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Attention-based models are proliferating in the space of image analytics, including segmentation. The standard method of feeding images to transformer encoders is to divide the images into patches and then feed the patches to the model as a linear sequence of tokens. For high-resolution images, e.g. microscopic pathology images, the quadratic compute and memory cost prohibits the use of an attention-based model, if we are to use smaller patch sizes that are favorable in segmentation. The solution is to either use custom complex multi-resolution models or approximate attention schemes. We take inspiration from Adapative Mesh Refinement (AMR) methods in HPC by adaptively patching the images, as a pre-processing step, based on the image details to reduce the number of patches being fed to the model, by orders of magnitude. This method has a negligible overhead, and works seamlessly with any attention-based model, i.e. it is a pre-processing step that can be adopted by any attention-based model without friction. We demonstrate superior segmentation quality over SoTA segmentation models for real-world pathology datasets while gaining a geomean speedup of $6.9\times$ for resolutions up to $64K^2$, on up to $2,048$ GPUs.

We analyze resonant x-ray scattering (RIXS) spectra in Na$_2$IrO$_3$ on the basis of the itinerant electron picture. Employing a multi-orbital tight-binding model on a honeycomb lattice, we find that the zigzag magnetic order is the most stable with sizable energy gap in the one-electron band within the Hartree-Fock approximation. We derive the RIXS spectra, which are connected to the generalized density-density correlation function. We calculate the spectra as a function of excitation energy $\omega$, within the random phase approximation. The spectra consist of the peaks with $\omega$ $<20$ meV, and of the peaks with $0.4<\omega<0.8$ eV. The former peaks are composed of four bound states in the density-density correlation function, and may be identified as the magnetic excitations, while the latter peaks are composed of sixteen bound states below the energy continuum of individual electron-hole pair excitations, and may be identified as the excitonic excitations. The calculated spectra agree qualitatively with the recent RIXS experiment., Comment: 7 pages, 5 figures

We study the collective excitations of Na$_2$IrO$_3$ in an itinerant electron approach. We consider a multi-orbital tight-binding model with the electron transfer between the Ir $5d$ states mediated via oxygen $2p$ states and the direct $d$-$d$ transfer on a honeycomb lattice. The one-electron energy as well as the ground state energy are investigated within the Hartree-Fock approximation. When the direct $d$-$d$ transfer is weak, we obtain nearly flat energy bands due to the formation of quasimolecular orbitals, and the ground state exhibits the zigzag spin order. The evaluation of the density-density correlation function within the random phase approximation shows that the collective excitations emerge as bound states. For an appropriate value of the direct $d$-$d$ transfer, some of them are concentrated in the energy region $\omega <$ 50 meV (magnetic excitations) while the others lie in the energy region $\omega >$ 350 meV (excitonic excitations). This behaviour is consistent with the resonant inelastic x-ray scattering spectra. We also show that the larger values of the direct $d$-$d$ transfer are unfavourable in order to explain the observed aspects of Na$_2$IrO$_3$ such as the ordering pattern of the ground state and the excitation spectrum. These findings may indicate that the direct $d$-$d$ transfer is suppressed by the structural distortions in the view of excitation spectroscopy, as having been pointed out in the \it{ab initio} calculation., Comment: 8 pages, 6 figures, Latex, Figures 5 and 6 have been replaced by those obtained for more appropriate parameter values. The concomitant descriptions have been also modified. To be published in Journal of Physics: Condensed Matter

We study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the $L$-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic terms is supported by numerical calculations on a two-dimensional spin cluster. We express the RIXS spectra in the form of spin-correlation functions with the coefficients evaluated on the cluster, and calculate the function in a two dimensional system within the $1/S$ expansion. Due to the anisotropic terms, the spectral intensities are considerably enhanced around momentum transfer $\textbf{q}=0$ in both one-magnon and two-magnon excitation channels. This finding may be experimentally confirmed by examining carefully the $\textbf{q}$-dependence of the spectra., Comment: Latex, 13 pages, 9 figures, to be published in Journal of Physics:Condensed Matter

We analyze the resonant x-ray scattering (RIXS) spectra from Sr$_2$IrO$_4$ in an itinerant electron approach. Employing a multi-orbital tight-binding model on the square lattice, we calculate the one-electron energy band within the Hartree-Fock approximation, which leads to an antiferromagnetic ground state. We then evaluate the two-particle Green's functions for the particle-hole pair excitations within the random phase approximation, which are connected to the RIXS spectra within the fast collision approximation. The calculated RIXS spectra exhibit two-peak structure with slightly different energies in the low-energy region, which are originated from the bound states in the two-particle Green's function. They may be interpreted as the split modes of magnon. We also obtain several $\delta$-function peaks, which arise from the bound states around the bottom of energy continuum. They may be called as the exciton modes. These characteristics are in qualitative agreement with the RIXS experiment, demonstrating that the weak coupling theory could explain both the magnon and the exciton peaks in the RIXS spectra on an equal footing., Comment: 10 pages, 5 figures, revtex, to be published in Physical Review B

