We investigate charge distribution in the recently discovered high-$T_c$ superconductors, layered nickelates. With increasing value of charge-transfer energy we observe the expected crossover from the cuprate to the local triplet regime upon hole dop
ing. We find that the $d-p$ Coulomb interaction $U_{dp}$ plays a role and makes Zhang-Rice singlets less favorable, while the amplitude of local triplets is enhanced. By investigating the effective two-band model with orbitals of $x^2-y^2$ and $s$ symmetries we show that antiferromagnetic interactions dominate for electron doping. The screened interactions for the $s$ band suggest the importance of rare-earth atoms in superconducting nickelates.
A spin-fermion model that captures the charge-transfer properties of Cu-based high critical temperature superconductors is introduced and studied via Monte Carlo simulations. The strong Coulomb repulsion among $d$-electrons in the Cu orbitals is phen
omenologically replaced by an exchange coupling between the spins of the itinerant electrons and localized spins at the Cu sites, formally similar to double-exchange models for manganites. This interaction induces a charge-transfer insulator gap in the undoped case (five electrons per unit cell). Adding a small antiferromagnetic Heisenberg coupling between localized spins reinforces the global tendency towards antiferromagnetic order. To perform numerical calculations the localized spins are considered classical, as in previous related efforts. In this first study, undoped and doped $8times 8$ clusters are analyzed in a wide range of temperatures. The numerical results reproduce experimental features in the one-particle spectral function and the density-of-states such as $(i)$ the formation of a Zhang-Rice-like band with a dispersion of order $sim 0.5$ eV and with rotational symmetry about wavevector $(pi/2,pi/2)$ at the top of the band, and $(ii)$ the opening of a pseudogap at the chemical potential upon doping. We also observed incipient tendencies towards spin incommensurability. This simple model offers a formalism intermediate between standard mean-field approximations, that fail at finite temperatures in regimes with short-range order, and sophisticated many-body techniques such as Quantum Monte Carlo, that suffer sign problems.
We study a spin-orbital model for 4$d^{1}$ or 5$d^{1}$ Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudo-orbital operators representing multipoles of th
e effective $j=3/2$ angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate Ba$_{2}$YMoO$_{6}$. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for double perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions.
We map the problem of the orbital excitation (orbiton) in a 2D antiferromagnetic and ferroorbital ground state onto a problem of a hole in 2D antiferromagnet. The orbiton turns out to be coupled to magnons and can only be mobile on a strongly renorma
lized scale by dressing with magnetic excitations. We show that this leads to a dispersion relation reflecting the two-site unit cell of the antiferromagnetic background, in contrast to the predictions based on a mean-field approximation and linear orbital-wave theory.
