Shot Noise in Magnetic Tunnel Junctions: Evidence for Sequential Tunneling

We report the experimental observation of sub-Poissonian shot noise in single magnetic tunnel junctions, indicating the importance of tunneling via impurity levels inside the tunnel barrier. For junctions with weak zero-bias anomaly in conductance, the Fano factor (normalized shot noise) depends on the magnetic configuration being enhanced for antiparallel alignment of the ferromagnetic electrodes. We propose a model of sequential tunneling through nonmagnetic and paramagnetic impurity levels inside the tunnel barrier to qualitatively explain the observations.

Figure 1

Typical dynamic resistance obtained in the P state for the Cr-free (a) and Cr-doped (b) junctions with 0.8 Å $\delta$-layer measured at 300, 77, and 2 K. (c) Reduction of the TMR with applied voltage for Cr-free and Cr-doped MTJ’s at $T=2\mathrm{K}$. (d) Dependence of the $\mathrm{ZBA}(\%)=100[R(0\mathrm{mV})-R(100\mathrm{mV})]/R(100\mathrm{mV})$ determined for the P alignment on Cr (at 2 K).

Figure 2

(a) Typical voltage noise measured for a Cr-free MTJ at $T=2\mathrm{K}$ with the applied currents (from bottom to up) of 3.4, 5 and $6\mu \mathrm{A}$. (b) Voltage dependence of $F$ on bias, for the Cr-free (filled) and 0.4 Å Cr-doped (open stars), also measured at $T=2\mathrm{K}$. The error bars show standard deviations.

Figure 3

(a) Dependence of the TMR and $F$ (for the P state) on the resistance area product ($R\times A$). Solid horizontal line marks $F=1$. Vertical dashed line separates the Cr-free and Cr-doped regions. (b) Dependence of the relative variation of $F$ with alignment $\Delta F/F_{\mathrm{P}}(\%)=100(F_{\mathrm{AP}}-F_{\mathrm{P}})/F_{\mathrm{P}}$ on the relative strength of the ZBA. Solid symbols point to the undoped samples. The lines are guides for the eye.

Figure 4

Two models: (a) a large normal region $R_M$ such that electrons can be treated as noninteracting, coupled to biased emitter and collector reservoirs in P or AP configuration, (b) $R_M$ is a single spin-polarized impurity level that can hold only one electron with spin at a (random) angle $\theta$ with respect to the collector magnetization.

Figure 5

Fano factor as a function of the left-right asymmetry parameter $\beta$ setting $\alpha =1/5$ for the two models sketched in Fig. 4. Solid lines are for the P and dashed lines for the AP magnetic configurations. Insets show the dimensionless current $i$ and noise $s=Fi$ defined in the text. Note the logarithmic scale for $\beta$: Assuming tunnel rates depend exponentially on the barrier thickness, this corresponds to a linear scale for the $R_M$ position inside the tunnel junction (small $\beta$ corresponding to the proximity to $R_L$ and large $\beta$ to $R_R$).