We study the elementary excitations in 5d transition metal oxideSr$_2$IrO$_4$ by calculating the particle-hole Green's function within the random phase approximation on an antiferromagnetic ground state in the two-dimensional multi-orbital Hubbard model. The obtained magnetic excitations of bound states show a characteristic dispersion in consistent with the experiments. In addition, two new types of excitations are found due to the interplay between spin-orbit interaction and Hund's coupling: a magnetic excitation as a bound state, which has energy gap at the $\Gamma$ point, and an exciton as a resonant mode in the continuum of electron-hole pair creation., Comment: 6 pages, 3 figures, Latex, final version, to be published in Journal of the Physical Society of Japan

We study the magnetic excitations in 5d transition-metal oxide Sr$_2$IrO$_4$ on the basis of the Heisenberg model with small anisotropic terms on a square lattice. We calculate the correlation functions by using the Green's functions in the spin-wave approximation. The spin waves are split into two modes with slightly different energies due to the anisotropic terms. It is shown that the spin correlation functions of the y and z components are composed of a single peak corresponding to each mode. We analyze the process of resonant inelastic x-ray scattering (RIXS) without relying on the fast collision approximation to obtain the local scattering operator. The RIXS intensity is derived as a sum of the correlation functions of the y and z spin components. We demonstrate that the RIXS intensity as a function of energy shows two-peak structure brought about by the two modes, which could be observed in the RIXS experiment., Comment: Latex, 10 pages, 3 figures, Descriptions are revised in Sects. II.D, III.B.4, and V

We study the low-lying excitations in 5d transition-metal oxide Sr_2IrO_4 on the localized electron picture. We find that Hund's coupling together with the spin-orbit interaction leads to exchange anisotropy which causes the spin wave gap. Introducing the isospin operators acting on Kramers' doublet in Ir atoms, we derive the effective spin Hamiltonian from a multi-orbital Hubbard model with the t_{2g} orbitals in the square lattice. We introduce the Green's functions including the anomalous type for the boson operators by expanding the spin operators in terms of boson operators in the lowest order of 1/S, and solve the coupled equations of motion for those functions. Two modes are found to emerge with slightly different energies, in contrast to the spin waves in the isotropic Heisenberg model. At the $\Gamma$-point, one mode has the zero excitation energy while another has a finite energy. They have the same excitation energy at the M point, but still have different energies at the X point., Comment: 6 pages, 2 figures, Latex; Figures are replaced by the revised ones. A few expressions in Secs.II and III are refined

We develop a formalism to calculate the L-edge resonant x-ray scattering (RIXS) spectra from transition-metal compounds. Using a multi-orbital tight-binding model, we derive useful formulas to calculate the spectra by collecting up the ladder diagrams on the basis of the Keldysh scheme, without relying on the fast collision approximation. They are feasible in the weak and intermediate coupling regimes of itinerant electron systems, where the charge and the magnetic excitations are mixed together. We examine the difference between the present formulas and those of the fast collision approximation. Finally, to demonstrate how our theory works, we employ the formulas to study the RIXS spectra on a simple model, the single-orbital Hubbard model on the square lattice at half-filling. The intensities originated from the magnon and from the continuous states are obtained on the equal footing in the antiferromagnetic ground state., Comment: 12 pages, 5 figures, Latex, to be published in Physical Review B

We study the resonant x-ray scattering at Si and Al K-edges from chiral materials, $\alpha$-quartz and $\alpha$-berlinite. We derive the general form of the scattering matrix for the dipole transition by summing up the local scattering matrices which satisfy the symmetry requirement. The oscillation term is obtained in the spectral intensity as a function of azimuthal angle with an expression of possible phase shift. We evaluate the parameters undetermined by the symmetry argument alone on the basis of underlying electronic structures given by the bond-orbital model. The spectra are calculated on forbidden spots $(001)$, $(00\bar{1})$, $(002)$, and $(00\bar{2})$ in circular polarizations without adjustable parameter, reproducing well the experimental curves depending on polarization, chirality, and scattering vector. Some discrepancies remain in the phase shift in $\alpha$-quartz., Comment: 25pages, 10 figures, 1 table

We study the magnetic excitation spectra of Cu L_{2,3}-edge resonant inelastic x-ray scattering (RIXS) from the spin-liquid ground state in two-leg spin ladder cuprates. Applying the projection method developed by the present authors, we have derived the formulas of the magnetic RIXS spectra, which are expressed by one- and two-spin correlation functions in the polarization changing and preserving channels, respectively. The one-spin correlation function includes both one- and two-triplon excitations and they are picked up separately by choosing rung wave vector -q_a=\pi and 0, respectively. An application to Sr_{14}Cu_{24}O_{41} reveals that the calculated RIXS spectrum captures well the dispersive behavior shown by the lower boundary of two-triplon continuum. By adjusting the geometrical configuration of the measurement, one-triplon dispersion around the zone center could be detectable in the RIXS experiment. The observed weak intensity in the higher energy region might be attributed to the two-spin correlation function, which could be detected more clearly at the M_{3}-edge RIXS spectra., Comment: 10 pages, 7 figures, Latex

