fields. The sharp decrease of MPC near B~0 for PTB7 (Fig. d) is simulated with J~0, whereas the flatter response in the other devices points toward a finite J for the CT excitons (see Table (1) ). As discussed in the text, both PP and CT excitons contribute to MPC; their contributions may have opposite signs (e.g. Figs. 1c, 1f) or identical signs. Therefore, the overall response is the sum of the PP and CT exciton contributions; thus, the narrow feature MPC N (that is caused by the HFI) may assume positive sign (Figs. 1c,d,f, b,c,e), negative sign (Fig. f) or be ~0 (Fig. d). In the simulations shown in Fig., we have taken these two contributions into account. Table (1) shows the relevant parameters used.

6 Supplementary References 1 Cohen-Tannoudji, C., Diu, B. & Laloe, F. Quantum Mechanics. Vol. (John Wiley & Sons, 1977). Pfister, G. & Scher, H. Dispersive transient transport in disordered solids. Advances in Physics 7, (1978). 3 Alvarez, F., Algeria, A. & Colmenero, J. Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation function. Phys. Rev. B 44, (1991). 4 Cole, K. S. & Cole, R. H. Dispersion and absorption in dielectrics. J. Chem. Phys. 9, (1941). 5 Bello, A., Laredo, E. & Grimau, M. Distribution of relaxation times from dielectric spectroscopy using Monte Carlo simulated annealing: application to PVDF. Phys. Rev. B 60, (1999). 6 Epshtein, O., Nakhmanovich, G., Eichen, Y. & Ehrenfreund, E. Dispersive dynamics of photoexcitations in conjugated polymers measured by photomodulation spectroscopy. Phys. Rev. B 63, 1506 (001). 7 Wang, J., Chepelianskii, A., Gao, F. & Greenham, N. C. Control of exciton spin statistics through spin polarization in organic optoelectronic devices. Nat Commun 3, 1191 (01).