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Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO$_2$, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La$_2$CuO$_4$ indicate that quantum fluctuations are much stronger in SrCuO$_2$ suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic N\'eel order as the ground state. Our results indicate that SrCuO$_2$ - due to strong quantum fluctuations - is a unique starting point for the exploration of novel magnetic ground states.

In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering (RIXS) study of weak charge correlations in La2-xSrxCuO4 (LSCO) and La1.8-xEu0.2SrxCuO4 (LESCO). Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Upon increasing doping x, the long-range temperature dependent stripe order is found to be replaced by short-range temperature independent correlations at a critical point xc = 0.15 distinct from the pseudogap critical doping. We argue that the doping and temperature independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In LSCO, long-range static stripe order vanishes in a quantum critical point around optimal doping.

We studied the magnetic excitations in the quasi-one-dimensional (q-1D) ladder subsystem of Sr_(14-x) Ca_x Cu_24 O_41(SCCO) using Cu L_3-edge resonant inelastic X-ray scattering (RIXS). By comparing momentum-resolved RIXS spectra with (x=12.2) and without (x=0) high Ca content, we track the evolution of the magnetic excitations from collective two-triplon (2T) excitations (x=0) to weakly-dispersive gapped modes at an energy of 280 meV (x=12.2). Density matrix renormalization group (DMRG) calculations of the RIXS response in the doped ladders suggest that the flat magnetic dispersion and damped excitation profile observed at x=12.2 originates from enhanced hole localization. This interpretation is supported by polarization-dependent RIXS measurements, where we disentangle the spin-conserving {\Delta}S=0 scattering from the predominant {\Delta}S=1 spin-flip signal in the RIXS spectra. The results show that the low-energy weight in the {\Delta}S=0 channel is depleted when Sr is replaced by Ca, consistent with a reduced carrier mobility. Our results demonstrate that off-ladder impurities can affect both the low-energy magnetic excitations and superconducting correlations in the CuO_4 plaquettes. Finally, our study characterizes the magnetic and charge fluctuations in the phase from which superconductivity emerges in SCCO at elevated pressures.

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical $XY$ models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations., Comment: 14 pages, 26 figures

Explaining the mechanism of superconductivity in the high-$T_c$ cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering (RIXS) to monitor the temperature dependence of the $\underline{d}d$ exciton spectrum of Bi$_2$Sr$_2$CaCu$_2$O$_{8-x}$ (Bi-2212) crystals with different charge carrier concentrations. We observe a significant change of the $\underline{d}d$ exciton spectra when the materials pass from the normal state into the superconductor state. Our observations show that the $\underline{d}d$ excitons start to shift up (down) in the overdoped (underdoped) sample when the material enters the superconducting phase. We attribute the superconductivity-induced effect and its sign-reversal from underdoped to overdoped to the exchange coupling of the site of the $\underline{d}d$ exciton to the surrounding copper spins., Comment: 13 pages, 10 figures

Investigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang-Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin-correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.

A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena., Comment: 11 pages, 18 figures

We present a combined oxygen $K$-egde x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) study of the bilayer ruthenate Ca$_3$Ru$_2$O$_7$. Our RIXS experiments on Ca$_3$Ru$_2$O$_7$ were carried out on the overlapping in-plane and inner apical oxygen resonances, which are distinguishable from the outer apical one. Comparison to equivalent oxygen $K$-edge spectra recorded on band-Mott insulating Ca$_2$RuO$_4$ is made. In contrast to Ca$_2$RuO$_4$ spectra, which contain excitations linked to Mott physics, Ca$_3$Ru$_2$O$_7$ spectra feature only intra-$t_{2g}$ ones that do not directly involve the Coulomb energy scale. As found in Ca$_2$RuO$_4$, we resolve two intra-$t_{2g}$ excitations in Ca$_3$Ru$_2$O$_7$. Moreover, the lowest lying excitation in Ca$_3$Ru$_2$O$_7$ shows a significant dispersion, revealing a collective character differently from what is observed in Ca$_2$RuO$_4$. Theoretical modelling supports the interpretation of this lowest energy excitation in Ca$_3$Ru$_2$O$_7$ as a magnetic transverse mode with multi-particle character, whereas the corresponding excitation in Ca$_2$RuO$_4$ is assigned to combined longitudinal and transverse spin modes. These fundamental differences are discussed in terms of the inequivalent magnetic ground-state manifestations in Ca$_2$RuO$_4$ and Ca$_3$Ru$_2$O$_7$., Comment: 10 pages, 5 figures. This manuscript has been submitted to PRB

We use resonant inelastic x-ray scattering to investigate charge-stripe correlations in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$. By differentiating elastic from inelastic scattering, it is demonstrated that charge-stripe correlations precede both the structural low-temperature tetragonal phase and the transport-defined pseudogap onset. The scattering peak amplitude from charge stripes decays approximately as $T^{-2}$ towards our detection limit. The in-plane integrated intensity, however, remains roughly temperature independent. Therefore, although the incommensurability shows a remarkably large increase at high temperature, our results are interpreted via a single scattering constituent. In fact, direct comparison to other stripe-ordered compounds (La$_{1.875}$Ba$_{0.125}$CuO$_4$, La$_{1.475}$Nd$_{0.4}$Sr$_{0.125}$CuO$_4$ and La$_{1.875}$Sr$_{0.125}$CuO$_4$) suggests a roughly constant integrated scattering intensity across all these compounds. Our results therefore provide a unifying picture for the charge-stripe ordering in La-based cuprates. As charge correlations in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$ extend beyond the low-temperature tetragonal and pseudogap phase, their emergence heralds a spontaneous symmetry breaking in this compound.