We study the 2p-core level x-ray photoemission spectra in ferromagnetic transition metals, Fe, Co, and Ni using a recently developed ab initio method.The excited final states are set up by distributing electrons on the one-electron states calculated under the fully screened potential in the presence of the core hole. We evaluate the overlap between these excited states and the ground state by using one-electron wave functions, and obtain the spectral curves as a function of binding energy. The calculated spectra reproduce well the observed spectra displaying interesting dependence on the element and on the spin of the removed core electron. The origin of the spectral shapes is elucidated in terms of the one-electron states screening the core hole. The magnetic splitting of the threshold energy is also estimated by using the coherent potential approximation within the fully screened potential approximation. It decreases more rapidly than the local spin moment with moving from Fe to Ni. It is estimated to be almost zero for Ni despite the definite local moment about 0.6\mu_B, in agreement with the experiment., Comment: 10 pages, 7 figures

We study the magnetic excitation spectra of L-edge resonant inelastic x-ray scattering (RIXS) from the spin singlet ground state in one-dimensional undoped cuprates. Analyzing the transition amplitudes of the magnetic excitations in the second-order dipole allowed process, we find that the magnetic excitations are brought about not only on the core-hole site but also on the neighboring sites. The RIXS spectra are expressed by the one-spin correlation function in the scattering channel with changing polarization, and the two-spin correlation function in the scattering channel without changing polarization. The latter could not be brought about within the so-called UCL approximation. We calculate these correlation functions on a finite-size ring. An application to the possible RIXS spectra in Sr_2CuO_3 demonstrates that the contribution of the two-spin correlation function could be larger than that of the one-spin correlation function in the \sigma polarization for the momentum transfer around the zone center.

We study the magnetic excitation spectra in L-edge resonant inelastic x-ray scattering (RIXS) from undoped cuprates. We analyze the second-order dipole allowed process that the strong perturbation works through the intermediate state in which the spin degree of freedom is lost at the core-hole site. Within the approximation neglecting the perturbation on the neighboring sites, we derive the spin-flip final state in the scattering channel with changing the polarization, which leads to the RIXS spectra expressed as the dynamical structure factor of the transverse spin components. We assume a spherical form of the spin-conserving final state in the channel without changing the polarization, which leads to the RIXS spectra expressed as the 'exchange'-type multi-spin correlation function. Evaluating numerically the transition amplitudes to these final states on a finite-size cluster, we obtain a sizable amount of the transition amplitude to the spin-conserving final state in comparison with that to the spin-flip final state. We treat the itinerant magnetic excitations in the final state by means of the 1/S-expansion method. Evaluating the higher-order correction with 1/S, we find that the peak arising from the one-magnon excitation is reduced with its weight, and the continuous spectra arising from the three-magnon excitations come out. The interaction between two magnons is treated by summing up the ladder diagrams. On the basis of these results, we analyze the L_3-edge RIXS spectra in Sr_2CuO_2Cl_2 in comparison with the experiment. It is shown that the three-magnon excitations as well as the two-magnon excitations give rise to the intensity in the high energy side of the one-magnon peak, making the spectral shape asymmetric with wide width, in good agreement with the experiment., Comment: 18 pages, 10 figures, Revtex

We have studied second harmonic generation (SHG) in a polar ferrimagnet GaFeO_3, employing a FeO_6 cluster model in which the Fe atom is slightly shifted from the center of the octahedron. The electric-dipole transition could take place between the 3d states through the effective hybridization of the 4p states with the 3d states, due to the breaking of the space-inversion symmetry. In the third-order perturbation with H_{int} = -(j.A)/c, we calculate the probability per unit time, I_{\eta aa}, for the process that two photons are absorbed with polarization parallel to the $a$ axis and one photon is emitted with polarization parallel to the \eta (=a,b,c) axis. The calculated SHG intensities consist of several peaks as a function of two-photon energy in agreement with the experiments. It is found that the corresponding amplitude S_{aaa} at each Fe site changes its sign while S_{baa} remains the same with the reversal of the direction of the local magnetic moment. This implies that I_{aaa} would disappear while I_{baa} would survive in the paramagnetic phase in accordance with the experiment., Comment: 17 pages, 4 figures, to be published in Phys. Rev. B

