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X-ray magnetic circular dichroism (XMCD) and resonant inelastic X-ray scattering with magnetic circular dichroism (RIXS-MCD) provide unparalleled insights into the electronic and magnetic dynamics of complex materials. Yet, their spectra remain challenging to interpret due to intricate many-body interactions. Here, we introduce a theoretical framework based on the Anderson impurity model, fully incorporating charge transfer (CT) and core-valence exchange correlation (CVEC) effects. Using epitaxial ferromagnetic La0.7Sr0.3MnO3 film as a model system, we capture elusive spectral features, demonstrating the necessity of CT inclusion for resolving XMCD subpeaks and revealing the profound impact of CVEC on RIXS-MCD spectra. Our approach not only successfully mirrors experimental results but also opens new avenues for exploring spin, orbital, and charge excitations in 3d transition metals and other correlated materials.

The normal state of high-Tc cuprates has been considered one of the essential topics in high-temperature superconductivity research. However, compared to the high magnetic fields study of it, understanding a photoinduced normal state remains elusive. Here, we explore a photoinduced normal state of YBa$_2$Cu$_3$O$_{6.67}$ (YBCO) through a charge density wave (CDW) with time-resolved resonant soft x-ray scattering, as well as a high-magnetic field x-ray scattering. In the non-equilibrium state in which people predict a quenched superconducting state based on the previous optical spectroscopies, we experimentally observed a similar analogy to the competition between superconductivity and CDW shown in the equilibrium state. We further observe that the broken pairing states in the superconducting CuO$_2$ plane via the optical pump lead to nucleation of three-dimensional CDW precursor correlation, revealing that the photoinduced CDW is similar to phenomena shown under magnetic fields. Ultimately, these findings provide a critical clue that the characteristics of the photoinduced normal state show a solid resemblance to those under magnetic fields in equilibrium conditions., Comment: 22 pages, 5 figures and Supplementary Materials with 6 pages, 9 figures

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La$_{1.885}$Sr$_{0.115}$CuO$_4$, by studying the effects of large magnetic fields ($H$) up to 24 Tesla. At low temperatures ($T$), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the $H-T$ phase diagram., Comment: 7 pages, 3 figures

The presence of a small concentration of in-plane Fe dopants in La$_{1.87}$Sr$_{0.13}$Cu$_{0.99}$Fe$_{0.01}$O$_4$ is known to enhance stripe-like spin and charge density wave (SDW and CDW) order, and suppress the superconducting $T_c$. Here, we show that it also induces highly two-dimensional (2D) superconducting correlations that have been argued to be signatures of a new form of superconducting order, so-called pair-density-wave (PDW) order. In addition, using the resonant soft x-ray scattering, we find that the 2D superconducting fluctuation is strongly associated with the CDW stripe. In particular, the PDW signature first appears when the correlation length of the CDW stripe grows over eight times the lattice unit ($\sim$ 8$a$). These results provide critical conditions for the formation of PDW order., Comment: Supplemental Material is available from the corresponding author (J.-S. Lee) upon request

A SrRuO$_3$ (SRO) thin film and its heterostructure have brought much attention because of the recently demonstrated fascinating properties, such as topological Hall effect and skyrmions. Critical to the understanding of those SRO properties is the study of the spin configuration. Here, we conduct resonant soft x-ray scattering (RSXS) at oxygen K-edge to investigate the spin configuration of a 4 unit-cell SRO film that was grown epitaxially on a single crystal SrTiO$_3$. The RSXS signal under a magnetic field (~0.4 Tesla) clearly shows a magnetic dichroism pattern around the specular reflection. Model calculations on the RSXS signal demonstrate that the magnetic dichroism pattern originates from a N\'eel-type chiral spin structure in this SRO thin film. We believe that the observed spin structure of the SRO system is a critical piece of information for understanding its intriguing magnetic and transport properties.

