Temperature dependence of enhanced spin relaxation time in metallic nanoparticles: Experiment and theory

We study the enhanced spin relaxation time of Au nanoparticles in nanopillar-shaped double-barrier junction devices with a stacked Fe/MgO/Au-nanoparticle/MgO/Fe structure. The size of Au nanoparticles located in a current path is deduced from a transmission electron micrograph and the Coulomb blockade behavior in the current-voltage characteristics of the devices. A finite tunnel magnetoresistance (TMR) is observed above a critical current and is attributable to spin accumulation in Au nanoparticles. Based on a simple model of TMR due to spin accumulation in a nanoparticle, the spin relaxation time ${\tau }_s$ is estimated from the magnitude of the critical current. The temperature and bias-voltage region where TMR appears are determined from systematic observations, showing that the appearance of TMR is not associated with the Coulomb blockade but with spin accumulation. We find that the obtained ${\tau }_s$ is anomalously extended (∼800 ns) at low temperatures and abruptly decreases above a critical temperature. Interestingly, the critical temperature strongly depends on the size of the Au nanoparticles and is much lower than the effective temperature corresponding to the discrete energy spacing. A theoretical analysis for the spin relaxation of electrons with discrete energy levels shows that not only the anomalously extended spin relaxation time, but also the strong temperature dependence of ${\tau }_s$ arise from the broadening of discrete energy levels due to coupling with phonons in the surrounding matrix. Numerical calculations using reasonable parameter values well reproduce the observed temperature and size dependence of the spin relaxation time in Au nanoparticles.

Figure 1

(a) Device structure of a ferromagnetic double tunnel junction with Au nanoparticles grown on the first MgO barrier. (b) Aberration corrected high-resolution TEM micrograph of Au nanoparticles in a MgO tunnel barrier.

Figure 2

(a) Current-voltage ($I\text{−}V$) curve of a microfabricated pillar with various temperatures. (b) dI/dV voltage of microfabricated pillar curves with various temperatures. (c) $I\text{−}V$ curves of different samples fabricated on a substrate at 7 K. (d) Temperature dependence of the CB voltage of different samples fabricated on a substrate.

Figure 3

(a) Bias voltage dependence of MR curves measured at 7, 20, 40, and 100 K in a device with Au nanoparticles with nominal diameters of 1.5 nm. (b) Mapping of the MR ratio as a function of temperature and bias voltage. The bias voltage $V_{\mathrm{C}}^{\mathrm{TMR}}$ for the appearance of TMR calculated theoretically is shown by the dashed curve. The vertical dashed lines stand for the threshold bias voltage $V_{\mathrm{th}}^{\mathrm{CB}}$ for the Coulomb blockade.

Figure 4

Temperature dependence of the spin relaxation time of Au nanoparticles with nominal diameters of 1.5, 1.9, and 2.2 nm (blue, green, and red closed circles, respectively). The spin relaxation time ${\tau }_s$ at various temperatures was estimated using the equation ${\tau }_s=\left|e\right|/I_{\mathrm{C}}^{\mathrm{TMR}}$, where $I_{\mathrm{C}}^{\mathrm{TMR}}$ is the current at the bias voltage for the appearance of TMR. Error bars define the range of ${\tau }_s$ given by the uncertainty of the bias voltage at which the MR appears in the resistance vs field measurements.