We study the resonant x-ray scattering (RXS) spectra of CeB_{6} in an antiferroquadrupole (AFQ) ordering phase, near the Ce L_3 edge under the applied magnetic field H // (-1,1,0). On the basis of a localized electron model equipped with a mechanism that the RXS signal is brought about by the intra-atomic Coulomb interaction in Ce, we calculate the RXS spectra. The obtained spectra exhibit two contributions around the electric dipole (E1) and quadrupole (E2) positions, and differ drastically when the orientation of H is reversed. The difference is brought about by the cross terms between the even-rank AFQ and magnetic-induced odd-rank contributions. At the E1 region, the relevant cross term is the one within the E1 process, while at the E2 region, they are ones within the E2 process and between the E1 and E2 processes. These findings capture the characteristic features the recent experimental data show, and provide a strong support and information of the field-induced multipole orderings. We also evaluate the RXS spectra near the L_{2} edge. Though the results show no E2 contribution, we find that the intensity around the E1 transition, which is as large as that at the L_{3} edge, can be detected experimentally., Comment: 23 pages, 6 figures, to be published in Phys. Rev. B

We calculate the $3s$- and $4s$-core-level x-ray photoemission spectroscopy (XPS) spectra in the ferromagnetic and nonmagnetic transition metals by developing an \emph{ab initio} method. We obtain the spectra exhibiting the characteristic shapes as a function of binding energy in good agreement with experimental observations. The spectral shapes are strikingly different between the majority spin channel and the minority spin channel for ferromagnetic metals Ni, Co, and Fe, that is, large intensities appear in the higher binding energy side of the main peak (satellite) in the majority spin channel. Such satellite or shoulder intensities are also obtained for nonmagnetic metals V and Ru. These behaviors are elucidated in terms of the change of the one-electron states induced by the core-hole potential., Comment: 11 pages, 12 figures, to appear in Phys. Rev. B

We study the directional dichroic absorption spectra in the x-ray region in a polar ferrimagnet GaFeO_3. The directional dichroism on the absorption spectra at the Fe pre-K-edge arises from the E1-E2 interference process through the hybridization between the 4p and 3d states in the noncentrosymmetric environment of Fe atoms. We perform a microscopic calculation of the spectra on a model of FeO_6 with reasonable parameter values for Coulomb interaction and hybridizations. We obtain the difference in the absorption coefficients when the magnetic field is applied parallel and antiparallel to the c axis. The spectra shus obtained have similar shapes to the experimental curves as a function of photon energy in the Fe pre-K-edge region, although they have opposite signs., Comment: 14 pages, three figures

We study the optical absorption spectra in a polar ferrimagnet GaFeO_3. We consider the E1, E2 and M1 processes on Fe atoms. It is shown that the magnetoelectric effect on the absorption spectra arises from the E1-M1 interference process through the hybridization between the 4p and 3d states in the noncentrosymmetry environment of Fe atoms. We perform a microscopic calculation of the spectra on a cluster model of FeO_6 consisting of an octahedron of O atoms and an Fe atom displaced from the center with reasonable values for Coulomb interaction and hybridization. We obtain the magnetoelectric spectra, which depend on the direction of magnetization, as a function of photon energy in the optical region 1.0-2.5 eV, in agreement with the experiment., Comment: 18 pages, 5 figures

We develop a method of the ab-initio calculation for the core-level x-ray photoemission spectroscopy (XPS). By calculating one-electron states in the presence of core-hole potential, excited states are constructed by distributing electrons on these one-electron states. The overlap integrals between the excited states and the ground state are evaluated by using the wavefunctions with and without the core-hole potential, and finally the XPS spectra are obtained. Implementing the procedure, we obtain the spin-resolved 3s-core XPS spectra in ferromagnetic iron without any adjustable parameters, in good agreement with the experiment. The spectral shapes are quite different for different spin channels. We explain the behavior in terms of the difference in the one-electron states screening the core-hole potential., Comment: 7 pages, 6 figures, To be published in PRB

We study noncentrosymmetric effects on resonant x-ray scattering (RXS) in magnetite. The noncentrosymmetry at A sites in spinel structure makes the 4p states strongly hybridize with the 3d states through neighboring oxygen 2p states, giving rise to the non-vanishing contribution of the dipole-quadrupole (E1-E2) process in the RXS spectra. We substantiate this observation by introducing a microscopic model of a FeO_4 cluster with multiplets and the 4p band. We show that the hybridization changes its sign between two kinds of A sites and accordingly the local amplitude from the E1-E2 process changes its sign, resulting in non-vanishing RXS intensities at forbidden spots (002) and (006) in the pre-edge region in agreement with the experiment. A large dependence of the pre-edge intensity on the direction of the applied magnetic field is predicted as a consequence of breaking both centrosymmetry and time-reversal symmetry. Furthermore we analyze the intensity difference between two opposite directions of the applied magnetic field at the allowed spot (222) in connection with the experiment. We obtain the intensity difference of a "dispersion" form, which resembles the observed spectra at the Mn pre-K-edge in MnCr_2O_4 but is quite different from the observed one in magnetite. Although the observed spectra are claimed to arise from "magnetoelectric" amplitude, we argue that this claim has no ground., Comment: 26 pages, 7 figures, to be published in J. Phys. Soc. Jpn. vol. 77, No 8

