By resonant inelastic x-ray scattering in the soft x-ray regime we probe the dynamical multiple-spin correlations in the antiferromagnetic cuprates La2CuO4 and CaCuO2. High resolution measurements at the copper L3 edge allow the clear observation of dispersing bimagnon excitations. Theory based on the ultrashort core-hole lifetime expansion fits the data on these coherent spin excitations without free parameters.

Recent experiments on La 2 CuO 4 suggest that indirect resonant inelastic x-ray scattering ͑RIXS͒ might provide a probe for transversal spin dynamics. We present in detail a systematic expansion of the relevant magnetic RIXS cross section by using the ultrashort core-hole lifetime ͑UCL͒ approximation. We compute the scattering intensity and its momentum dependence in leading order of the UCL expansion. The scattering is due to two-magnon processes and is calculated within a linear spin-wave expansion of the Heisenberg spin model for this compound, including longer range and cyclic spin interactions. We observe that the latter terms in the Hamiltonian enhance the first moment of the spectrum if they strengthen the antiferromagnetic ordering. The theoretical spectra agree very well with experimental data, including the observation that scattering intensity vanishes for the transferred momenta q = ͑0,0͒ and q = ͑ , ͒. We show that at finite temperature, there is an additional single-magnon contribution to the scattering with a spectral weight proportional to T 3 . We also compute the leading corrections to the UCL approximation and find them to be small, setting the UCL results on a solid basis. All this univocally points to the conclusion that the observed low temperature RIXS intensity in La 2 CuO 4 is due to two-magnon scattering.

In indirect resonant inelastic X-ray scattering (RIXS) an intermediate state is created with a corehole that has an ultrashort lifetime. The core-hole potential therefore acts as a femtosecond pulse on the valence electrons. We show that this fact can be exploited to integrate out the intermediate states from the expressions for the scattering cross section. By this we obtain an effective scattering cross section that only contains the initial and final scattering states. We derive in detail the effective cross section which turns out to be a resonant scattering factor times a linear combination of the charge response function S(q, ω) and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials and ultrashort lifetimes. The resonant scattering pre-factor is shown to be weakly temperature dependent. We also derive a sum-rule for the total scattering intensity and generalize the results to multi-band systems. One of the remarkable outcomes is that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.

We assess the capabilities of magnetic Resonant Inelastic X-ray Scattering (RIXS) at the O K edge in undoped cuprates by taking La2CuO4 as a benchmark case, based on a series of RIXS measurements that we present here. By combining the experimental results with basic theory we point out the fingerprints of bimagnon in the O K edge RIXS spectra. These are a dominant peak around 450 meV, the almost complete absence of dispersion both with π and σ polarization and the almost constant intensity vs. the transferred momentum with σ polarization. This behavior is quite different from Cu L3 edge RIXS giving a strongly dispersing bimagnon tending to zero at the center of the Brillouin zone. This is clearly shown by RIXS measurements at the Cu L3 edge that we present. The Cu L3 bimagnon spectra and those at Cu K edge -both from the literature and from our data -however, have the same shape. These similarities and differences are understood in terms of different sampling of the bimagnon continuum. This panorama points out the unique possibilities offered by O K RIXS in the study of magnetic excitations in cuprates near the center of the BZ.

The strongly correlated insulator Ca2RuO4 is considered as a paradigmatic realization of both spin-orbital physics and a band-Mott insulating phase, characterized by orbitally selective coexistence of a band and a Mott gap. We present a high-resolution oxygen K-edge resonant inelastic X-ray scattering study of the antiferromagnetic Mott insulating state of Ca2RuO4. A set of lowenergy (∼80 and 400 meV) and high-energy (∼ 1.3 and 2.2 eV) excitations are reported that show strong incident light polarization dependence. Our results strongly support a spin-orbit coupled band-Mott scenario and explore in detail the nature of its exotic excitations. Guided by theoretical modelling, we interpret the low-energy excitations as a result of composite spin-orbital excitations. Their nature unveil the intricate interplay of crystal-field splitting and spin-orbit coupling in the band-Mott scenario. The high-energy excitations correspond to intra-atomic singlet-triplet transitions at an energy scale set by the Hund's coupling. Our findings give a unifying picture of the spin and orbital excitations in the band-Mott insulator Ca2RuO4.Introduction. Spin-orbit coupling (SOC) is a central thread in the search for novel quantum material physics [1]. A particularly promising avenue is the combination of SOC and strong electron correlations in multiorbital systems. This scenario is realized in heavy transition metal oxides composed of 4d and 5d elements. Iridium-oxides (iridates) such as Sr 2 IrO 4 are prime examples of systems where SOC plays a defining role in shaping the Mott insulating ground state [2]. In fact, spin-orbit entanglement essentially outplays the effectiveness of the usually influential crystal field δ. Of equal interest is the complex regime where SOC and crystal field energy scales are comparable. Here Ca 2 RuO 4 is a topical material that displays a wealth of physical properties. A record high non-superconducting diamagnetic response has, for example, been reported recently [3]. Superconductivity emerges in strained films [4] or upon application of hydrostatic pressure to bulk crystals [5]. Neutron and Raman scattering experiments have demonstrated both phase and amplitude spin-excitation modes consistent with the existence of a spin-orbit exciton [6][7][8]. Moreover, measurements of the paramagnetic insulating band structure [9] were interpreted in favor of an orbitally differentiated band-Mott insulating ground state [10,11]. This rich phenomenology of Ca 2 RuO 4 is a manifestation of the interplay between multiple energy scales, specifically, the Coulomb interaction U , the Hund's coupling J H , the crystal field splitting δ and SOC λ. In particular, a tendency towards an orbital selective Mott state is expected to be driven by the Hund's coupling [12]. Furthermore, the band-Mott scenario is triggered by a

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We study the dynamical, momentum dependent two-and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped t − J system the four-spin response vanishes at π, whereas the two-spin correlator is peaked around π/2, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at π changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.

We use relativistic ab-initio methods combined with model Hamiltonian approaches to analyze the normal-phase electronic and structural properties of the recently discovered WP superconductor. Remarkably, the outcomes of such study can be employed to set fundamental connections among WP and the pressure induced superconductors CrAs and MnP compounds belonging to the same space group. One of the key features of the resulting electronic structure is represented by the occurrence of multiple band crossings along specific high symmetry lines of the Brilloiun zone. In particular, we demonstrate that an eight-fold band degeneracy is obtained along the S-R path at (kx,ky)=(π,π), due to time reversal invariance and a pair of nonsymmorphic symmetries. The presence of multiple degenerate Fermi points along the S-R direction constraints the topology of the Fermi surface, which manifests distinctive marks when considering its evolution upon band filling variation. We show that, by changing the relative position of the Fermi level with respect to the eight-fold degenerate bands, one can tune the effective dimensionality of the Fermi surface. If the Fermi level does not cross the multifold degenerate bands, as for the WP and CrAs compounds, the degeneracy forces the occurrence of two-dimensional (2D) Fermi surface sheets centered around the S-R line with a corrugated profile along the kz direction. On the contrary, these surfaces are converted into open or closed Fermi pockets, if the bands along the SR line cross the Fermi level, as it happens in MnP. Moreover, we show that the spin-orbit interaction determines a selective removal of the band degeneracy and, consequently, a splitting of the quasi 2D Fermi sheets, as it happens in WP.