Sum rules are derived for the circular dichroic response of a core line (CMXD). They relate the intensity of the CMXD signal to the ground-state expectation value of the magnetic field operators (orbital, spin, and magnetic dipole) of the valence electrons. The results obtained are discussed and tested for transition metals and rare earths. PACS numbers: 78.70.Dm, 78.20.Ls For circular dichroism in the x-ray region (CMXD), Thole et al [I] ha. ve recently derived a new magneto-optical sum rule. It shows that, to a good approximation, the intensity of the CMXD signal, integrated over a complete core-level edge of a ferromagnet (or ferrimagnet), is proportional to the ground-state expectation value of the orbital angular momentum operator L, . The derivation was carried out for electric dipole transitions in a localized model, considering a single ion in an arbitrary crystal-field symmetry and including hybridization effects.In this Letter we show that, within the same framework, another sum rule can be obtained. It relates the CMXD signal, integrated over a single partner of a spinorbit-split core-level edge, to the ground-state expectation value of the operators (L"total spin S"and magnetic di-(+~r C~' ( W' jm ) = g (+ ) c/t !i ]l+j 'm )(cjm~Cq ' (l!i )R, t = X,&+lc, t 4~,. I+'& pole [g;s; -3r";(r"; s;)l, ) that describe the magnetic field generated by the valence electrons. Our results indicate that, besides (L, ), as described in Ref.[I], CMXD spectroscopy can provide an independent determination of the ground-state expectation value of S, [2]; this has been tested using CMXD data, taken at the L23 edges of the ferromagnetic metals Fe, Co, and Ni [3]. Furthermore, valuable, site-specific information on the magnetic anisotropy of the sample can be obtained, as discussed below. We consider the electric dipole transitions of a single partner of spin-orbit-split edge, in an ion with the valence shell only partly filled. Let~+) denote any state of the ground configuration l" of the ion. The final-state configuration is represented by~+ 'jm) =~cj~l"+'(%')); here +' denotes any state of the outer shell l"+' and cj stands for a hole in a core level. The dipole matrix element is given by I/2 c j c I I x ( -) r '/ [ ] I/2Po. y -m -yqT he notation is as follows: cj and l~represent creation operators for core and valence electrons, respectively; Cq . . (]) denotes a normalized spherical harmonic; [j] =2j+ I, R,t stands for the radial matrix element of the c 1 dipole transition; and P,t =(c~~C '~~l )R,t. The total intensity of the j edge is expressed by r '4l 44'

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Synchrotron light sources have produced a revolution in X-ray science in the last decades. The remarkable progress in brilliance of storage ring sources is however attaining some basic physical limits, and further progress can only be at the cost of versatility and ease of operation. There is at present a worldwide effort to implement free electron laser (FEL) X-ray sources, to produce spatially coherent, ultra-short (~ 10 fs) pulses with very high peak brilliance (in excess of 10 28-10 32 photons /s/ mm 2 /mrad 2 /0.1% bandwidth). These sources overcome the intrinsic limits of brilliance imposed by the storage ring geometry, with a single-pass geometry, based on linear accelerators (linacs). The scientific case includes time-resolved studies of dynamics on sub-ps scales, structural studies by imaging of non-periodic systems, especially in structural biology, and investigation of high-energy density phenomena such as the phase diagram of warm dense matter and non-linear x-ray optics. The ambitious scientific goals and the status of the European X-ray Free-Electron Laser project, under construction in Hamburg, Germany, aiming to attain the hard X-ray region, with wavelengths down to 0.05 nm, and with the high repetition rate allowed by the superconducting linac technology (27 000 pulses/s), are described in particular.