Developing an expression of resonant x-ray scattering (RXS) amplitude which is convenient for investigating the contributions from the higher rank tensor on the basis of a localized electron picture, we analyze the RXS spectra from the magnetic phases of Ho near the $M_{4,5}$ absorption edges. At the $M_5$ edge in the uniform helical phase, the calculated spectra of the absorption coefficient, the RXS intensities at the first and second satellite spots capture the properties the experimental data possess, such as the spectral shapes and the peak positions. This demonstrates the plausibility of the adoption of the localized picture in this material and the effectiveness of the spectral shape analysis. The latter point is markedly valuable since the azimuthal angle dependence, which is one of the most useful informations RXS can provides, is lacking in the experimental conditions. Then, by focusing on the temperature dependence of the spectral shape at the second satellite spot, we expect that the spectrum is the contribution of the pure rank two profile in the uniform helical and the conical phases while that is dominated by the rank one profile in the intermediate temperature phase, so-called spin slip phase. The change of the spectral shape as a function of temperature indicates a direct evidence of the change of magnetic structures undergoing. Furthermore, we predict that the intensity, which is the same order observed at the second satellite spot, is expected at the fourth satellite spot from the conical phase in the electric dipolar transition., Comment: 24 pages, 5 figures

We study two-magnon spectra in resonant inelastic x-ray scattering (RIXS) from the Heisenberg antiferromanets by extending the formula of Nomura andIgarashi (Phys. Rev. B 71, 035110 (2005)). The core-hole potential in the intermediate state of RIXS gives rise to a change in the exchange coupling between 3d electrons, leading to an effective interaction between the core hole and spins of 3d electrons. We derive a formula suitable to calculate the two-magnon RIXS intensities, replacing the bare core-hole potential responsible to charge excitations by this effective interaction creating two magnons in our previous formula. It consists of two factors, one of which determines the incident-photon-energy dependence and another is the two-magnon correlation function. We evaluate the former factor for La_{2}CuO_{4} in terms of the density of states of the 4p states obtained by the band calculation. We also calculate the two-magnon correlation function as a function of energy loss \omega and momentum transfer \textbf{q} of the Heisenberg model on a square lattice,by summing up the ladder diagrams after transforming the magnon-magnon interaction into a separable form. The calculated spectra form a broad peak around \omega=3J for S=1/2 on the magnetic Brillouin zone boundary and vanish at \textbf{q}=(0,0) and (\pi,\pi). Such momentum dependence of the RIXS spectra could provide an excellent opportunity to study the dynamics in the Heisenberg model., Comment: 21 pages, 6 figures

We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the Ni $K$ edge in an antiferromagnetic insulator NiO by applying the theory developed by the present authors. It is based on the Keldysh Green's function formalism, and treats the core-hole potential in the intermediate state within the Born approximation. We calculate the single-particle energy bands within the Hartree-Fock approximation on the basis of the multi-orbital tight-binding model. Using these energy bands together with the $4p$ density of states from an ab initio band structure calculation, we calculate the RIXS intensities as a function of energy loss. By taking account of electron correlation within the random phase approximation (RPA), we obtain quantitative agreement with the experimental RIXS spectra, which consist of prominent two peaks around 5 eV and 8 eV, and the former shows considerable dispersion while the latter shows no dispersion. We interpret the peaks as a result of a band-to-band transition augmented by the RPA correlation., Comment: 11 pages, 10 figures, submitted to PRB

We develop a theory of resonant inelastic x-ray scattering (RIXS) at the $K$ edge in La$_2$CuO$_4$ on the basis of the Keldysh Green's function formalism. In our previous analysis (Phys. Rev. B 71, 035110 (2005)), the scattering by the core-hole potential was treated within the Born approximation, and a crude-model density of states was used for the $4p$ band. We improve the analysis by taking account of the multiple scattering in Cu3d-O$2p$ bands and by using a realistic $4p$ DOS obtained from a band calculation. The multiple scattering effect is evaluated with the use of the time representation developed by Nozi\`eres and De Dominicis. It is found that the multiple scattering effect makes the $K$-edge peak in the absorption coefficient shift to the lower energy region as a function of photon energy, that is, the photon energy required to excite the $1s$ electron to the $K$-edge peak reduces. It is also found that the multiple-scattering effect does not change the two-peak structure in the RIXS spectra but modifies slightly the shape as a function of energy loss. These findings suggests that the multiple scattering effect could mainly be included into a renormalization of the core-level energy and partly justify the Born approximation, leading to a future application to the RIXS in three-dimensional systems., Comment: revised version with extended discussion, 24 pages, 12 figures, accepted for PRB

