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

Effective critical behaviour of diluted Heisenberg-like magnets

In agreement with the Harris criterion, asymptotic critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point $T_c$ as observed experimentally. In the asymptotic limit (at $T_c$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.Comment: 15 pages, 4 figure

Experimental Observation of the Inverse Proximity Effect in Superconductor/Ferromagnet Layered Structures

We have studied the nuclear magnetic resonance (NMR) of 51V nuclei in the superconductor/ferromagnet thin film heterostructures Ni/V/Ni and Pd{1-x}Fe{x}/V/Pd{1-x}Fe{x} in the normaland 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 inverse proximity effect.Comment: about 5 pages, 3 figures, 1 tabl

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

Intrinsic room temperature ferromagnetism in Co-implanted ZnO

We report on the structural and magnetic properties of a cobalt-implanted ZnO film grown on a sapphire substrate. X-ray diffraction and transmission electron microscopy reveal the presence of a ( )-oriented hexagonal Co phase in the Al2O3 sapphire substrate, but not in the ZnO film. Co clusters, with a diameter of about 5-6 nm, form a Co rich layer in the substrate close to the ZnO/Al2O3 interface. Magnetization measurements indicate that there exist two different magnetic phases in the implanted region. One originates from the Co clusters in Al2O 3, the other one belongs to a homogeneous ferromagnetic phase with a ferromagnetic Curie temperature far above room temperature. In the latter case, the ferromagnetism can be attributed to Co substitution on Zn sites in the ZnO layer. We have observed magnetic dichroism at the Co L2,3 and O K edges at room temperature as well as the multiplet structure in x-ray absorption spectra around the Co L3 edge, supporting the intrinsic nature of the observed ferromagnetism in a Co-implanted ZnO film. The magnetic moment per substituted cobalt is found to be about 2.81 νB, which is very close to the theoretical expected value of 3 νB/Co for Co 2+ in its high spin state. © 2008 IOP Publishing Ltd

Effect of anisotropic impurity scattering in superconductors

We discuss the weak-coupling BCS theory of a superconductor with the impurities, accounting for their anisotropic momentum-dependent potential. The impurity scattering process is considered in the t-matrix approximation and its influence on the superconducting critical temperature is studied in the Born and unitary limit for a d- and (d+s)-wave superconductors. We observe a significant dependence of the pair-breaking strength on the symmetry of the scattering potential and classify the impurity potentials according to their ability to alter T_c. A good agreement with the experimental data for Zn doping and oxygen irradiation in the overdoped cuprates is found.Comment: 31 pages, RevTex, 15 PostScript figure

Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.Comment: 35 pages, 23 figures, submitted to Phys Rev.

TcT_c suppression in co-doped striped cuprates

We propose a model that explains the reduction of $T_c$ due to the pinning of stripes by planar impurity co-doping in cuprates. A geometrical argument about the planar fraction of carriers affected by stripe pinning leads to a a linear $T_c$ suppression as a function of impurity concentration $z$. The critical value $z_c$ for the vanishing of superconductivity is shown to scale like $T_c^2$ in the under-doped regime and becomes universal in the optimally- and over-doped regimes. Our theory agrees very well with the experimental data in single- and bi-layer cuprates co-doped with Zn, Li, Co, etc...Comment: 4 pages, 4 figure

High-temperature ferromagnetism in Co-implanted TiO2 rutile

We report on structural, magnetic and electronic properties of Co-implanted TiO2(1 0 0) rutile single crystals for different implantation doses. Strong ferromagnetism at room temperature and above is observed in TiO 2 rutile plates after cobalt ion implantation, with magnetic parameters depending on the cobalt implantation dose. While the structural data indicate the presence of metallic cobalt clusters, the multiplet structure of the Co L3 edge in the XAS spectra provides evidence that a sizeable portion of the dopants occupy substitutional Co2+ sites. The detailed analysis of the structural and magnetic properties indicates that there are two magnetic phases in Co-implanted TiO2 plates. One is a ferromagnetic phase due to the formation of long range ferromagnetic ordering between implanted magnetic cobalt ions in the rutile phase, and the second one is a superparamagnetic phase which originates from the formation of metallic cobalt clusters in the implanted region. Using x-ray resonant magnetic scattering, the element specific magnetizations of cobalt, oxygen and titanium in Co-implanted TiO2 single crystals are investigated. Magnetic dichroism was observed at the Co L2,3 edges as well as at the O K edge. Anomalous Hall effect measurement indicates n-type carriers in Co-implanted TiO 2 rutile. The interaction mechanism, which leads to ferromagnetic ordering of substituted cobalt ions in the host matrix, is also discussed. © 2009 IOP Publishing Ltd