Ferromagnetic resonance of a two-dimensional array of nanomagnets: Effects of surface anisotropy and dipolar interactions

We develop an analytical approach for studying the FMR frequency shift due to dipolar interactions and surface effects in two-dimensional arrays of nanomagnets with (effective) uniaxial anisotropy along the magnetic field. For this we build a general formalism on the basis of perturbation theory that applies to dilute assemblies but which goes beyond the point-dipole approximation as it takes account of the size and shape of the nano-elements, in addition to their separation and spatial arrangement. The contribution to the frequency shift due to the shape and size of the nano-elements has been obtained in terms of their aspect ratio, their separation and the lattice geometry. We have also varied the size of the array itself and compared the results with a semi-analytical model and reached an agreement that improves as the size of the array increases. We find that the red-shift of the ferromagnetic resonance due to dipolar interactions decreases for smaller arrays. Surface effects may induce either a blue-shift or a red-shift of the FMR frequency, depending on the crystal and magnetic properties of the nano-elements themselves. In particular, some configurations of the nano-elements assemblies may lead to a full compensation between surface effects and dipole interactions.Comment: 14 pages, 5 figure

Momentum dependent light scattering in insulating cuprates

We investigate the problem of inelastic x-ray scattering in the spin$-{1/2}$ Heisenberg model on the square lattice. We first derive a momentum dependent scattering operator for the $A_{1g}$ and $B_{1g}$ polarization geometries. On the basis of a spin-wave analysis, including magnon-magnon interactions and exact-diagonalizations, we determine the qualitative shape of the spectra. We argue that our results may be relevant to help interpret inelastic x-ray scattering experiments in the antiferromagnetic phase of the cuprates.Comment: 5 pages, 3 figures, to appear in PR

Systematic computation of crystal field multiplets for X-ray core spectroscopies

We present a new approach to computing multiplets for core spectroscopies, whereby the crystal field is constructed explicitly from the positions and charges of surrounding atoms. The simplicity of the input allows the consideration of crystal fields of any symmetry, and in particular facilitates the study of spectroscopic effects arising from low symmetry environments. The interplay between polarization directions and crystal field can also be conveniently investigated. The determination of the multiplets proceeds from a Dirac density functional atomic calculation, followed by the exact diagonalization of the Coulomb, spin-orbit and crystal field interactions for the electrons in the open shells. The eigenstates are then used to simulate X-ray Absorption Spectroscopy and Resonant Inelastic X-ray Scattering spectra. In examples ranging from high symmetry down to low symmetry environment, comparisons with experiments are done with unadjusted model parameters as well as with semi-empirically optimized ones. Furthermore, predictions for the RIXS of low-temperature MnO and for Dy in a molecular complex are proposed.Comment: Accepted for publication in Phys. Rev.

Cu KK-edge Resonant Inelastic X-Ray Scattering in Edge-Sharing Cuprates

We present calculations for resonant inelastic x-ray scattering (RIXS) in edge-shared copper oxide systems, such as CuGeO$_{3}$ and Li$_{2}$CuO$_{2}$, appropriate for hard x-ray scattering where the photoexcited electron lies above oxygen 2p and copper 3d orbital energies. We perform exact diagonalizations of the multi-band Hubbard and determine the energies, orbital character and resonance profiles of excitations which can be probed via RIXS. We find excellent agreement with recent results on Li$_{2}$CuO$_{2}$ and CuGeO$_{3}$ in the 2-7 eV photon energy loss range.Comment: Updated with new data, expanded 9 pages, 9 figure

Theory of inelastic light scattering in spin-1 systems: resonant regimes and detection of quadrupolar order

Motivated by the lack of an obvious spectroscopic probe to investigate non-conventional order such as quadrupolar orders in spin S>1/2 systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S=1/2 case, where the only type of local excited state is a doubly occupied state of energy $U$, several local excited states with occupation up to 4 electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For $\hbar\omega_{in}\lesssim U$, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-1/2 case. For $\hbar\omega_{in}\lesssim4U$, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling \sim({\bf S}_{i}\cdot{\bf S}_{j)^{2}. Consequences for the Raman spectra of S=1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.Comment: 10 Pages, 6 Figures, Submitted to PR

The CXCL12/CXCR4 Axis Plays a Critical Role in Coronary Artery Development

The chemokine CXCL12 and its receptor CXCR4 have many functions during embryonic and post-natal life. We used murine models to investigate the role of CXCL12/CXCR4 signaling in cardiac development and found that embryonic Cxcl12-null hearts lacked intra-ventricular coronary arteries (CAs) and exhibited absent or misplaced CA stems. We traced the origin of this phenotype to defects in the early stages of CA stem formation. CA stems derive from the peritruncal plexus, an encircling capillary network that invades the wall of the developing aorta. We showed that CXCL12 is present at high levels in the outflow tract, while peritruncal endothelial cells (ECs) express CXCR4. In the absence of CXCL12, ECs were abnormally localized and impaired in their ability to anastomose with the aortic lumen. We propose that CXCL12 is required for connection of peritruncal plexus ECs to the aortic endothelium and thus plays a vital role in CA formation

Unraveling the Nature of Charge Excitations in La2_2CuO4_4 with Momentum-Resolved Cu KK-edge Resonant Inelastic X-ray Scattering

Results of model calculations using exact diagonalization reveal the orbital character of states associated with different Raman loss peaks in Cu $K$-edge resonant inelastic X-ray scattering (RIXS) from La$_{2}$CuO$_{4}$. The model includes electronic orbitals necessary to highlight non-local Zhang-Rice singlet, charge transfer and $d$-$d$ excitations, as well as states with apical oxygen 2$p_z$ character. The dispersion of these excitations is discussed with prospects for resonant final state wave-function mapping. A good agreement with experiments emphasizes the substantial multi-orbital character of RIXS profiles in the energy transfer range 1-6 eV.Comment: Original: 4.5 pages. Replaced: 4 pages and 4 figures with updated content and reference

A Systematic Study of Electron-Phonon Coupling to Oxygen Modes Across the Cuprates

The large variations of T$_c$ across the cuprate families is one of the major unsolved puzzles in condensed matter physics, and is poorly understood. Although there appears to be a great deal of universality in the cuprates, several orders of magnitude changes in T$_c$ can be achieved through changes in the chemical composition and structure of the unit cell. In this paper we formulate a systematic examination of the variations in electron-phonon coupling to oxygen phonons in the cuprates, incorporating a number of effects arising from several aspects of chemical composition and doping across cuprate families. It is argued that the electron-phonon coupling is a very sensitive probe of the material-dependent variations of chemical structure, affecting the orbital character of the band crossing the Fermi level, the strength of local electric fields arising from structural-induced symmetry breaking, doping dependent changes in the underlying band structure, and ionicity of the crystal governing the ability of the material to screen $c$-axis perturbations. Using electrostatic Ewald calculations and known experimental structural data, we establish a connection between the material's maximal T$_c$ at optimal doping and the strength of coupling to $c$-axis modes. We demonstrate that materials with the largest coupling to the out-of-phase bond-buckling (``$B_{1g}$") oxygen phonon branch also have the largest T$_c$'s. In light of this observation we present model T$_c$ calculations using a two-well model where phonons work in conjunction with a dominant pairing interaction, presumably due to spin fluctuations, indicating how phonons can generate sizeable enhancements to T$_c$ despite the relatively small coupling strengths. Combined, these results can provide a natural framework for understanding the doping and material dependence of T$_c$ across the cuprates.Comment: 29 Pages, 21 Figures, Submitted to PR