Voltage-dependent plasticity of spin-polarized conductance in phenyl-based single-molecule magnetic tunnel junctions

Abstract

Synaptic strengths between neurons in brain networks are highly adaptive due to synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity induced by temporal correlations between the firing activity of neurons. The development of experimental techniques in recent years enabled the realization of brain-inspired neuromorphic devices. Particularly, magnetic tunnel junctions (MTJs) provide a suitable means for the implementation of learning processes in molecular junctions. Here, we first considered a two-neuron motif subjected to STDP. By employing theoretical analysis and computer simulations we showed that the dynamics and emergent structure of the motif can be predicted by introducing an effective two-neuron synaptic conductance. Then, we considered a phenyl-based single-molecule MTJ connected to two ferromagnetic (FM) cobalt electrodes and investigated its electrical properties using the non-equilibrium Green's function (NEGF) formalism. Similar to the two-neuron motif, we introduced an effective spin-polarized conductance in the MTJ. Depending on the polarity, frequency and strength of the bias voltage applied to the MTJ, the system can learn input signals by adaptive changes of the effective conductance. Interestingly, this voltage-dependent plasticity is an intrinsic property of the MTJ where its behavior is reminiscent of the classical temporally asymmetric STDP. Furthermore, the shape of voltage-dependent plasticity in the MTJ is determined by the molecule-electrode coupling strength or the length of the molecule. Our results may be relevant for the development of single-molecule devices that capture the adaptive properties of synapses in the brain.

Fig 1. Schematic representation of the two-neuron motif and MTJ.

(A) (Top) Two neuronal phase oscillators (1/2) reciprocally connected via synapses of strength g₂₁/g₁₂. (Bottom) The synaptic change governed by the classical temporally asymmetric STDP profile. STDP parameters were A₊ = A₋ = 0.005 and τ₊ = τ_- = 20 ms. (B) (Top) A single-molecule MTJ composed of a PDT molecule connected to two FM cobalt electrodes (L/R) characterized by tunneling conductance in parallel (G_P) and anti-parallel (G_AP) configurations. (Bottom) The derivative of the effective conductance is calculated to provide a measure of its change.

Fig 2. Theoretical and simulation results for the two-neuron motif.

(A1) Theoretical prediction of the fixed point of phase lag between the two neurons in terms of the effective synaptic strength and delay calculated by Eq (4). (A2) Theoretical prediction of the two-neuron synaptic change (arrows) in terms of the effective synaptic strength at a given delay (indicated above panel) calculated by Eq (5). (B1-B3) Simulation results of the steady-state phase lag between neurons for different values of the effective synaptic strength (denoted in the figure) are consistent with the theoretical predictions.

Fig 3. Activity-dependent learning in the two-neuron motif by STDP.

(A1,A2) Activity of the neurons in terms of the phase of oscillations characterized with strong phase synchronization (χ ≈ 0), when delay is ψ = π/4 (A1), and the corresponding LTP of the synapses (A2). (B1,B2) Activity of the neurons in terms of the phase of oscillations associated with a loosely synchronized state (i.e. small non-zero χ), when delay is ψ = π/2 (B1), and the corresponding LTD of the synapses (B2).

Fig 4. Voltage-dependent plasticity of effective conductance in the PDT-based MTJ.

(A1) Current-voltage characteristics for parallel and anti-parallel configurations. (A2) The corresponding tunneling conductance derived from the spin-polarized current for parallel and anti-parallel states. (B1) The effective tunneling conductance introduced by Eq (13). (B2) The derivative of the effective conductance is calculated to provide a measure of its change which is reminiscent of the classical asymmetric STDP profile. The molecule-electrode coupling strength was γ = 0.1.

Fig 5. The effect of molecule-electrode coupling strength on the voltage-dependent plasticity of effective conductance in the PDT-based MTJ.

(A1,A2) Current-voltage characteristics in parallel (A1) and anti-parallel (A2) configurations for different values of the molecule-electrode coupling strength. (B1,B2) The corresponding tunneling conductance derived from the spin-polarized current for parallel (B1) and anti-parallel (B2) states. (C1) The effective tunneling conductance is calculated when the molecule-electrode coupling strength is varied. (C2) The derivative of the effective conductance as a measure of its asymmetric change.

Fig 6. The length of the molecule determines the voltage-dependent plasticity of effective conductance.

(A1,A2) Current-voltage characteristics in parallel (A1) and anti-parallel (A2) configurations for different values of the molecule-electrode coupling strength in the BPDT-based MTJ. (B1,B2) The corresponding tunneling conductance derived from the spin-polarized current for parallel (B1) and anti-parallel (B2) states. (C1) The effective tunneling conductance is calculated when the molecule-electrode coupling strength is varied. (C2) The derivative of the effective conductance as a measure of its asymmetric change.

Fig 7. Voltage-dependent learning in the MTJ.

(A) (Top) A sinusoidal voltage signal with amplitude (strength) V_max = 0.2 V and frequency ω = 100 Hz is applied to the MTJ. (Bottom) Calculated effective conductance of the MTJ in response to the applied voltage. Arrows show LTP-like and LTD-like behavior of the effective conductance depending on the polarity of the input signal. (B) Frequency dependency of learning in the MTJ for different values of the signal strength. The molecule-electrode coupling strength was γ = 0.1.