The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difficult to fully elucidate the relationship between the density wave orders and SC. Here using resonant soft X-ray scattering we study the archetypal cuprate, La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order with developing SDW stripe order near the superconducting $T_{\rm c}$. These findings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO$_2$ planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders., Comment: 28 pages, 11 figures

The recently demonstrated x-ray scattering approach using a free electron laser with a high field pulsed magnet has opened new opportunities to explore the charge density wave (CDW) order in cuprate high temperature superconductors. Using this approach, we substantially degrade the superconductivity with magnetic fields up to 33 T to investigate the onset of CDW order in YBa$_2$Cu$_3$O$_x$ at low temperatures near a putative quantum critical point (QCP) at $p_1\sim $ 0.08 holes per Cu. We find no CDW can be detected in a sample with a doping concentration less than $p_1$. Our results indicate that the onset of the CDW ground state lies inside the zero-field superconducting dome, and broken translational symmetry is associated with the putative QCP at $p_1$, Comment: 4 figures

The frustrated magnet has been regarded as a system that could be a promising host material for the quantum spin liquid (QSL). However, it is difficult to determine the spin configuration and the corresponding mechanism in this system, because of its geometrical frustration (i.e., crystal structure and symmetry). Herein, we systematically investigate one of the geometrically frustrated magnets, the TbB$_{4}$ compound. Using resonant soft x-ray scattering (RSXS), we explored its spin configuration, as well as Tb's quadrupole. Comprehensive evaluations of the temperature and photon energy / polarization dependences of the RSXS signals reveal the mechanism of spin reorientation upon cooling down, which is the sophisticated interplay between the Tb spin and the crystal symmetry rather than its orbit (quadrupole). Our results and their implications would further shed a light on the search for possible realization of QSL.

One of the central questions in the cuprate research is the nature of the "normal state" which develops into high temperature superconductivity (HTSC). In the normal state of hole-doped cuprates, the existence of charge density wave (CDW) is expected to shed light on the mechanism of HTSC. With evidence emerging for CDW order in the electron-doped cuprates, the CDW would be thought to be a universal phenomenon in high-$T_c$ cuprates. However, the CDW phenomena in electron-doped cuprate are quite different than those in hole-doped cuprates. Here we study the nature of the putative CDW in an electron-doped cuprate through direct comparisons between as-grown and post-annealed Nd$_{1.86}$Ce$_{0.14}$CuO$_4$ (NCCO) single crystals using Cu $L_3$-edge resonant soft x-ray scattering (RSXS) and angle resolved photoemission spectroscopy (ARPES). The RSXS result reveals that the non-superconducting NCCO shows the same reflections at the wavevector (~1/4, 0, $l$) as like the reported superconducting NCCO. This superconductivity-insensitive signal is quite different with the characteristics of the CDW reflection in hole-doped cuprates. Moreover, the ARPES result suggests that the fermiology cannot account for such wavevector. These results call into question the universality of CDW phenomenon in the cuprates., Comment: 18 pages, 4 figures, 5 pages of Supplemental Material

Compelling efforts to improve the critical temperature ($T_{c}$) of superconductors have been made through high-pressure application. Understanding the underlying mechanism behind such improvements is critically important, however, much remains unclear. Here we studied ortho-III YBa$_{2}$Cu$_{3}$O$_{6.73}$ (YBCO) using x-ray scattering under hydrostatic-pressure (HP) up to ~6.0 GPa. We found the reinforced oxygen order (OO) of YBCO under HP, revealing an oxygen rearrangement in the Cu-O layer, which evidently shows the charge transfer phenomenon between the CuO$_{2}$ plane and Cu-O layer. Concurrently, we also observed no disorder-pinned charge density wave (CDW) signature in CuO$_{2}$ plane under HP. This indicates that the oxygen rearrangement modifies the quenched disorder state in the CuO$_{2}$ plane. Using these results, we appropriately explain why pressure-condition can achieve higher $T_{c}$ compared with the optimal $T_{c}$ under ambient pressure in YBa$_{2}$Cu$_{3}$O$_{6+x}$. As an implication of these results, finally, we have discussed that the change in disorder could make it easier for YBa$_{2}$Cu$_{3}$O$_{6+x}$ to undergo a transition to the nematic order under an external magnetic field., Comment: 24 pages, 6 figures

The existence of charge density wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the ground state order has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to a dozen unit cells or less. Here we explore the CDW correlations in YBa2Cu3Ox (YBCO) ortho-II and ortho-VIII crystals, which belong to the cleanest available cuprate family, at magnetic fields in excess of the resistive upper critical field (Hc2) where the superconductivity is heavily suppressed. We find an incommensurate, unidirectional CDW with a well-defined onset at a critical field strength that is proportional to Hc2. It is related to but distinct from the short-range bidirectional CDW that exists at zero magnetic field. The unidirectional CDW possesses a long inplane correlation length as well as significant correlations between neighboring CuO2 planes, yielding a correlation volume that is at least 2 - 3 orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground-state of an "ideal" disorder-free cuprate.

