Spin-dependent shot noise in MgO-based magnetic tunnel junctions under noncollinear magnetization alignment

We report experimental measurements of shot noise in MgO-based magnetic tunnel junctions (MTJs) upon angular magnetization rotation in the free layer. The normalized shot noise (the Fano factor) is found to be sub-Poissonian and exhibits a sinusoidal-like variation over the relative magnetic orientation between the free and the pinned layer inside the MTJs. The observed sub-Poissonian statistics provides direct evidence of electron sequential tunneling mediated by localized states inside the tunnel barrier. The variation of the Fano factor can be interpreted in terms of a semi-classical model that we propose. Based on this model, the variation of the Fano factor can be used to reveal microscopic details of the tunneling barrier.

Figure 1

Resistance (labeled by triangles) and Johnson-Nyquist noise (labeled by solid circles) of a MTJ as a function of the relative angle between the magnetization vectors of the ferromagnetic electrodes. Theoretical predictions for the resistance and Johnson noise are also plotted as solid lines. The error bar represents the experimental error from 10 power spectra taken for each angle.

Figure 2

(a) Noise power spectral density for a MTJ sample with the relative orientation between the magnetic moments at $0^{\circ }$, ${90}^{\circ }$, and ${180}^{\circ }$. The measurements were performed at constant current $I=20\mu \mathrm{A}$ (bias voltages were 0.232, 0.328, and 0.531 V, respectively), set by a resistor in series with MTJ. The open circles denote the experimental data, and the solid lines denote the mathematical fit. (b) The spectrum shows the frequency-independent component of the device noise. The $1/f$ noise is subtracted away according to Eq. (1).

Figure 3

(a) Fano factor as a function of the relative angle between the magnetization vectors of the ferromagnetic electrodes. The error bars represent the standard deviation. A theoretical fitting curve is also plotted for comparison, which is discussed in the text. (b) Fano factor measurements performed on two other similar MTJ samples. The solid lines connecting the squares are to guide the eye.

Figure 4

Fano factor as a function of the ratio between the tunneling rates on a logarithmic scale, ${\log }_{10}\left({\gamma }_R/{\gamma }_L\right)$, and the relative orientation between the magnetic moments of ferromagnetic electrodes $\theta$, for the spin polarization $p=0.2$ (a), 0.35 (b), 0.5 (c), and 0.65 (d).

Figure 5

(a) Valley position and (b) valley depth in the Fano factor curve as a function of the ratio of tunneling rates on a logarithmic scale, ${\log }_{10}\left({\gamma }_R/{\gamma }_L\right)$, for various spin polarizations $p$.