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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.

This paper extends our recent theoretical study Kalvova et al. (J. Supercon. and Novel Mag. 26, 773 2013) of transient currents through molecular bridges to magnetic tunneling. We calculate the excess magnetization on a molecular bridge shunting the magnetic junction. The system is represented by two ferromagnetic electrodes bridged by a molecular size island with a few discrete electronic levels and a local Hubbard type correlation. The island is linked to the electrodes by tunneling junctions. One of the junctions is permanent, the coupling strength of the other one is assumed to undergo rapid changes modulating the connectivity of the system. The sudden switching events give rise to transient magnetic currents resulting in changes of magnetization at the island. They vary with the constant galvanic bias between the electrodes. Depending on the time scale of the switching series, the transients are dominated by the initial quantum correlations, or reach the kinetic stage controlled by a simple relaxation mechanism. We employ the nonequilibrium Green’s functions. The finite-time correlated initial conditions are taken into account using the partitioning-in-time method we developed previously Velický et al. (Phys. Rev. B 81, 235116 2010). The numerical solution is obtained solving the real-time Dy-son equation in the integro-differential form self-consistently. For long time asymptotic, a generalized master equation is matched to the initial stage solution.

We consider current flow between two metallic leads joined by tunneling junctions to a molecular island. The junctions are assumed to be “wiggly,” that is, switching on and off intermittently. The resulting sequence of current transients overlaps in dependence on the interplay between the switching times and the decay time of “initial” correlations induced by each switching event. The process is described in terms of nonequilibrium Green’s functions.