We study time-dependent electronic and spin transport through an electronic level connected to two leads and coupled with a single-molecule magnet via exchange interaction. The molecular spin is treated as a classical variable and precesses around an external magnetic field. We derive expressions for charge and spin currents by means of the Keldysh nonequilibrium Green's functions technique in linear order with respect to the time-dependent magnetic field created by this precession. The coupling between the electronic spins and the magnetization dynamics of the molecule creates inelastic tunneling processes which contribute to the spin currents. The inelastic spin currents, in turn, generate a spin-transfer torque acting on the molecular spin. This back-action includes a contribution to the Gilbert damping and a modification of the precession frequency. The Gilbert damping coefficient can be controlled by the bias and gate voltages or via the external magnetic field and has a nonmonotonic dependence on the tunneling rates.

The supercurrent through a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states outside the superconducting gap region and the Andreev levels. This redistribution of the quasiparticles leads to a nonequilibrium population of the Andreev levels and an enhancement of the supercurrent which is visible as a modified current-phase relation as well as a nonmonotonous critical current as function of temperature. The nonmonotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.

The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi- particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current–phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable 2conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even–odd effect attributable to precession-assisted multiple Andreev reflections. This article is part of the theme issue ‘Andreev bound states’.

We investigate the charge and spin transport of a voltage-biased superconducting point contact coupled toa nanomagnet. The magnetization of the nanomagnet is assumed to precess with the Larmor frequencyωLwhen exposed to ferromagnetic resonance conditions. The Larmor precession locally breaks the spin-rotationsymmetry of the quasiparticle scattering and generates spin-polarized Shapiro steps for commensurate Josephsonand Larmor frequencies that lead to magnetization reversal. This interplay between the ac Josephson current andthe magnetization dynamics occurs at voltages|V|=ωL/2enforn=1,2,..., and the subharmonic steps withn>1 are a consequence of multiple Andreev reflection (MAR). Moreover, the spin-precession-assisted MARgenerates quasiparticle scattering amplitudes that, due to interference, lead to current-voltage characteristics ofthe dc charge and spin currents with subharmonic gap structures displaying an even-odd effect.

We present a theoretical study of a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin. When an external magnetic field is applied, the classical spin will precess with the Larmor frequency. This magnetically active interface results in a time-dependent boundary condition with different tunneling amplitudes for spin-up and spin-down quasiparticles and where the precession produces spin-flip scattering processes. We show that as a result, the Andreev states develop sidebands and a nonequilibrium population which depend on the precession frequency and the angle between the classical spin and the external magnetic field. The Andreev states lead to a steady-state Josephson current whose current-phase relation could be used for characterizing the precessing spin. In addition to the charge transport, a magnetization current is also generated. This spin current is time dependent and its polarization axis rotates with the same precession frequency as the classical spin.

A study of the dc Josephson current between two superconducting leads in thepresence of a precessing classical spin is presented. The precession gives rise to a time-dependenttunnel potential which not only creates different tunneling probabilities for spin-up and spin-down quasiparticles, but also introduces a time-dependent spin-flip term. In particular, westudy the effects of the spin-flip term alone on the Josephson current between two spin-singletsuperconductors as a function of precession frequency and junction transparency. The systemdisplays a steady-state solution although the magnitude and nature of the current is indeedaffected by the precession frequency of the classical spin.

Using the non-equilibrium Green’s function method and the Keldysh formalism, we study the effects of spin–orbit interactions and time-reversal symmetry breaking exchange fields on non-equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in nonequilibrium edge transport by calculating the spin-resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin–orbit coupling, is characterized by chiral counter-propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin–orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance  . Increasing the intrinsic spin–orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non-equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time-reversal and sublattice translational symmetry.

Antiferromagnets may exhibit spin superfluidity since the dipole interaction is weak. We seek toestablish that this phenomenon occurs in insulators such as NiO, which is a good spin conductor accordingto previous studies. We investigate nonlocal spin transport in a planar antiferromagnetic insulator witha weak uniaxial anisotropy. The anisotropy hinders spin superfluidity by creating a substantial thresholdthat the current must overcome. Nevertheless, we show that applying a high magnetic field removes thisobstacle near the spin-flop transition of the antiferromagnet. Importantly, the spin superfluidity can thenpersist across many micrometers, even in dirty samples.

