Symmetry-dependent electron-electron interaction in coherent tunnel junctions resolved by measurements of zero-bias anomaly

We provide conclusive experimental evidence that zero-bias anomaly in the differential resistance of magnetic tunnel junctions is due to electron-electron interaction (EEI), clarifying a longstanding issue. The magnon effect that caused confusion is now excluded by measuring at low temperatures down to 0.2 K and with reduced ac measurement voltages down to 0.06 mV. The normalized change of conductance is proportional to $ln(eV/k_{B}T)$, consistent with the Altshuler-Aronov theory of tunneling that describes the reduction of density of states due to EEI, but inconsistent with magnetic impurity scattering. The slope of the $ln(eV/k_{B}T)$ dependence is symmetry dependent: the slopes for parallel and antiparallel states are different for coherent tunnel junctions with symmetry filtering, while nearly the same for those without symmetry filtering (amorphous barriers). This observation may be helpful for verifying symmetry-preserved filtering in search of new coherent tunneling junctions, and for probing and separating electron Bloch states of different symmetries in other correlated systems.

Figure 1

(a) First and (b) second derivative at 3.6 K in the P (red line, 500 G) and AP (blue line, $-300$ G) states. ZB, M, and Ph peaks in IETS are clearly visible. The maximum modulation voltage is about 4 mV.

Figure 2

Differential conductance vs bias for the (a) P state and (c) AP state, and $\Delta G$ vs $eV/k_{B}T$ on a log scale in the (b) P and (d) AP states, where $\Delta G\left(V\right)=G\left(V\right)-G\left(0\right)$. Curves in the P state are measured with 0.06 mV excitation voltage. An effective temperature $T_{\mathrm{fit}}=1.2$ K is assumed for the 0.8 K curve. The curves in the AP state are measured with 0.1 mV excitation voltage. And $T_{\mathrm{fit}}=1.1$ and 0.7 K are assumed for the 0.8 and 0.2 K data. (e) $\Delta G$ curves with $\theta$ from $0^{\circ }$ (P) to ${180}^{\circ }$ (AP) at 0.2 K; (f) the angle dependence of fitted slopes and the resistance. Dashed lines in (b), (d), and (e) are fits using Eq. (1). The dashed line in (c) is a fit for background subtraction. The dashed line in (f) is a fit based on Eq. (2).

Figure 3

Conductance change at 0.2 K in the (a) P and (b) AP states within $\pm 3$ mV; to emphasize the small change, we redefine $\Delta G\left(V\right)=G\left(V\right)-G\left(3\mathrm{mV}\right)$. For IETS, the second harmonic reading directly from lock-in $\mathrm{[}(d^{2}V/d{I}^2)\times I_{ac}^2\text{]}$ is presented in the (c) P and (d) AP states, and $d^{2}V/d{I}^2$ (after dividing $I_{ac}^2)$ in the (e) P and (f) AP states. Different modulation voltages are denoted with colors.

Figure 4

First and second derivatives at 3.6 K for sample A1. (a) Differential resistance in the P (red line) and AP (blue line) states. (b) IETS in the P (red line, left coordinate) and AP (blue line, right coordinate) states. The maximum modulation voltage is about 0.5 mV.

Figure 5

Differential conductance vs bias voltage in the (a) P and (c) AP states, and normalized $\Delta G$ vs $eV/kT$ on a log scale in the (b) P and (d) AP states. The dashed lines in (a) and (c) are fittings for background subtraction. The dashed lines in (b) and (d) are fittings with 2D EEI theory.

Figure 6

(a) Conductance vs bias for sample M3. Solid lines are fits with Eq. (C1). The fitted parameters are $E_0=100$ mV, $G_2=321.5$ $\mu \text{S}$, and $G_3/G_2=0.0076$. (b) Normalized $\Delta G$ vs $eV/kT$ for different temperatures. The temperatures in the parentheses are $T_{\mathrm{fit}}$ assumed in Eq. (C1).

Figure 7

(a) Normalized $G$ vs $\sqrt{V}$ measured at 10 K for different $T_{ann}$ in the P state, copied from Ref. [27]. (b) The same data fitted with the 2D EEI model with different $T_{\mathrm{fit}}$.