A sequential regularization method for time-dependent incompressible Navier--Stokes equations

The objective of the paper is to present a method, called sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs) , and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is O(ffl m ), where m is the number of the SRM iterations and ffl is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes. It appears that the SRM formulation is new in the Navier-Stokes context. Unlike other regularizations or pseudo-compressibility methods in the Navier-Stokes context, the regularization parameter ffl in the SRM need not be very small, and the regularized..

Transmission electron microscopy and ferromagnetic resonance investigations of tunnel magnetic junctions using Co2MnGe Heusler alloy as magnetic electrodes

HRTEM, nano-beam electronic diffraction, energy dispersive X-rays scanning spectroscopy, Vibrating Sample Magnetometry (VSM) and FerroMagnetic Resonance (FMR) techniques are used in view of comparing (static and dynamic) magnetic and structural properties of Co2MnGe (13 nm)/Al2O3 (3 nm)/Co (13 nm) tunnel magnetic junctions (TMJ), deposited on various single crystalline substrates (a-plane sapphire, MgO(100) and Si(111)). They allow for providing a correlation between these magnetic properties and the fine structure investigated at atomic scale. The Al2O3 tunnel barrier is always amorphous and contains a large concentration of Co atoms, which, however, is significantly reduced when using a sapphire substrate. The Co layer is polycrystalline and shows larger grains for films grown on a sapphire substrate. The VSM investigation reveals in-plane anisotropy only for samples grown on a sapphire substrate. The FMR spectra of the TMJs are compared to the obtained ones with a single Co and Co2MnGe films of identical thickness deposited on a sapphire substrate. As expected, two distinct modes are detected in the TMJs while only one mode is observed in each single film. For the TMJ grown on a sapphire substrate the FMR behavior does not significantly differ from the superposition of the individual spectra of the single films, allowing for concluding that the exchange coupling between the two magnetic layers is too small to give rise to observable shifts. For TMJs grown on a Si or on a MgO substrate the resonance spectra reveal one mode which is nearly identical to the obtained one in the single Co film, while the other observed resonance shows a considerably smaller intensity and cannot be described using the magnetic parameters appropriate to the single Co2MnGe film.Comment: 11 pages, 10 figures, Thin Solid Film

Probing the Dzyaloshinskii-Moriya interaction in CoFeB ultrathin films using domain wall creep and Brillouin light spectroscopy

We have characterized the strength of the interfacial Dyzaloshinskii-Moriya interaction (DMI) in ultrathin perpendicularly magnetized CoFeB/MgO films, grown on different underlayers of W, TaN, and Hf, using two experimental methods. First, we determined the effective DMI field from measurements of field-driven domain wall motion in the creep regime, where applied in-plane magnetic fields induce an anisotropy in the wall propagation that is correlated with the DMI strength. Second, Brillouin light spectroscopy was employed to quantify the frequency non-reciprocity of spin waves in the CoFeB layers, which yielded an independent measurement of the DMI. By combining these results, we show that DMI estimates from the different techniques only yield qualitative agreement, which suggests that open questions remain on the underlying models used to interpret these results.Comment: 8 page

Magnetization dynamics in Co2MnGe/Al2MnGe/Al2O3$/Co tunnel junctions grown on different substrates

We study static and dynamic magnetic properties of Co2MnGe (13 nm)/Al2O3 (3 nm)/Co (13 nm) tunnel magnetic junctions (TMJ), deposited on various single crystalline substrates (a-plane sapphire, MgO(100), Si(111)). The results are compared to the magnetic properties of Co and of Co$_{2}$MnGe single films lying on sapphire substrates. X-rays diffraction always shows a (110) orientation of the Co$_{2}$MnGe films. Structural observations obtained by high resolution transmission electron microscopy confirmed the high quality of the TMJ grown on sapphire. Our vibrating sample magnetometry measurements reveal in-plane anisotropy only in samples grown on a sapphire substrate. Depending on the substrate, the ferromagnetic resonance spectra of the TMJs, studied by the microstrip technique, show one or two pseudo-uniform modes. In the case of MgO and of Si substrates only one mode is observed: it is described by magnetic parameters (g-factor, effective magnetization, in-plane magnetic anisotropy) derived in the frame of a simple expression of the magnetic energy density; these parameters are practically identical to those obtained for the Co single film. With a sapphire substrate two modes are present: one of them does not appreciably differ from the observed mode in the Co single film while the other one is similar to the mode appearing in the Co$_{2}$MnGe single film: their magnetic parameters can thus be determined independently, using a classical model for the energy density in the absence of interlayer exchange coupling.Comment: 5 pages, 6 figure

Magnetic properties of exchange biased and of unbiased oxide/permalloy thin layers: a ferromagnetic resonance and Brillouin scattering study

Microstrip ferromagnetic resonance and Brillouin scattering are used to provide a comparative determination of the magnetic parameters of thin permalloy layers interfaced with a non-magnetic (Al2O3) or with an antiferromagnetic oxide (NiO). It is shown that the perpendicular anisotropy is monitored by an interfacial surface energy term which is practically independent of the nature of the interface. In the investigated interval of thicknesses (5-25 nm) the saturation magnetisation does not significantly differ from the reported one in bulk permalloy. In-plane uniaxial anisotropy and exchange-bias anisotropy are also derived from this study of the dynamic magnetic excitations and compared to our independent evaluations using conventional magnetometryComment: 7 pages, 6 figures, submited to Journal of Physics: Condensed Matte