We study the electric quadrupole (E2) contribution to resonant x-ray scattering (RXS). Under the assumption that the rotational invariance is preserved in the Hamiltonian describing the intermediate state of scattering, we derive a useful expression for the RXS amplitude. One of the advantages the derived expression possesses is the full information of the energy dependence, lacking in all the previous studies using the fast collision approximation. The expression is also helpful to classify the spectra into multipole order parameters which are brought about. The expression is suitable to investigate the RXS spectra in the localized f electron systems. We demonstrate the usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3} edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra as a function of energy in agreement with the experiment of Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the \sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends strongly on the domain distribution. The sixfold symmetry in the AFQ phase arises from the simultaneously induced hexadecapole order. Although the AFO order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the AFQ order may not be ruled out on the basis of azimuthal angle dependence alone., Comment: 12 pages, 6 figures

We derive an expression for the scattering amplitude of resonant x-ray scattering under the assumption that the Hamiltonian describing the intermediate state preserves spherical symmetry. On the basis of this expression, we demonstrate that the energy profile of the RXS spectra expected near U and Np M_4 edges from the triple-k antiferromagnetic ordering phase in UO_{2} and U_{0.75}Np_{0.25}O_{2} agree well with those from the experiments. We demonstrate that the spectra in the \sigma-\sigma' and \sigma-\pi' channels exhibit quadrupole and dipole natures, respectively., Comment: 3 pages, 3 figures, to be published in J. Phys. Soc. Jpn. Suppl

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the \Gamma_{8}-quartet ground state, we construct the triple-\textbf{k} ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses., Comment: 10 pages, 7 figures

The 4p states in transition metals and their compounds usually play minor roles on their physical quantities. Recent development of resonant x-ray scattering (RXS) at the K-edge of transition metals, however, casts light on the 4p states, because the signals on orbital and magnetic superlattice spots are brought about by the modulation in the 4p states. The 4p states are extending in solids and thereby sensitive to electronic states at neighboring sites. This characteristic determines the mechanism of RXS that the intensity on the orbital superlattice spots are mainly generated by the lattice distortion and those on magnetic superlattice spots by the coupling of the 4p states with the orbital polarization in the 3d states at neighboring sites. Taking up typical examples for orbital and magnetic RXS, we demonstrate these mechanisms on the basis of the band structure calculation. Finally, we study the MCD spectra at the K-edge, demonstrating that the same mechanism as the magnetic RXS is working., Comment: 9 pages, 9 figures, submitted to Physica Scripta (comment)

We study the effects of quantum fluctuations on excitation spectra in the two-dimensional Heisenberg antiferromagnet by means of the 1/S expansion. We calculate the spin-wave dispersion and the transverse dynamical structure factor up to the second order of 1/S in comparison with inelastic neutron scattering experiments. The spin-wave energy at momentum $(\pi,0)$ is found to be about 2% smaller than that at $(\pi/2,\pi/2)$ due to the second-order correction. In addition, we study the dimensional crossover from two dimensions to one dimension by weakening exchange couplings in one direction. It is found that the second-order correction becomes large with approaching the quasi-one dimensional situation and makes the spin-wave energy approach to the des Cloizeaux-Pearson boundary for $S=1/2$. The transverse dynamical structure factor is also calculated up to the second order of 1/S. It is shown that the intensity of spin-wave peak is strongly reduced while the intensity of three-spin-wave continuum becomes large and exceeds that of the spin-wave peak in the quasi-one dimensional situation., Comment: 20 pages, 6 figures, revised text, added curves in Figs. 3 and 6 for J'/J=0.075 and corrected typos in Tables

Based on a localized crystal electric field model for the U^{4+} in the (5f)^2-configuration, we analyze the resonant x-ray scattering spectra around U M_{IV} and M_{V} edges in URu_{2}Si_{2}, taking full Coulomb and spin-orbit interactions into account. We consider two level schemes, a singlet model of Santini and Amoretti and a doublet model of Ohkawa and Shimizu, and assume the antiferroquadrupolar order and the antiferromagnetic order as candidates for the ambient pressure phase and the high pressure phase. It is found that the spectral shapes as a function of photon energy are independent of the assumed level scheme, but are quite different between the antiferroquadrupole and antiferromagnetic phases, This may be useful to determine the character of the ordered phase., Comment: 8 pages, 5 figures, submitted to JPSJ

Using ab-initio band structure calculation based on the local density approximation, Cr K-edge resonant X-ray magnetic scattering spectra are analyzed in the spin density wave (SDW) state of chromium. We perform band structure calculation, assuming an ideal bcc lattice structure with the lattice constant observed at the spin-flip temperature T_{SF} and a commensurate SDW state with the propagation vector close to the observed value at T_{SF}. Taking account of the spin-orbit interaction, we obtain the orbital moment on each Cr site induced in proportion to the local spin moment, which is quite small, at most a tenth of those in nickel or iron. In spite of the tiny 3d orbital moment, the orbital polarization is found to have large fluctuations as a function of energy. We obtain the scattering intensity at the Cr K-edge on the SDW magnetic Bragg spot, which shows resonant enhancement in good agreement with the experiment. The 3d orbital polarization is found to be highly correlated with the intensity of the resonant main peak, indicating that the 4p orbital polarization is mainly induced by the 3d orbital polarization through the p-d hybridization., Comment: 9 pages, 10 figures, submitted to PRB

