High-resolution resonant inelastic x-ray scattering (RIXS) at the oxygen K edge has been used to study the orbital excitations of Ca 2 RuO 4 and Sr 2 RuO 4 . In combination with linear dichroism x-ray absorption spectroscopy, the ruthenium 4d-orbital occupation and excitations were probed through their hybridization with the oxygen p orbitals. These results are described within a minimal model, taking into account crystal field splitting and a spin-orbit coupling λ so = 200 meV. The effects of spin-orbit interaction on the electronic structure and implications for the Mott and superconducting ground states of (Ca,Sr) 2 RuO 4 are discussed.

A resonant inelastic x-ray scattering study of overdamped spin excitations in slightly underdoped La 2−x Sr x CuO 4 (LSCO) with x = 0.12 and 0.145 is presented. Three high-symmetry directions have been investigated: (1) the antinodal (0,0) → ( 1 2 ,0), (2) the nodal (0,0) → ( 1 4 , 1 4 ), and (3) the zone-boundary direction ( 1 2 ,0) → ( 1 4 , 1 4 ) connecting these two. The overdamped excitations exhibit strong dispersions along (1) and (3), whereas a much more modest dispersion is found along (2). This is in strong contrast to the undoped compound La 2 CuO 4 (LCO) for which the strongest dispersions are found along (1) and (2). The t − t − t − U Hubbard model used to explain the excitation spectrum of LCO predicts-for constant U/t-that the dispersion along (3) scales with (t /t) 2 . However, the diagonal hopping t extracted on LSCO using single-band models is low (t /t ∼ −0.16) and decreasing with doping. We therefore invoked a two-orbital (d x 2 −y 2 and d z 2 ) model which implies that t is enhanced. This effect acts to enhance the zone-boundary dispersion within the Hubbard model. We thus conclude that hybridization of d x 2 −y 2 and d z 2 states has a significant impact on the zone-boundary dispersion in LSCO.

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The transition temperature Tc 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 La2−xSrxCuO4 thin films, such substrates are sub-optimal and the highest Tc is instead obtained using LaSrAlO4. An outstanding challenge is thus to understand the optimal conditions for superconductivity in thin films: which microscopic parameters drive the change in Tc 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 La2CuO4 thin films can be enhanced by compressive strain. Our experiments and theoretical calculations establish that the substrate producing the largest Tc 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.

We report magnetic and thermodynamic properties of a 4d 1 (Mo 5+ ) magnetic insulator MoOPO4 single crystal, which realizes a J1-J2 Heisenberg spin-1/2 model on a stacked square lattice. The specific-heat measurements show a magnetic transition at 16 K which is also confirmed by magnetic susceptibility, ESR, and neutron diffraction measurements. Magnetic entropy deduced from the specific heat corresponds to a two-level degree of freedom per Mo 5+ ion, and the effective moment from the susceptibility corresponds to the spin-only value. Using ab initio quantum chemistry calculations we demonstrate that the Mo 5+ ion hosts a purely spin-1/2 magnetic moment, indicating negligible effects of spin-orbit interaction. The quenched orbital moments originate from the large displacement of Mo ions inside the MoO6 octahedra along the apical direction. The ground state is shown by neutron diffraction to support a collinear Néel-type magnetic order, and a spin-flop transition is observed around an applied magnetic field of 3.5 T. The magnetic phase diagram is reproduced by a mean-field calculation assuming a small easy-axis anisotropy in the exchange interactions. Our results suggest 4d molybdates as an alternative playground to search for model quantum magnets.