We demonstrate the microscopic role of oxygen vacancies spatially confined within nanometer inter-spacing (about 1 nm) in BiFeO3, using resonant soft X-ray scattering techniques and soft X-ray spectroscopy measurements. Such vacancy confinements and total number of vacancy are controlled by substitution of Ca2+ for Bi3+ cation. We found that by increasing the substitution, the in-plane orbital bands of Fe3+ cations are reconstructed without any redox reaction. It leads to a reduction of the hopping between Fe atoms, forming a localized valence band, in particular Fe 3d-electronic structure, around the Fermi level. This band localization causes to decrease the conductivity of the doped BiFeO3 system., Comment: 24 pages, 4 figures, and 4 supplementary figures

Charge density wave (CDW) correlations have recently been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured by x-ray scattering at zero and low fields. Here we combine a pulsed magnet with an x-ray free electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields up to 28 Tesla. While the zero-field CDW order, which develops below T ~ 150 K, is essentially two-dimensional, at lower temperature and beyond 15 Tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW onsets around the zero-field superconducting transition temperature, yet the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

Ultrafast light pulses can modify the electronic properties of quantum materials by perturbing the underlying, intertwined degrees of freedom. In particular, iron-based superconductors exhibit a strong coupling among electronic nematic fluctuations, spins, and the lattice, serving as a playground for ultrafast manipulation. Here we use time-resolved x-ray scattering to measure the lattice dynamics of photo-excited BaFe2As2. Upon optical excitation, no signature of an ultrafast change of the crystal symmetry is observed, but the lattice oscillates rapidly in time due to the coherent excitation of an A1g mode that modulates the Fe-As-Fe bond angle. We directly quantify the coherent lattice dynamics and show that even a small photo-induced lattice distortion can induce notable changes in the electronic and magnetic properties. Our analysis implies that transient structural modification can generally be an effective tool for manipulating the electronic properties of multi-orbital systems, where electronic instabilities are sensitive to the orbital character of bands near the Fermi level.

The unoccupied states of complex materials are difficult to measure, yet play a key role in determining their properties. We propose a technique that can measure the unoccupied states, called time-resolved Compton scattering, which measures the time-dependent momentum distribution (TDMD). Using a non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a lattice in a pump-probe setup. We find a direct relation between temporal oscillations in the TDMD and the dispersion of the underlying unoccupied states, suggesting that both can be measured by time-resolved Compton scattering. We demonstrate the experimental feasibility by applying the method to a model of MgB$_2$ with realistic material parameters.

We investigated the mechanism of the spin-reorientation transition (SRT) in the Ni/Fe/Ni/W(110) system using in situ low-energy electron microscopy, x-ray magnetic circular dichroism measurements, and first principles electronic structure calculations. We discovered that the growth of Fe on a flat Ni film on a W (110) crystal resulted in the formation of nanosized particles, instead of a uniform monolayer of Fe as commonly assumed. This interfacial nanostructure leads to a change of the system's dimensionality from two dimensional- to three dimensional-like, which simultaneously weakens the dipolar interaction and enhances the spin-orbit coupling in the system and drives the observed SRT., Comment: 4 figures

Epitaxial FeRh(100) films (CsCl structure, $\sim 10\ ML\ $ thick), prepared {\it in-situ} on a W(100) single crystal substrate, have been investigated via valence band and core level photoemission. The presence of the temperature-induced, first-order, antiferromagnetic to ferromagnetic (AF$\rightarrow$ FM) transition in these films has been verified via linear dichroism in photoemission from the Fe 3$p$ levels. Core level spectra indicate a large moment on the Fe atom, practically unchanged in the FM and AF phases. Judging from the valence band spectra, the metamagnetic transition takes place without substantial modification of the electronic structure. In the FM phase, the spin-resolved spectra compare satisfactorily to the calculated spin-polarized bulk band structure., Comment: 7 pages, 5 figures

We report the formation of a novel ferromagnetic state in the antiferromagnet BiFeO3 at the interface with La0.7Sr0.3MnO3. Using x-ray magnetic circular dichroism at Mn and Fe L2,3-edges, we discovered that the development of this ferromagnetic spin structure is strongly associated with the onset of a significant exchange bias. Our results demonstrate that the magnetic state is directly related with an electronic orbital reconstruction at the interface, which is supported by the linearly polarized x-ray absorption measurement at oxygen K-edge., Comment: 17 pages, 4 figures, PRL in press