Resonant x-ray scattering experiments at the vanadium K edge demonstrate the existence of orbital ordering in V 2 O 3 . Bragg peaks due to the long-range order of 3d orbitals occupancy are observed when the photon energy is tuned to the threshold of the vanadium 3d bands. The azimuthal dependence of the resonant intensities confirms that the resonance arises from the ordering of the vanadium orbital occupancy. The observed orbital structure accounts for the complex magnetic structure of V 2 O 3 . The measured magnetic and orbital responses have the same critical temperature T N .[S0031-9007 (99)09287-X] PACS numbers: 78.70.Ck, 71.30. + h, 75.50.EeTwenty years ago, Castellani et al. [1] proposed that long-range order in the occupancy of the vanadium 3d orbitals was responsible for the complex magnetic properties of V 2 O 3 . Upon doping with Cr and/or under the application of hydrostatic pressure [2,3] V 2 O 3 exhibits both insulating and metallic phases with peculiar magnetic correlations [4][5][6]. It was suggested [1] that the spatial ordering of the occupancy of degenerate electronic orbitals accounts for the anisotropic exchange integrals found in the antiferromagnetic insulator phase (AFI) [5]. Furthermore, fluctuations in the orbital occupancy have been invoked to explain the evolution of the magnetic correlations in various phases of the V 2 O 3 system [6]. It appears that orbital occupancy plays a central role in the physics of V 2 O 3 , but no direct proof for orbital order could be produced experimentally since the original proposal in the late 1970s.In this Letter we present resonant x-ray scattering (RXS) experiments at the K edge of vanadium that demonstrate unambiguously the existence of orbital order in V 2 O 3 and provide information on the type of ordering. RXS is sensitive to the occupancy of electronic orbitals because it probes the symmetry of vacant electronic states through resonant multipole electric transitions; the variation of the orbital resonant scattering cross section with the direction of the incident polarization (azimuthal angle F) reflects the spatial symmetry of ordered orbitals. Furthermore, RXS may be tuned to probe selectively the electronic shells where orbital order takes place. In the case of V 2 O 3 , theoretical calculations [7] have shown that the resonance at the vanadium K edge provides observable cross sections arising from the order of the 3d vanadium states.RXS experiments were performed at the ID20 magnetic scattering undulator beam line at the European Synchrotron Radiation Facility [8]. A double crystal, Si(111), monochromator located between two focusing mirrors defined a narrow energy band around the vanadium K edge (FHWM 0.8 eV) with a high degree of linear s polarization. The x-ray beam was diffracted by the sample onto a pyrolitic graphite crystal analyzer [(004) reflection] to separate the s and p components of the scattered radiation. The sample was mounted with beeswax in a closed cycle refrigerator which could be rotated about the scattering vector to p...

Two-dimensional materials, obtained by van der Waals stacking of layers, are fascinating objects of contemporary condensed matter research, exhibiting a variety of new physics. Inspired by the breakthroughs of twisted bilayer graphene (TBG), we demonstrate that twisted bilayer boron nitride (TBBN) is an even more exciting novel system that turns out to be an excellent platform to realize new correlated phases and phenomena; exploration of its electronic properties shows that in contrast to TBG in TBBN multiple families of 2,4, and 6-fold degenerate flat bands emerge without the need to fine tune close to a “magic angle”, resulting in dramatic and tunable changes in optical properties and exciton physics, and providing an additional platform to study strong correlations. Upon doping, unforeseen new correlated phases of matter (insulating and superconducting) emerge. TBBN could thus provide a promising experimental platform, insensitive to small deviations in the twist angle, to study novel exciton condensate and spatial confinement physics, and correlations in two dimensions.

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Angular x-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of coherent x-ray scattering experiments. Here, we present the results of simulations that validate our theoretical findings for XCCA obtained in a previous paper [M. Altarelli et al., Phys. Rev. B 82, 104207 (2010)]. We consider as a model two-dimensional (2D) disordered systems composed of non-interacting colloidal clusters with fivefold symmetry and with orientational and positional disorder. We simulate a coherent x-ray scattering in the far field from such disordered systems and perform the angular cross-correlation analysis of calculated diffraction data. The results of our simulations show the relation between the Fourier series representation of the cross-correlation functions (CCFs) and different types of correlations in disordered systems.The dependence of structural information extracted by XCCA on the density of disordered systems and the degree of orientational disorder of clusters is investigated. The statistical nature of the fluctuations of the CCFs in the model 'single-shot' experiments is demonstrated and the potential of extracting structural information from the analysis of CCFs averaged over a set of diffraction patterns is discussed. We also demonstrate the effect of partial coherence of x-rays on the results of XCCA.