Rotational Coupling in Methyl-Tunneling Electron Spin Echo Envelope Modulation

Coherence between tunnel-split states of a methyl quantum rotor can be generated and observed in stimulated and spin-locked echo experiments, if hyperfine coupling of a nearby electron spin to the methyl protons breaks C$$_3$$ 3 symmetry and is of the same order of magnitude as the tunnel splitting. Here, we consider the case of two methyl groups bound to the same sp$$^{3}$$ 3 -hybridized atom, which is important in the context of common nitroxide spin labels. For a simple form of the rotor-rotor coupling Hamiltonian, we provide an approach that allows for density operator computations of this system with 1152 quantum states with moderate computational effort. We find that, in the regime where the ratio between rotor-rotor coupling and rotational barrier is much smaller than unity, three-pulse ESEEM and hyperfine-decoupled ESEEM depend only on the tunnel splitting, but not on this ratio. This finding may simplify the treatment of tunnel-induced electron decoherence in systems where the methyl groups are bound to sp$$^{3}$$ 3 -hybridized atoms.

Magnetic excitation and readout of methyl group tunnel coherence

Methyl groups are ubiquitous in synthetic materials and biomolecules. At sufficiently low temperature, they behave as quantum rotors and populate only the rotational ground state. In a symmetric potential, the three localized substates are degenerate and become mixed by the tunnel overlap to delocalized states separated by the tunnel splitting νt. Although νt can be inferred by several techniques, coherent superposition of the tunnel-split states and direct measurement of νt have proven elusive. Here, we show that a nearby electron spin provides a handle on the tunnel transition, allowing for its excitation and readout. Unlike existing dynamical nuclear polarization techniques, our experiment transfers polarization from the electron spin to methyl proton spins with an efficiency that is independent of the magnetic field and does not rely on an unusually large tunnel splitting. Our results also demonstrate control of quantum states despite the lack of an associated transition dipole moment.

Quadrupole Excitation in Tunnel Splitting Oscillation in Nanoparticle

We analyze the interference between tunneling paths that occur for a spin system with special Hamiltonian both for dipole and quadrupole excitations. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting for both excitations is modulated, with zeros occurring periodically and the number of quenching points for quadrupole excitation decreasing. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.