On lacunary analogs of the Poincaré theta-series and their applications

We consider Fuchsian groups of linear-fractional transformations such that each vertex of the fundamental polygon is common for an even or infinite number of fundamental congruent polygons meeting at this point. The whole collection of transformations splits into two disjoint sets. For these sets we introduce two lacunary kernels whose sum represents the well-known analog of Chibrikova and Sil'vestrov's kernel and study their properties. We introduce automorphic forms of dimension -4m that differ from the Poincaré theta-series. We indicate an application of one of the constructed lacunary kernels which does not include the Cauchy kernel to solving some boundary value problem with a shift of the contour inside the domain

Constructing an automorphic form from the orbit of a transformation

We consider the Fuchsian groups of linear-fractional transformations. We propose a new method for presenting automorphic forms as gap series over an appropriate subset of transformations of the group which is not a subgroup. Comparative analysis of the Poincaré theta-series and gap series demonstrates that the use of gap series requires less transformations and parameters that the summands of series depend on. © 2007 Springer Science+Business Media, Inc

Knight shift in superconducting vanadium

The Knight shift in metallic vanadium in the normal and superconducting states has been measured. In contrast to the previously obtained results, this shift appears to change after the transition to the superconducting state. The behavior of the Knight shift in the superconducting state in vanadium samples doped with iron impurities has been found to be different from that in the "pure" samples. As a possible explanation of the effect, the broadening of the peak of the density of states near the Fermi level due to the scattering of conduction electrons on the iron impurities and the earlier predicted impurity polarization shift of the NMR line are discussed. © 2008 Pleiades Publishing, Ltd

Experimental observation of the spin screening effect in superconductor/ferromagnet thin film heterostructures

When studying the nuclear magnetic resonance (NMR) of 51V nuclei in superconductor/ferromagnet thin film heterostructures, anomalous behavior of the NMR signal was observed. This effect was manifested as a systematic distortion of the high-field wing of the resonance line. We consider this to be the first experimental evidence for penetration of ferromagnetism into a superconductor. © 2010 Allerton Press, Inc

Spin screening effect in superconductor/ferromagnet thin film heterostructures studied using nuclear magnetic resonance

Using NMR spectroscopy of the V 51 nuclei in the superconducting state of Ni/V/Ni and Pd1-x Fex /V/ Pd1-x Fex trilayers we reported in a recent letter an experimental observation of the spin screening effect. This effect, which designates the formation of a spin polarization in the superconducting state, was predicted previously by Bergeret. Here, we extend our earlier experiments by varying the thickness of the superconducting V layer and by applying the magnetic field not only perpendicular to the film plane as in the previous experiments, but also in the parallel direction. For the latter geometry, which for experimental reasons is difficult to realize, the film is in the vortex-free state. This allows a direct quantitative comparison of the experimental screening effect as derived from a characteristic distortion of the high-field wing of the resonance line in the superconducting state and the theoretical model calculations. We derive a reasonable agreement between theory and experiment, confirming the spin screening effect in the superconductor. © 2009 The American Physical Society

Experimental observation of the spin screening effect in superconductor/ferromagnet thin film heterostructures

We have studied the nuclear magnetic resonance (NMR) of V51 nuclei in the superconductor/ferromagnet thin film heterostructures Pd1-xFex/V/Pd1-xFex and Ni/V/Ni in the normal and superconducting state. Whereas the position and shape of the NMR line in the normal state for the trilayers is identical to that observed in a single V layer, in the superconducting state the line shape definitely changes, developing a systematic distortion of the high-field wing of the resonance line. We consider this as the first experimental evidence for the penetration of ferromagnetism into the superconducting layer, a phenomenon which has been theoretically predicted recently and dubbed the spin screening effect. © 2009 The American Physical Society