The search for oxide materials with physical properties similar to the cuprate high Tc superconductors, but based on alternative transition metals such as nickel, has grown and evolved over time. The recent discovery of superconductivity in doped infinite-layer nickelates RNiO2 (R = rare-earth element) further strengthens these efforts.With a crystal structure similar to the infinite-layer cuprates - transition metal oxide layers separated by a rare-earth spacer layer - formal valence counting suggests that these materials have monovalent Ni1+ cations with the same 3d electron count as Cu2+ in the cuprates. Here, we use x-ray spectroscopy in concert with density functional theory to show that the electronic structure of RNiO2 (R = La, Nd), while similar to the cuprates, includes significant distinctions. Unlike cuprates with insulating spacer layers between the CuO2 planes, the rare-earth spacer layer in the infinite-layer nickelate supports a weakly-interacting three-dimensional 5d metallic state. This three-dimensional metallic state hybridizes with a quasi-two-dimensional, strongly correlated state with 3dx2-y2 symmetry in the NiO2 layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare earth intermetallics, well-known for heavy Fermion behavior, where the NiO2 correlated layers play an analogous role to the 4f states in rare-earth heavy Fermion compounds. This unique Kondo- or Anderson-lattice-like "oxide-intermetallic" replaces the Mott insulator as the reference state from which superconductivity emerges upon doping., Comment: 28 pages, 5 figures

$Fe_3O_4$ is a mixed-valence strongly correlated transition metal oxide which displays the intriguing metal to insulator Verwey transition. Here we investigate the electronic and magnetic structure of $Fe_3O_4$ by a unique combination of high-resolution Fe 2p3d resonant inelastic scattering magnetic circular (RIXS-MCD) and magnetic linear (RIXS-MLD) dichroism. We show that by coupling the site selectivity of RIXS with the magnetic selectivity imposed by the incident polarization handedness, we can unambiguously identify spin-flip excitations and quantify the exchange interaction of the different sublattices. Furthermore, our RIXS-MLD measurements show spin-orbital excitations that exhibit strong polarization and magnetic field dependence. Guided by theoretical simulations, we reveal that the angular dependence arises from a strong interplay between trigonal crystal-field, magnetic exchange and spin-orbit interaction at the nominal $Fe^{2+}$ sites. Our results highlight the capabilities of RIXS magnetic dichroism studies to investigate the ground state of complex systems where in-equivalent sites and bonds are simultaneously present.

The transition temperature $T_\textrm{c}$ of unconventional superconductivity is often tunable. For a monolayer of FeSe, for example, the sweet spot is uniquely bound to titanium-oxide substrates. By contrast for La$_{2-\mathrm{x}}$Sr$_\mathrm{x}$CuO$_4$ thin films, such substrates are sub-optimal and the highest $T_\textrm{c}$ is instead obtained using LaSrAlO$_4$. An outstanding challenge is thus to understand the optimal conditions for superconductivity in thin films: which microscopic parameters drive the change in $T_\mathrm{c}$ and how can we tune them? Here we demonstrate, by a combination of x-ray absorption and resonant inelastic x-ray scattering spectroscopy, how the Coulomb and magnetic-exchange interaction of La$_2$CuO$_4$ thin films can be enhanced by compressive strain. Our experiments and theoretical calculations establish that the substrate producing the largest $T_\textrm{c}$ under doping also generates the largest nearest neighbour hopping integral, Coulomb and magnetic-exchange interaction. We hence suggest optimising the parent Mott state as a strategy for enhancing the superconducting transition temperature in cuprates., Comment: 15 pages, 7 figures and 2 tables (including Supplementary Information)

We have measured the effect of uniaxial stress on the threshold field ET for the motion of the upper CDW in NbSe3. ET exhibits a critical behavior, ET ~ (1 - e/ec)^g, wher e is the strain, and ec is about 2.6% and g ~ 1.2. This ecpression remains valid over more than two decades of ET, up to the highest fields of about 1.5keV/m. Neither g nor ec is very sensitive to the impurity concentraction. The CDW transition temperature Tp decreases linearly with e at a rate dTp/de = -10K/%, and it does not show any anomaly near ec. Shubnikov de-Haas measurements show that the extremal area of the Fermi surface decreases with increasing strain. The results suggest that there is an intimate relationship between pinning of the upper CDW and the Fermiology of NbSe3., Comment: 4 pages, 5 figures