Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms

We investigate Poincar\'e series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincar\'e series are almost holomorphic as well. In general this is not the case. The main point of this paper is the study of Siegel-Poincar\'e series of degree $2$ attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincar\'e series. We surprisingly discover that these Poincar\'e series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls

Sturm Bounds for Siegel Modular Forms

We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properties of specializations of Jacobi forms to torsion points. In particular, our approach is completely different from the proofs of the previously known cases g=1,2, which do not extend to the case of general g

Harmonic Maa{\ss}-Jacobi forms of degree 1 with higher rank indices

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.Comment: 28 page

Optical and magneto-optical properties of ferromagnetic full-Heusler films: experiments and first-principles calculations

We report a joint theoretical and experimental study focused on understanding the optical and magneto-optical properties of Co-based full-Heusler compounds. We show that magneto-optical spectra calculated within ab-initio density functional theory are able to uniquely identify the features of the experimental spectra in terms of spin resolved electronic transitions. As expected for 3d-based magnets, we find that the largest Kerr rotation for these alloys is of the order of 0.3o in polar geometry. In addition, we demonstrate that (i) multilayered structures have to be carefully handled in the theoretical calculations in order to improve the agreement with experiments, and (ii) combined theoretical and experimental investigations constitute a powerful approach to designing new materials for magneto-optical and spin-related applicationsComment: 20 pages, including 6 figures and 1 table. 40 refs. To be published in Phys. Rev.

Preparation and structural properties of thin films and multilayers of the Heusler compounds Cu2MnAl, Co2MnSn, Co2MnSi and Co2MnGe

We report on the preparation of thin films and multilayers of the intermetallic Heusler compound CuMnAl, Co2MnSn, Co2MnSi and Co2MnGe by rf-sputtering on MgO and Al2O3 substrates. Cu2MnAl can be grown epitaxially with (100)-orientation on MgO (100) and in (110)-orientation on Al2O3 a-plane. The Co based Heusler alloys need metallic seedlayers to induce high quality textured growth. We also have prepared multilayers with smooth interfaces by combining the Heusler compounds with Au and V. An analysis of the ferromagnetic saturation magnetization of the films indicates that the Cu2MnAl-compound tends to grow in the disordered B2-type structure whereas the Co-based Heusler alloy thin films grow in the ordered L21 structure. All multilayers with thin layers of the Heusler compounds exhibit a definitely reduced ferromagnetic magnetization indicating substantial disorder and intermixing at the interfaces.Comment: 21 pages, 8 figure

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

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

Almost holomorphic Poincar\ue9 series corresponding to products of harmonic Siegel–Maass forms

\ua9 2016, The Author(s). We investigate Poincar\ue9 series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincar\ue9 series are almost holomorphic as well. In general, this is not the case. The main point of this paper is the study of Siegel–Poincar\ue9 series of degree\ua02 attached to products of terms of Fourier series of harmonic Siegel–Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel–Poincar\ue9 series. We surprisingly discover that these Poincar\ue9 series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel–Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls