Abstract:
Spin-polarized current effect is studied on the static and dynamic magnetization of the antiferromagnet in a ferromagnet - antiferromagnet nanojunction. The macrospin approximation is generalized to antiferromagnets. Canted antiferromagnetic configuration and resulting magnetic moment are induced by an external magnetic field. The resonance frequency and damping are calculated, as well as the threshold current density corresponding to instability appearance. A possibility is shown of generating low-damping magnetization oscillations in terahertz range. The fluctuation effect is discussed on the canted antiferromagnetic configuration. Numerical simulation is carried out of the magnetization dynamics of the antiferromagnetic layer in the nanojunction with spin-polarized current. Outside the instability range, the simulation results coincide completely with analytical calculations using linear approximation. In the instability range, undamped oscillations occur of the longitudinal and transverse magnetization components.

Abstract:
Recently [Phys. Rev. B 91, 125433 (2015)] we derived a general formula for the time-dependent quantum electron current through a molecular junction subject to an arbitrary time-dependent bias within the Wide Band Limit Approximation (WBLA) and assuming a single particle Hamiltonian. Here we present an efficient numerical scheme for calculating the current and particle number. Using the Pad\'e expansion of the Fermi function, it is shown that all frequency integrals occurring in the general formula for the current can be removed analytically. Furthermore, when the bias in the reservoirs is assumed to be sinusoidal it is possible to manipulate the general formula into a form containing only summations over special functions. To illustrate the method, we consider electron transport through a one-dimensional molecular wire coupled to two leads subject to out-of-phase biases. We also investigate finite size effects in the current response and particle number that results from the switch-on of such a bias.

Abstract:
Here we present a theoretical analysis of the effect of inelastic electron scattering on spin-dependent transport characteristics (conductance, current-voltage dependence, magnetoresistance, shot noise spectrum, Fano factor) for magnetic nanojunction. Such device is composed of molecular quantum dot (with discrete energy levels)connected to ferromagnetic electrodes (treated within the wide-band approximation), where molecular vibrations are modeled as dispersionless phonons. Non-perturbative computational scheme, used in this work, is based on the Green's function theory within the framework of mapping technique (GFT-MT) which transforms the many-body electron-phonon interaction problem into a single-electron multi-channel scattering problem. The consequence of the localized electron-phonon coupling is polaron formation. It is shown that polaron shift and additional peaks in the transmission function completely change the shape of considered transport characteristics.

Abstract:
We demonstrate that an {\it ac} Josephson current is pumped through the Single Molecular Magnets (SMM) by the spin nutation. The spin nutation is generated by applying a time dependent magnetic field to the SMM. We obtain the flowing charge current through the junction by working in the tunneling limit and employing Green's function technique. At the resonance conditions some discontinuities and divergencies are appeared in the normal and Josephson currents, respectively. Such discontinuities and divergencies reveal themselves when the absorbed/emitted energy, owing to the interaction of the quasiparticles with the spin dynamics are in the range of the superconducting gap.

Abstract:
The dynamical stability of nonstationary states of homogeneous spin-2 rubidium Bose-Einstein condensates is studied. The states considered are such that the spin vector remains parallel to the magnetic field throughout the time evolution, making it possible to study the stability analytically. These states are shown to be stable in the absence of an external magnetic field, but they become unstable when a finite magnetic field is introduced. It is found that the growth rate and wavelength of the instabilities can be controlled by tuning the strength of the magnetic field and the size of the condensate.

Abstract:
Magnetic switching of a single molecular magnet (SMM) due to spin-polarized current flowing between ferromagnetic metallic electrodes is investigated theoretically. Magnetic moments of the electrodes are assumed to be collinear and parallel to the magnetic easy axis of the molecule. Electrons tunneling through a barrier between magnetic leads are coupled to the SMM via exchange interaction. The current flowing through the system as well as the spin relaxation times of the SMM are calculated from the Fermi golden rule. It is shown that spin of the SMM can be reversed by applying a voltage between the two magnetic electrodes. Moreover, the switching is reflected in the corresponding current-voltage characteristics.

Abstract:
We present a simple model of electrical transport through a metal-molecule-metal nanojunction that includes charging effects as well as aspects of the electronic structure of the molecule. The interplay of a large charging energy and an asymmetry of the metal-molecule coupling can lead to various effects in non-linear electrical transport. In particular, strong negative differential conductance is observed under certain conditions.

Abstract:
The stability of nonstationary states of homogeneous spin-1 Bose-Einstein condensates is studied by performing Bogoliubov analysis in a frame of reference where the state is stationary. In particular, the effect of an external magnetic field is examined. It is found that a nonzero magnetic field introduces instability in a $^{23}$Na condensate. The wavelengths of this instability can be controlled by tuning the strength of the magnetic field. In a $^{87}$Rb condensate this instability is present already at zero magnetic field. Furthermore, an analytical bound for the size of a stable condensate is found, and a condition for the validity of the single-mode approximation is presented. Realization of the system in a toroidal trap is discussed and the full time development is simulated.

Abstract:
Current-induced magnetic switching of a single magnetic molecule attached to two ferromagnetic contacts is considered theoretically, with the main emphasis put on the role of intrinsic spin relaxation processes. It is shown that spin-polarized current can switch magnetic moment of the molecule, despite of the intrinsic spin relaxation in the molecule. The latter processes increase the threshold voltage (current) above which the switching takes place.

Abstract:
We study spin dependent transport through a magnetic bilayer graphene nanojunction configured as two dimensional normal/ferromagnetic/normal structure where the gate-voltage is applied on the layers of ferromagnetic graphene. Based on the fourband Hamiltonian, conductance is calculated by using Landauer Butikker formula at zero temperature. For parallel configuration of the ferromagnetic layers of bilayer graphene, the energy band structure is metallic and spin polarization reaches to its maximum value close to the resonant states, while for antiparallel configuration, the nanojunction behaves as a semiconductor and there is no spin filtering. As a result, a huge magnetoresistance is achievable by altering the configurations of ferromagnetic graphene especially around the band gap.