We report on room temperature ferromagnetic resonance (FMR) studies of [$t$ Co$|2t$ Ni]$\times$N sputtered films, where $0.1 \leq t \leq 0.6$ nm. Two series of films were investigated: films with same number of Co$|$Ni bilayer repeats (N=12), and samples in which the overall magnetic layer thickness is kept constant at 3.6 nm (N=1.2/$t$). The FMR measurements were conducted with a high frequency broadband coplanar waveguide up to 50 GHz using a flip-chip method. The resonance field and the full width at half maximum were measured as a function of frequency for the field in-plane and field normal to the plane, and as a function of angle to the plane for several frequencies. For both sets of films, we find evidence for the presence of first and second order anisotropy constants, $K_1$ and $K_2$. The anisotropy constants are strongly dependent on the thickness $t$, and to a lesser extent on the total thickness of the magnetic multilayer. The Land\'e g-factor increases with decreasing $t$ and is practically independent of the multilayer thickness. The magnetic damping parameter $\alpha$, estimated from the linear dependence of the linewidth, $\triangle H$, on frequency, in the field in-plane geometry, increases with decreasing $t$. This behaviour is attributed to an enhancement of spin-orbit interactions with $t$ decreasing and in thinner films, to a spin-pumping contribution to the damping., Comment: 18 pages, 13 figures

A sharp feature in the charge-density excitation spectra of single-crystal MgB$_{2}$, displaying a remarkable cosine-like, periodic energy dispersion with momentum transfer ($q$) along the $c^{*}$-axis, has been observed for the first time by high-resolution non-resonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-$q$ collective mode residing in the single-particle excitation gap of the B $\pi$ bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB$_{2}$., Comment: 5 pages, 4 figures, submitted to PRL

We demonstrate a layer- and time-resolved measurement of ferromagnetic resonance (FMR) in a Ni81Fe19 / Cu / Co93Zr7 trilayer structure. Time-resolved x-ray magnetic circular dichroism has been developed in transmission, with resonant field excitation at a FMR frequency of 2.3 GHz. Small-angle (to 0.2 degree), time-domain magnetization precession could be observed directly, and resolved to individual layers through elemental contrast at Ni, Fe, and Co edges. The phase sensitivity allowed direct measurement of relative phase lags in the precession oscillations of individual elements and layers. A weak ferromagnetic coupling, difficult to ascertain in conventional FMR measurements, is revealed in the phase and amplitude response of individual layers across resonance., Comment: 22 pages, 6 figures submitted to Physical Review B

We present a time-resolved measurement of magnetization dynamics during ferromagnetic resonance (FMR) in a single layer of Ni81Fe19. Small-angle (<1 deg.) precession of elemental Ni, Fe moments could be measured directly and quantitatively using time-resolved x-ray magnetic circular dichroism (XMCD) in transmission. The high temporal and rotational sensitivity of of this technique has allowed characterization of the phase and amplitude of driven FMR motion at 2.3 GHz, verifying basic expectations for a driven resonance., Comment: 3 pages, 4 figures, submitted to APL, 2006

The magnetic properties and magnetization dynamics of polycrystalline ultra-thin Co layers were investigated using a broadband ferromagnetic resonance (FMR) technique at room temperature. A variable thickness (1 nm $\leq t \leq$ 10 nm) Co layer is sandwiched between 10 nm thick Cu layers (10 nm Cu| t Co|10 nm Cu), while materials in contact with the Cu outer interfaces are varied to determine their influence on the magnetization damping. The resonance field and the linewidth were studied for in-plane magnetic fields in field swept experiments at a fixed frequency, from 4 to 25 GHz. The Co layers have a lower magnetization density than the bulk, and an interface contribution to the magnetic anisotropy normal to the film plane. The Gilbert damping, as determined from the frequency dependence of the linewidth, increases with decreasing Co layer thickness for films with outer Pt layers. This enhancement is not observed in structures without Pt layers. The result can be understood in terms of a non-local contribution to the damping due to spin pumping from Co through the Cu layer and spin relaxation in Pt layers. Pt layers just 1.5 nm thick are found to be sufficient to enhance the damping and thus act as efficient "spin-sinks". In structures with Pt outer layers, this non-local contribution to the damping becomes predominant when the Co layer is thinner than 4 nm.

