Spin-mediated Photomechanical Coupling of a Nanoelectromechanical Shuttle

We show that nanomechanical vibrations in a magnetic shuttle device can be strongly affected by external microwave irradiation through photo-assisted electronic spin-flip transitions. Mechanical consequences of these spin flips are due to a spin-dependent magnetic force, which may lead to a nanomechanical instability in the device. We derive a criterion for the instability to occur and analyze different regimes of nanomechanical oscillations. Possible experimental realizations of the spin-mediated photomechanical instability and detection of the device backaction are discussed.

Figure 1

(a) Sketch of a device with a suspended CNT resonator in tunneling contact with two ferromagnetic electrodes (L,R) with opposite magnetization directions. Flexural CNT vibrations are actuated by a magnetic force caused by the Zeeman interaction between the spin of CNT electrons and an inhomogeneous magnetic field $B_z(z)$ from a magnetic gate (tip). (b) A microwave field $h\cos (\mathrm{\Omega }t)$ induces electron spin flips in the CNT, which are resonant at $u=u_r$ where the photon energy $\hslash \mathrm{\Omega }$ equals the deflection-dependent Zeeman energy splitting $g{\mu }_B{B}_z(u)$. Since the magnetic force is spin dependent, the spin in this way mediates the photomechanical coupling discussed in the text.

Figure 2

Ratio between work done on the NEM system by the magnetic force ($\propto W_1$) and energy dissipated due to intrinsic friction ($\propto W_0$) plotted as a function of CNT oscillation amplitude $A$ for $\mathrm{\Gamma }=0.6\times 10^9{\mathrm{s}}^{-1}$, $\mathrm{\Delta }-\mathrm{\Omega }=\mathrm{\Gamma }$, $u_0=2\mathrm{pm}$, $\partial B_z/\partial z=5\times 10^6\mathrm{T}/\mathrm{m}$, $Q_0=10^6$, and three different microwave field intensities ${\nu }_h$. If $W_1/W_0<1$ for some $A$, then $A$ decreases with time according to Eq. (15), while if $W_1/W_0>1$, $A$ increases with time. If $W_1/W_0=1$ (black horizontal help line) for some finite amplitude, then Eq. (15) has a nontrivial ($A\ne 0$) stationary solution for that amplitude. The red (bottom) curve (${\nu }_h=0.4\mathrm{\Gamma }$) describes the behavior of the NEM system below the instability threshold and illustrates the text’s regime (i), which has no nontrivial stationary solution. The green (middle) curve (${\nu }_h=0.6\mathrm{\Gamma }$) corresponds to regime (ii), where the mechanical system is characterized by two nontrivial stationary solutions. The blue (top) curve (${\nu }_h=1.0\mathrm{\Gamma }$) corresponds to regime (iii), with a single nontrivial stationary solution to Eq. (15) for $A=A_{\lim }$. In this regime, a mechanical instability leads to self-sustained resonator oscillations of amplitude $A_{\lim }$ [20].