Transient Magnetic Currents Through a Molecular Bridge: Limits to Reduction of Nonequilibrium Green’s Functions to a Generalized Master Equation

Abstract

Transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island are calculated. The island is represented by an Anderson type local center. The tunneling spectral functions simulate nickel. Transient magnetic currents under a constant galvanic bias between the electrodes are invoked by sudden switching of the junctions. The process is treated numerically using the non-equilibrium Greens functions (NEGF) (Kalvova et al., J. Supercon. Novel Mag. 26, 773, 2013, J. Supercon. Novel Mag. 28, 1087, 2015) from the early stages of the transient depending on the finite time initial conditions to the late asymptotics of free relaxation to the steady state. This serves as a reference for testing the simpler and physically transparent description by a generalized master equation, resulting from the NEGF scheme approximated by the Generalized Kadanoff-Baym Ansatz (GKBA) (Spicka et al., Internat. J. Mod. Phys. 28 1430013-1, 2014). It turns out that decisive for the applicability of GKBA is the spectral structure of tunneling functions and their positioning with respect to the island level dependent on the bias and the exchange splitting. Favorable for the validity of GKBA are weak tunneling and spectrally flat tunneling functions. Stretching of these conditions toward the realistic situation for transition metal electrodes with their complex sd surface-modified spectral properties is limited.