In ferromagnets, magnons may condense into a single quantum state. Analogous to superconductors,this quantum state may support transport without dissipation. Recent works suggest that longitudinal spintransport through a thin-film ferromagnet is an example of spin superfluidity. Although intriguing, thistantalizing picture ignores long-range dipole interactions; here, we demonstrate that such interactionsdramatically affect spin transport. In single-film ferromagnets,“spin superfluidity”only exists at lengthscales (a few hundred nanometers in yttrium iron garnet) somewhat larger than the exchange length. Overlonger distances, dipolar interactions destroy spin superfluidity. Nevertheless, we predict the reemergenceof spin superfluidity in trilayer ferromagnet-normal metal-ferromagnet films that are∼1μm in size. Suchsystems also exhibit other types of long-range spin transport in samples that are several micrometers in size.

Josephson currents are carried by sharp Andreev states within the superconducting energy gap. We theoretically study the electronic transport of a magnetically tunable nanoscale junction consisting of a quantum dot connected to two superconducting leads and coupled to the spin of a molecular magnet. The exchange interaction between the molecular magnet and the quantum dot modifies the Andreev states due to a spin-dependent renormalization of the quantum dot's energy level and the induction of spin flips. A magnetic field applied to the central region of the quantum dot and the molecular magnet further tunes the Josephson current and starts a precession of the molecular magnet's spin. We use a nonequilibrium Green's function approach to evaluate the transport properties of the junction. Our calculations reveal that the energy level of the dot, the magnetic field, and the exchange interaction between the molecular magnet and the electrons occupying the energy level of the quantum dot can trigger transitions from a 0 to a π state of the Josephson junction. The redistribution of the occupied states induced by the magnetic field strongly modifies the current-phase relation. The critical current exhibits a sharp increase as a function of either the energy level of the dot, the magnetic field, or the exchange interaction.

We study dc-transport and magnetization dynamics in a junction of arbitrary transparency consisting of two spin-singlet superconducting leads connected via a single classical spin precessing at the frequency Ω. The presence of the spin in the junction provides different transmission amplitudes for spin-up and spin-down quasiparticles as well as a time-dependent spin-flip transmission term. For a phase-biased junction, we show that a steady-state superconducting charge current flows through the junction and that an out-of-equilibrium circularly polarized spin current, of frequency Ω, is emitted in the leads. Detailed understanding of the charge and spin currents is obtained in the entire parameter range. In the adiabatic regime, ℏΩ⪡2Δ, where Δ is the superconducting gap, and for high transparencies of the junction, a strong suppression of the current takes place around φ≈0 due to an abrupt change in the occupation of the Andreev bound states. At higher values of the phase and/or precession frequency, extended (quasiparticlelike) states compete with the bound states in order to carry the current. Well below the superconducting transition, these results are shown to be weakly affected by the backaction of the spin current on the dynamics of the precessing spin. Indeed, we show that the Gilbert damping due to the quasiparticle spin current is strongly suppressed at low temperatures, which goes along with a shift of the precession frequency due to the condensate. The results obtained may be of interest for ongoing experiments in the field of molecular spintronics.

A study of the dc Josephson current between two superconducting leads in the presence of a precessingclassical spin is presented. The precession gives rise to a time-dependent tunnel potential which notonly implies different tunneling probabilities for spin-up and spin-down quasiparticles, but introducesalso a time-dependent spin-flip term. We provide an exact general analytic solution for the out-of-equilibrium steady-state permanent current between two spin-singlet superconductors as a functionof the superconducting phase difference, the precession frequency and for arbitrary junction transparency.As an application we focus on the effects of the spin-flip term alone and show that the magnitude andnature of the Josephson current are indeed strongly affected by the precession of the classical spin.

Understanding tunneling from an atomically sharp tip to a metallic surface requires to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [Phys. Rev. Lett. 102, 057401 (2009)] indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by over-bias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with an LRC circuit modeling the local plasmon-polariton mode. To explain the over-bias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.

Understanding tunneling from an atomically sharp tip to a metallic surface requires us to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [G. Schull et al., Phys. Rev. Lett. 102, 057401 (2009)] indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by overbias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with a LRC circuit modeling the local plasmon-polariton mode. To explain the overbias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.

Inelastic tunneling of electrons can generate the emission of photons with energies intuitively limited by the applied bias voltage. However, experiments indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission with overbias energies. We recently proposed a model of this observation in Phys. Rev. Lett. 113, 066801 (2014), in analogy to the dynamical Coulomb blockade, originally developed for treating the electromagnetic environment in mesoscopic circuits. This model describes the correlated tunneling of two electrons interacting with a local plasmon-polariton mode, represented by a resonant circuit, and shows that the overbias emission is due to the non-Gaussian fluctuations. Here we extend our model to study the overbias emission at finite temperature. We find that the thermal smearing strongly masks the overbias emission. Hence, the detection of the correlated tunneling processes requires temperatures k(B)T much lower than the bias energy eV and the plasmon energy h omega(0), a condition which is fortunately realized experimentally.