We investigate theoretically the resonant inelastic x-ray scattering (RIXS) at the $K$ edge of Si on the basis of an ab initio calculation. We calculate the RIXS spectra with systematically varying transfered-momenta, incident-photon energy and incident-photon polarization. We confirm the anisotropy of the experimental spectra by Y. Ma {\it et al}. (Phys. Rev. Lett. 74, 478 (1995)), providing a quantitative explanation of the spectra., Comment: 18 pages, 11 figures

We study theoretically the resonant inelastic x-ray scattering in quasi-one-dimensional insulating copper oxides, where the incident photon energy is tuned to the Cu1s-4p absorption energy. Our attention is focused particularly on the strong momentum-transfer dependence of the spectral shape observed in recent experiments. We describe the antiferromagnetic ground state within the Hartree-Fock theory, and consider charge excitations from the ground state within the random phase approximation. By taking account of the electron correlation effects perturbatively, we obtain detailed momentum-transfer dependence of the spectra in a semiquantitative agreement with the experiments., Comment: 4 pages, 5 figures, submitted to J. Phys. Soc. Jpn

We provide a semiquantitative explanation of a recent experiment on the resonant inelastic x-ray scattering (RIXS) in insulating cuprate La2CuO4 (Y.J. Kim et al., Phys. Rev. Lett. 89, 177003 (2002).). We show theoretically that there are three characteristic peaks in RIXS spectra, two of which are attributed to the charge transfer excitation and are reasonably assigned to those observed experimentally. The lowest energy peak has a relatively large dispersion ($\sim 0.8$ eV) and is suppressed near the zone corner (\pi, \pi), in agreement with the experiment. We stress that electron correlation is an essential factor for explaining the overall energy-momentum dependence of the RIXS spectra consistently., Comment: 5 pages, 5 figures, to be published in Phys. Rev. B

We investigate the magnetic resonant x-ray scattering spectra around the $K$ edge of Ni in antiferromagnetic NiO using an \textit{ab-initio} band-structure calculation based on the density-functional theory. By taking account of orbital polarization through the spin-orbit interaction, we reproduce well the spectra obtained experimentally, thus demonstrating the usefulness of the \textit{ab-initio} calculation. It is shown that the main-edge peak, which mainly comes from the dipolar ($1s \to 4p$) transition, is a direct reflection of the orbital polarization of the $4p$ states. It is clarified that the $4p$ orbital polarization is mainly induced from the spin polarization on the $4p$ states by the spin-orbit interaction. The 3d orbital polarization at neighboring Ni sites gives rise to only a minor contribution to the $4p$ orbital polarization through a $p$-$d$ mixing. It is also shown that the pre-edge peak, which mainly originates from the quadrupolar ($1s \to 3d$) transition, is a direct reflection of the orbital polarization of the unoccupied 3d states. It shows a Fano-type antiresonant dip due to interference with the nonresonant contribution, in agreement with the experimental result., Comment: Accepted to Phys. Rev. B

We study the resonant inelastic x-ray scattering (RIXS) at the $K$ edge of Ge. We measure RIXS spectra with systematically varying momenta in the final state. The spectra are a measure of exciting an electron-hole pair. We find a single peak structure (except the elastic peak) as a function of photon energy, which is nearly independent of final-state momenta. We analyze the experimental data by means of the band structure calculation. The calculation reproduces well the experimental shape, clarifying the implication of the spectral shape., Comment: 17 pages,9 figures, Please also see our related paper: cond-mat/0405009

We theoretically investigate the origin of the x-ray magnetic circular dichroism (XMCD) spectra at the K edges of Mn and Ga in the ferromagnetic phase of Mn3GaC on the basis of an ab initio calculation. Taking account of the spin-orbit interaction in the LDA scheme, we obtain the XMCD spectra in excellent agreement with the recent experiment. We have analyzed the origin of each structure, and thus elucidated the mechanism of inducing the orbital polarization in the p symmetric states. We also discuss a simple sum rule connecting the XMCD spectra with the orbital moment in the p symmetric states., Comment: 5 pages, 5 figures, accepted for publication in Physical Review B