We demonstrate an element-specific measurement of magnetization precession in a metallic ferromagnetic alloy, separating Ni and Fe moment motion in Ni81Fe19. Pump-probe X-ray magnetic circular dichroism (XMCD), synchronized with short magnetic field pulses, is used to measure free magnetization oscillations up to 2.6 GHz with elemental specificity and a rotational resolution of < 2 deg. Magnetic moments residing on Ni sites and Fe sites in a Ni81Fe19(50nm) thin film are found to precess together at all frequencies, coupled in phase within instrumental resolution of 90 ps., Comment: see http://magnet.ap.columbia.edu/pubs for related work

We report direct evidence of charge/orbital ordering of low energy electronic states of $Cu$ in YBa$_2$Cu$_3$O$_{6+x}$ ortho-II phase in both the $CuO_3$ chain and the CuO$_2$ plane. Huge enhancement of the $({1/2},0,0)$ superstructure Bragg peak is observed when photon energy is tuned to the $Cu L_{2,3}$ absorption edge with large polarization dependence. The ordering in the $CuO_2$ plane discovered here sheds new light on how the one dimensional $Cu-O$ chains affect the $CuO_2$ plane, and why many normal and superconducting state properties of this system exhibit strong anisotropy., Comment: 4 pages, 3 figures

The local structure about the Mn site in the half doped system La0.5Ca0.5MnO3 was measured in magnetic fields up 10 T to probe the melting of the charge ordered state. Examination of the Mn-O and Mn-Mn correlations reveal three distinct regions in the structure-field diagram. A broad region with weak field dependence (mainly antiferromatnetic phase below 7.5 T), a narrow-mixed phase region near ~ 8.5 T followed by a ferromagnetic phase region with strong field-structure coupling. At high field the Mn-O radial distribution becomes Gaussian and the Mn-Mn correlations are enhanced - consistent with the dominance of a ferromagnetic phase. The exponential change in resistivity in the first region (observed in transport measurements) is dominated by the reordering of the moments on the Mn sites from CE type antiferromagnetic to ferromagnetic order with only a weak change in the local distortions of the MnO6 octahedra.

We report an x-ray scattering study of octahedral tilt ordering in the manganite series Pr$_{1-x}$Ca$_x$MnO$_3$ with x=0.4 and 0.25 and in LaMnO$_3$. The sensitivity to tilt ordering is achieved by tuning the incident x-ray energy to the L$_I$, L$_{II}$ and L$_{III}$ absorption edges of Pr and La, respectively. The resulting energy-dependent profiles are characterized by a dipole-resonant peak and higher energy fine structure. The polarization dependence is predominantly $\sigma$-to-$\pi$ and the azimuthal dependence follows a sin-squared behavior. These results are similar to those obtained in recent x-ray scattering studies of orbital ordering carried out in these same materials at the Mn K edge. They lead to a description of the cross-section in terms of Templeton scattering in which the tilt ordering breaks the symmetry at the rare earth site. The most interesting result of the present work is our observation that octahedral tilt ordering persists above the orbital ordering transition temperatures in all three samples. Indeed, we identify separate structural transitions which may be associated with the onset of orbital and tilt ordering, respectively, and characterize the loss of tilt ordering versus temperature in LaMnO$_3$., Comment: 24 pages, 8 figures

We present the results of a systematic x-ray scattering study of the charge and orbital ordering in the manganite series Pr$_{1-x}$Ca$_x$MnO$_3$ with $x$=0.25, 0.4 and 0.5. The temperature dependence of the scattering at the charge and orbital wavevectors, and of the lattice constants, was characterized throughout the ordered phase of each sample. It was found that the charge and orbital order wavevectors are commensurate with the lattice, in striking contrast to the results of earlier electron diffraction studies of samples with $x$=0.5. High momentum-transfer resolution studies of the x=0.4 and 0.5 samples further revealed that while long-range charge order is present, long-range orbital order is never established. Above the charge/orbital ordering temperature T$_o$, the charge order fluctuations are more highly correlated than the orbital fluctuations. This suggests that charge order drives orbital order in these samples. In addition, a longitudinal modulation of the lattice with the same periodicity as the charge and orbital ordering was discovered in the x=0.4 and 0.5 samples. For x=0.25, only long-range orbital order was observed with no indication of charge ordering, nor of an additional lattice modulation. We also report the results of a preliminary investigation of the loss of charge and orbital ordering in the x=0.4 sample by application of a magnetic field. Finally, the polarization and azimuthal dependence of the charge and orbital ordering in these compounds is characterized both in the resonant and nonresonant limits, and compared with the predictions of current theories. The results are qualitatively consistent with both cluster and LDA+U calculations of the electronic structure., Comment: 37 pages, 22 figures