Macrospin Tunneling and Magnetopolaritons with Nanomechanical Interference

We theoretically address the quantum dynamics of a nanomechanical resonator coupled to the macrospin of a magnetic nanoparticle by both instanton and perturbative approaches. We demonstrate suppression of the tunneling between opposite magnetizations and destruction of magnetopolaritons (coherent magnetomechanical oscillations) by nanomechanical interference. The predictions can be verified experimentally by a molecular magnet attached to a nanomechanical bridge.

Figure 1

(a) A torsional resonator consisting of a beam (e.g., nanotube) and a load (e.g., a magnetic nanoparticle or a SMM attached to a paddle). (b) Probability of finding the resonator at a given angle for the four lowest energy levels. (c) The first excited state of the resonator is effectively a superposition of two states with positive and negative torsion angles. The spin-reversal tunnel path on a unit sphere with a rigid resonator (middle geodesic) splits into two equivalent ones (fuzzy paths represent uncertainty in the tilt of the mechanical resonator), allowing interference.

Figure 2

(a) A particle falls in a camelback-shaped potential following the quasiclassical path (bold curve). (b) Results of a numerical integration of Eq. (5) for different frequencies of the mechanical resonator.

Figure 3

(a) Tunnel splittings as a function of the macrospin-resonator coupling $\alpha$ for the first three excited states of the resonator. The curves show analytical results, while the squares are based on the numerical diagonalization of the Hamiltonian corresponding to an ${\mathrm{Fe}}_8$ SMM. (b) Analogous plot for tunnel splittings of the magnetopolariton modes corresponding to the Fock states differing by one phonon. (c) Lowest energy levels of the ${\mathrm{Fe}}_8$ SMM coupled to a mechanical resonator obtained by numerical diagonalization. ${\Delta }_0/\hslash {\omega }_r=3\times {10}^{-6}$ (the energy is offset by $-28.239\mathrm{K}$).