We study the resonant x-ray scattering (RXS) spectra at the Dy $L_{\rm III}$ absorption edge in the quadrupole ordering phase of DyB$_2$C$_2$. Analyzing the buckling of sheets of B and C atoms, we construct an effective model that the crystal field is acting on the $5d$ and $4f$ states with the principal axes different for different sublattices. Treating the $5d$ states as a band and the $4f$ states as localized states, we calculate the spectra within the dipole transition. We take account of processes that (1) the lattice distortion directly modulates the $5d$ states and (2) the charge anisotropy of the quadrupole ordering $4f$ states modulates the $5d$ states through the $5d$-$4f$ Coulomb interaction. Both processes give rise to the RXS intensities on $(00\frac{\ell}{2})$ and $(h0\frac{\ell}{2})$ spots. Both give similar photon-energy dependences and the same azimuthal-angle dependences for the main peak, in agreement with the experiment. The first process is found to give the intensities much larger than the second one in a wide parameter range of crystal field. This suggests that the main-peak of the RXS spectra is not a direct reflection of the quadrupole order but mainly controlled by the lattice distortion., Comment: 8 pages, 8 figures, Latex, To be published in J. Phys. Soc. Jpn

We calculate the resonant x-ray scattering (RXS) spectra near the Ce $L_{\rm III}$ absorption edge in CeB$_6$, on the basis of a microscopic model that the $4f$ states of Ce are atomic while the $5d$ states form an energy band with a reasonable density of states. In the initial state, we employ an effective Hamiltonian of Shiina {\it et al}. in the antiferro-quadrupole (AFQ) ordering phase, while we construct the wave function consistent with the neutron scattering experiment in the magnetic ground state. In the intermediate state, we take full account of the intra-atomic Coulomb interaction. Without assuming any lattice distortion, we obtain sufficient RXS intensities on the AFQ superlattice spot. We obtain the spectral shape, the temperature and magnetic field dependences in good agreement with the experiment, thus demonstrating the mechanism that the intensity is brought about by the modulation of $5d$ states through the anisotropic term of the $5d$-$4f$ Coulomb interaction. In the magnetic ground state, a small pre-edge peak is found by the $E_2$ process. On the magnetic superlattice spot, we get a finite but considerably small intensity. The magnetic form factor is briefly discussed., Comment: Latex, 10 pages, 12 figures. To be published in J. Phys. Soc. Jpn., Vol.71, No. 7 (2002)

We theoretically investigate the origin of the resonant x-ray scattering (RXS) signal near the Ce $L_{III}$ absorption edge in the quadrupolar ordering phase of CeB$_6$, considering the intersite interaction between the $\Gamma_8$ states in the initial state. The anisotropic charge distribution of the $4f$ states modulates the $5d$ states through the intra-atomic Coulomb interaction and thereby generates a large RXS superlattice intensity. The temperature and magnetic field dependence indicates that the induced dipolar and octupolar orders have little influence on the RXS spectra, in good agreement with the recent experiment., Comment: 4 pages, 4 figures

We investigate the mechanism of the resonant X-ray scattering on the Ti $K$ edge region of YTiO$_3$ using the band structure calculation combined with the local density approximation. A large intensity is obtained for the orbital superlattice spots. The calculated spectra consist of several peaks as a function of photon energy in agreement with the recent experiments. Against a naive interpretation that directly relates the intensity to the orbitally polarized $3d$ states, the obtained large intensity arises from the distorted crystal structure, i.e., the tilt of the TiO$_6$ octahedra and the Jahn-Teller distortion, which considerably modifies the $4p$ states in the intermediate states of the dipolar process. This casts doubt on a prevailing assertion that the resonant x-ray scattering is a direct observation of the orbital order., Comment: 7 pages, 6 figures, REVTeX3, submitted to PRB

We study the resonant x-ray magnetic scattering (RXMS) around the K edge of Ni in the antiferromagnet NiO, by treating the 4p states of Ni as a band and the 3d states as localized states. We propose a mechanism that the 4p states are coupled to the magnetic order through the intra-atomic Coulomb interaction between the 4p and the 3d states and through the p-d mixing to the 3d states of neighboring Ni atoms. These couplings induce the orbital moment in the 4p band, and thereby give rise to the RXMS intensity at the K edge in the dipolar process. It is found that the spin-orbit interaction in the 4p band has negligibly small contribution to the RXMS intensity. The present model reproduces well the experimental spectra. We also discuss the azimuthal angle dependence of the intensity., Comment: 10 pages (revtex) and 7 postscript figures

We analyze the recent experiment [W. Neubeck {\em et al.}, Phys. Rev. B \vol(60,1999,R9912)] for the resonant x-ray magnetic scattering (RXMS) around the K edge of Co in the antiferromagnet CoO. We propose a mechanism of the RXMS to make the $4p$ states couple to the magnetic order: the intraatomic exchange interaction between the $4p$ and the $3d$ states and the $p$-$d$ mixing to the $3d$ states of neighboring Co atoms. These couplings induce the orbital moment in the $4p$ states and make the scattering tensor antisymmetric. Using a cluster model, we demonstrate that this modification gives rise to a large RXMS intensity in the dipole process, in good agreement with the experiment. We also find that the pre-edge peak is generated by the transition to the $3d$ states in the quadrupole process, with negligible contribution of the dipole process. We also discuss the azimuthal angle dependence of the intensity., Comment: 15 pages, 8 figures