Spin-flip noise due to nonequilibrium spin accumulation

When current flows through a magnetic tunnel junction (MTJ), there is spin accumulation at the electrode-barrier interfaces if the magnetic moments of the two ferromagnetic electrodes are not aligned. Here we report that such nonequilibrium spin accumulation generates its own characteristic low frequency noise (LFN). Past work viewed the LFN in MTJs as an equilibrium effect arising from resistance fluctuations $\left(S_R\right)$ which a passively applied current $\left(I\right)$ converts to measurable voltage fluctuations $\left(S_V=I^2{S}_R\right)$. We treat the LFN associated with spin accumulation as a nonequilibrium effect, and find that the noise power can be fitted in terms of the spin-polarized current by $S_{I}f=aIcoth\left(\frac{I}{b}\right)-ab$, resembling the form of the shot noise for a tunnel junction, but with current now taking the role of the bias voltage, and spin-flip probability taking the role of tunneling probability.

Figure 1

(a) A simple schematic of the MTJ stack. (b) Magnetoresistance (MR) with field ramping up (blue) and down (red) at a fixed bias current of 6.5 $\mu \mathrm{A}$ at 296 K for sample M8. The vertical dashed lines denote different fields (ramping down) where noise measurements are shown in Fig. 2. P, AP, and ${\mathrm{P}}^{\prime }$ denote parallel, antiparallel, and another parallel state, respectively. The inset shows four continuous runs near the free layer reversal field (ramping down) for sample M9. Three fields ($-62$, $-64$, and $-67$ Oe) are chosen for noise measurements shown in Fig. S2. (c) Schematic of the spin accumulation in the antiparallel state. With the assumption of ideal symmetry filtering of the MgO barrier, the down-spin ${\mathrm{\Delta }}_1$ electrons from the left side dominate the tunnel process at large bias. In the right side there are no available down-spin ${\mathrm{\Delta }}_1$ states, so these electrons undergo spin-flip scattering and become the up-spin ${\mathrm{\Delta }}_1$ states. The nonequilibrium spin accumulation is characterized by chemical potential difference $\mathrm{\Delta }\mu$ between up- and down-spin ${\mathrm{\Delta }}_1$ states. The density of state (DOS) energy diagram follows that of the calculated band dispersions [19, 20] but not to the scale.

Figure 2

Bias dependence of normalized power spectrum density (a) $\sqrt{S_{V}f}$ and (b) $\alpha =A{S}_{V}f/V^2$ at different magnetic field points and at 296 K. The current noise $S_{I}f$ in (c) and (d) are derived by $\sqrt{S_{V}f}$ in (a) and $dV/dI$ in (e), which shows an almost linear dependence on the bias current without saturation. The $y$ scale in (c) is larger than that in (d). In (e), nonlinearity around 0.4 V can be seen for $dV/dI$. (f) Bias dependence of $S_{I}f$ in double-log scale. The slope approaches one at high bias except for the P (200 Oe) and ${\mathrm{P}}^{\prime }$ states ($-1500$ Oe). The solid lines are fits following Eq. (1).

Figure 3

Bias dependence of normalized power spectrum density $S_{I}f$ at different temperatures: (a) 296, (b) 78, (c) 50, and (d) 17 K. The solid lines are fits following Eq. (1). The 400 Oe data at 17 K are not shown because the $1/f$ noise is too small to be reliably extracted from the background noise.

Figure 4

Field dependence of the fitting parameters (a) $a$ and (b) $b$ following Eq. (1) at different temperatures. Note that $H_{\mathrm{\Lambda }}$, the position of the broad peak, moves when temperature decreases from 296 to 78 K. (d) The MR measured with small bias and (c) field derivative of MR at different temperatures.