Vibrationally-mediated Dzyaloshinskii-Moriya interaction as the origin of Chirality-Induced Spin Selectivity in donor-acceptor molecules

Abstract

Chirality-induced spin selectivity (CISS) was recently observed in photo-excited donor-chiral bridge-acceptor molecules, but a predictive theory able to explain available experiments is still lacking. Here we show that low-energy torsional modes modulating hopping and spin-orbit coupling give rise to a Dzyaloshinskii-Moriya interaction between the transferred electron and the one sitting on the donor, producing high spin polarization for perfectly realistic parameters. Our model introduces a low energy scale in the spin dynamics which explains the magnetic field dependence observed in EPR measurements and predicts a non-trivial temperature dependence, as demonstrated by numerical simulations. The present theory lays the foundations for future test-bed experiments and for the design of applications in spintronics and quantum technologies.

Figures (12)

• Figure 1: (a) Scheme of the minimal electron-transfer model with ground and excited orbitals on the donor (D, De), an intermediate orbital on the bridge (B) and one on the acceptor (A). The dynamics is ruled by incoherent spin-independent jumps from De to B and from B to A at rates $\Gamma$ and by a Hamiltonian $H$ including fermionic and bosonic degrees of freedom. (b) The Hamiltonian $H$ with a single electron localized on $D$ and one on $B$ is mapped onto an effective spin Hamiltonian involving spin operators ${\bf s}_D$ and ${\bf s}_B$. (c,d) Simulated time evolution of the charge $\langle n_{i\uparrow}+n_{i\downarrow}\rangle$ (c) and of the local spin polarization $2\langle s_{zi} \rangle=\langle n_{i\uparrow}-n_{i\downarrow}\rangle$ (d) on different orbitals. Solid lines: simulation with the full Hamiltonian $H$ and up to 9 bosons. Dashed: simulation with the effective Hamiltonian $H_{\rm eff}$. Parameters: $t=1$ meV, $\lambda=0.1$ meV, $U=3.5$ eV, $\Delta=5$ eV, $t_1=1$ meV, $\lambda_1=1$ meV, $\hbar\omega=2$ meV, $J_{CE} = -10^{-3}$ meV, $\Gamma=5\times 10^{-3}$ meV and we initialized the system with a fixed number of bosons $n=3$.
• Figure 2: Top panels: spin polarization, corresponding to twice the real part of the singlet-triplet coherence. Middle panels: spin rotation about chiral axis, i.e. imaginary component of the singlet-triplet coherence. Bottom: triplet population. All the values are at the end of the ET, as a function of $\lambda_1$ and $t_1$. Other parameters of the simulation: $t=1$ meV, $\Gamma = 5\times10^{-3}$ meV (corresponding to ET time in the few hundreds of ps range $\hbar/\Gamma \approx 100$ ps), direct exchange contribution $J_{CE}=-10^{-3}$ meV, $\lambda=0.1$ meV, $U=3.5$ eV, $\Delta=5$ eV, $\hbar \omega_0 = 2$ meV. Simulations with larger $t_1$ and $\Gamma$ are reported in the Supporting Information.
• Figure 3: (a) Energy level diagram as a function of the magnetic field applied at $\theta=90^\circ$ with respect to the chiral anisotropy axis, using parameters $t_1=8$ meV, $\lambda_1=2.5$ meV. Solid (dashed) curves refer to $n=0(1)$ boson, leading to avoided level crossing at different fields and of different width. (b) CISS efficiency at 80 K as usually obtained by fitting EPR spectra, corresponding to twice the triplet component $P_T$. Different solid lines refer to different $t_1$ as indicated in the legend, while dashed line of the same color are obtained by considering doubling the boson energy while keeping the temperature fixed ($\hbar \omega=2\rightarrow4$ meV). Dashed lines indicate the fields probed by EPR at X-, Q- and W-band. The other parameters are kept fixed to $J_{CE}=-1\times10^{-2}$ meV, $t=1$ meV, $\lambda=0.1$ meV, $U=3.5$ eV, $\Delta=5$ eV.
• Figure 4: Evolution of the spin polarization on A (black) and D (red) for systems with one, two, and three sites on the bridge. Parameters are reported in Table \ref{['tab:dinamiche_over50incoherent']} of the Supporting Information. Full population and spin polarization evolution is displayed in Fig. \ref{['fig:dinamiche_over50incoherent']}
• Figure S1: Population and spin polarization evolution accounting for spin-orbit assisted incoherent transfer from donor to bridge, according to approach 1. Parameters are set as describe in Section \ref{['sec:incoherent_soc']}. The transfer rates are set as $\Gamma_{D,tot}=\Gamma_A=4.3e-3meV$, and different columns refer to different values of $\theta$. Left: $\theta=0$. Center: $\theta=\arctan(0.1)$. Right: $\theta=\arctan(0.5)$.