Analytical description of ballistic spin currents and torques in magnetic tunnel junctions

In this work we demonstrate explicit analytical expressions for both charge and spin currents which constitute the 2x2 spinor in magnetic tunnel junctions with noncollinear magnetizations under applied voltage. The calculations have been performed within the free electron model in the framework of the Keldysh formalism and WKB approximation. We demonstrate that spin/charge currents and spin transfer torques are all explicitly expressed through only three irreducible quantities, without further approximations. The conditions and mechanisms of deviation from the conventional sine angular dependence of both spin currents and torques are shown and discussed. It is shown in the thick barrier approximation that all tunneling transport quantities can be expressed in an extremely simplified form via Slonczewski spin polarizations and our effective spin averaged interfacial transmission probabilities and effective out-of-plane polarizations at both interfaces. It is proven that the latter plays a key role in the emergence of perpendicular spin torque as well as in the angular dependence character of all spin and charge transport considered. It is demonstrated directly also that for any applied voltage, the parallel component of spin current at the FM/I interface is expressed via collinear longitudinal spin current components. Finally, spin transfer torque behavior is analyzed in a view of transverse characteristic length scales for spin transport.Comment: 10 pages, 6 figure

Generation of Attosecond Pulses with Controllable Carrier-Envelope Phase via High-order Frequency Mixing

Advancing table-top attosecond sources in brightness and pulse duration is of immense interest and importance for an expanding sphere of applications. Recent theoretical studies [New J. Phys., 22 093030 (2020)] have found that high-order frequency mixing (HFM) in a two-color laser field can be much more efficient than high-order harmonic generation (HHG). Here we study the attosecond properties of the coherent XUV generated via HFM analytically and numerically, focusing on the practically important case when one of the fields has much lower frequency and much lower intensity than the other one. We derive simple analytical equations describing intensities and phase locking of the HFM spectral components. We show that the duration of attosecond pulses generated via HFM, while being very similar to that obtained via HHG in the plateau, is shortened for the cut-off region. Moreover, our study demonstrates that the carrier-envelope phase of the attopulses produced via HFM, in contrast to HHG, can be easily controlled by the phases of the generating fields

Macroscopic effects in generation of attosecond XUV pulses via high-order frequency mixing in gases and plasma

We study the generation of attosecond XUV pulses via high-order frequency mixing (HFM) of two intense generating fields, and compare this process with the more common high-order harmonic generation (HHG) process. We calculate the macroscopic XUV signal by numerically integrating the 1D propagation equation coupled with the 3D time-dependent Schr\"odinger equation. We analytically find the length scales which limit the quadratic growth of the HFM macroscopic signal with propagation length. Compared to HHG these length scales are much longer for a group of HFM components, with orders defined by the frequencies of the generating fields. This results in a higher HFM macroscopic signal despite the microscopic response being lower than for HHG. In our numerical simulations, the intensity of the HFM signal is several times higher than that for HHG in a gas, and it is up to three orders of magnitude higher for generation in plasma; it is also higher for longer generating pulses. The HFM provides very narrow XUV lines ($\delta \omega / \omega = 4.6 \times 10^{-4}$) with well-defined frequencies, thus allowing for a simple extension of optical frequency standards to the XUV range. Finally, we show that the group of HFM components effectively generated due to macroscopic effects provides a train of attosecond pulses such that the carrier-envelope phase of an individual attosecond pulse can be easily controlled by tuning the phase of one of the generating fields.Comment: 14 pages, 7 figure

Temperature dependence of the probability of "small heating" and total losses of ucns on the surface of fomblin oils of different molecular mass

We measured the temperature dependence of the probability of small heating and total losses of UCNs on the PFPE Fomblin Y surface with various molecular masses Mw=2800, 3300, 6500 amu in the temperature range of 100-300 K. The probability of small heating sharply decreases with increasing Mw and decreasing temperature. The probability of total loss weakly decreases with decreasing temperature and takes the minimum value at Mw=3300 amu. As this oil provides a homogeneous surface with minimal probabilities of small heating and total losses of UCNs, it is the preferred candidate for experiments on measuring the neutron lifetime

Does Giant Magnetoresistance Survive in Presence of Superconducting Contact?

The giant magnetoresistance (GMR) of ferromagnetic bilayers with a superconducting contact (F1/F2/S) is calculated in ballistic and diffusive regimes. As in spin-valve, it is assumed that the magnetization in the two ferromagnetic layers F1 and F2 can be changed from parallel to antiparallel. It is shown that the GMR defined as the change of conductance between the two magnetic configurations is an oscillatory function of the thickness of F2 layer and tends to an asymptotic positive value at large thickness. This is due to the formation of quantum well states in F2 induced by Andreev reflection at the F2/S interface and reflection at F1/F2 interface in antiparallel configuration. In the diffusive regime, if only spin-dependent scattering rates in the magnetic layers are considered (no difference in Fermi wave-vectors between spin up and down electrons) then the GMR is supressed due to the mixing of spin up and down electron-hole channels by Andreev reflection.Comment: 7 pages, 4 figures, submitted to Phys.Rev.Let

Finite Element Modeling of Charge and Spin-currents in Magnetoresistive Pillars with Current Crowding Effects

The charge and spin diffusion equations taking into account spin-flip and spin-transfer torque were numerically solved using a finite element method in complex non-collinear geometry. This approach was used to study the spin-dependent transport in giant magnetoresistance metallic pillars sandwiched between extended electrodes as in magnetoresistive heads for hard disk drives. The charge current crowding around the boundaries between the electrodes and the pillar has a quite significant influence on the spin current.Comment: 11 pages, 4 figure