Abstract:
We propose a simple theoretical description of the metal-insulator transition of rare-earth nickelates. The theory involves only two orbitals per nickel site, corresponding to the low-energy anti-bonding $e_g$ states. In the monoclinic insulating state, bond-length disproportionation splits the manifold of $e_g$ bands, corresponding to a modulation of the effective on-site energy. We show that, when subject to a local Coulomb repulsion $U$ and Hund's coupling $J$, the resulting bond-disproportionated state is a paramagnetic insulator for a wide range of interaction parameters. Furthermore, we find that when $U-3J$ is small or negative, a spontaneous instability to bond disproportionation takes place for large enough $J$. This minimal theory emphasizes that a small or negative charge-transfer energy, a large Hund's coupling, and a strong coupling to bond-disproportionation are the key factors underlying the transition. Experimental consequences of this theoretical picture are discussed.

Abstract:
For most metals, increasing temperature (T) or disorder will quicken electron scattering. This hypothesis informs the Drude model of electronic conductivity. However, for so-called bad metals this predicts scattering times so short as to conflict with Heisenberg's uncertainty principle. Here we introduce the rare-earth nickelates (RNiO_3, R = rare earth) as a class of bad metals. We study SmNiO_3 thin films using infrared spectroscopy while varying T and disorder. We show that the interaction between lattice distortions and Ni-O bond covalence explains both the bad metal conduction and the insulator-metal transition in the nickelates by shifting spectral weight over the large energy scale established by the Ni-O orbital interaction, thus enabling very low \sigma while preserving the Drude model and without violating the uncertainty principle.

Abstract:
We report on tunneling measurements that reveal for the first time the evolution of the quasi-particle state density across the bandwidth controlled Mott metal to insulator transition in the rare earth perovskite nickelates. In this, a canonical class of transition metal oxides, we study in particular two materials close to the T=0 metal-insulator transition: NdNiO3 , an antiferromagnetic insulator, and LaNiO3, a correlated metal. We measure a sharp gap in NdNiO3, which has an insulating ground state, of ~ 30 meV. Remarkably, metallic LaNiO3 exhibits a pseudogap of the same order that presages the metal insulator transition. The smallness of both the gap and pseudogap suggests they arise from a common origin: proximity to a quantum critical point at or near the T=0 metal-insulator transition. It also supports theoretical models of the quantum phase transition in terms of spin and charge instabilities of an itinerant Fermi surface.

Abstract:
The perovskite nickelates RNiO$_3$ (R: rare-earth) have been studied as potential multiferroic compounds. A certain degree of charge disproportionation in the Ni ions has been confirmed by high resolution synchrotron power diffraction: instead of the nominal Ni$^{3+}$ valence, they can have the mixed-valence state Ni$^{(3-\delta)+}$ and Ni$^{(3+\delta)+}$, though agreement has not been reached on the precise value of $\delta$ (e.g. for NdNiO$_3$, $\delta=0.0$ and $\delta=0.29$ were reported). Also, the magnetic ground state is not yet clear: collinear and non-collinear Ni-O magnetic structures have been proposed to explain neutron diffraction and soft X-ray resonant sccattering results in these compounds, and more recently a canted antiferromagnetic spin arrangement was proposed on the basis of magnetic susceptibility measurements. This scenario is reminiscent of the situation in the half-doped manganites. In order to gain insight into the ground state of these compounds, we studied the magnetic excitations of some of the different phases proposed, using a localized spin model for a simplified spin chain which could describe these compounds. We first analize the stability of the collinear, orthogonal, and intermediate phases in the classical case. We then explore the quantum ground state indirectly, calculating the spin excitations obtained for each phase, using the Holstein-Primakoff transformation and the linear spin-wave approximation. For the collinear and orthogonal ($\theta=\pi/2$) phases, we predict differences in the magnon spectrum which would allow to distinguish between them in future inelastic neutron scattering experiments.

Abstract:
Motivated by recent Fermi surface and transport measurements on LaNiO3, we study the Mott Metal-Insulator transitions of perovskite nickelates, with the chemical formula RNiO3, where R is a rare-earth ion. We introduce and study a minimal two-band model, which takes into account only the eg bands. In the weak to intermediate correlation limit, a Hartree-Fock analysis predicts charge and spin order consistent with experiments on R=Pr, Nd, driven by Fermi surface nesting. It also produces an interesting semi-metallic electronic state in the model when an ideal cubic structure is assumed. We also study the model in the strong interaction limit, and find that the charge and magnetic order observed in experiment exist only in the presence of very large Hund's coupling, suggesting that additional physics is required to explain the properties of the more insulating nickelates, R=Eu,Lu,Y. Next, we extend our analysis to slabs of finite thickness. In ultra-thin slabs, quantum confinement effects substantially change the nesting properties and the magnetic ordering of the bulk, driving the material to exhibit highly anisotropic transport properties. However, pure confinement alone does not significantly enhance insulating behavior. Based on these results, we discuss the importance of various physical effects, and propose some experiments.

Abstract:
We show that charge ordered rare-earth nickelates of the type RNiO3 (R= Ho, Lu, Pr and Nd) are multiferroic with very large magnetically induced ferroelectric (FE) polarizations. This we determine from first principles electronic structure calculations. The emerging FE polarization is directly tied to the long-standing puzzle of which kind of magnetic ordering is present in this class of materials: its direction and size indicate the type of ground-state spin configuration that is realized. Vice versa, the small energy differences between the different magnetic orderings suggest that a chosen magnetic ordering can be stabilized by cooling the system in presence of an electric field.

Abstract:
We present a study of the magnetic properties of YNiO$_{3}$ in the paramagnetic range, above and below the metal-insulator (MI) transition. The dc susceptibility, $\chi_{dc}$ (measured up to 1000 K) is a decreasing function of T for $T >$150 K (the N\'{e}el temperature) and we observe two different Curie-Weiss regimes corresponding to the metallic and insulator phases. In the metallic phase, this behaviour seems to be associated with the small ionic radius of Y% $^{3+}$. The value of the Curie constant for T$<$ T$_{MI}$ allows us to discard the possibility of Ni$^{3+}$ localization. An electron spin resonance (ESR) spectrum is visible in the insulator phase and only a fraction of the Ni ions contributes to this resonance. We explain the ESR and $\chi _{dc}$ behaviour for T $<$ T$_{MI}$ in terms of charge disproportionation of the type 2Ni$% ^{3+}\to $ Ni$^{2+}$+Ni$^{4+},$ that is compatible with the previously observed structural transition across T$_{MI}$.

Abstract:
Neutron and X-ray scattering studies have provided strong evidence for coupled spatial modulations of charge and spin densities in layered nickelates and cuprates. The accumulated results for La(2-x)Sr(x)NiO(4+d) are consistent with the strongly-modulated topological-stripe concept. Clues from Nd-doped La(2-x)Sr(x)CuO(4) suggest similar behavior for the cuprates. The experimental results are summarized, and features that conflict with an interpretation based on a Fermi-surface instability are emphasized. A rationalization for the differences in transport properties between the cuprates and nickelates is given.

Abstract:
Three charge-ordering lanthanum nickelates La2-xAxNiO4, substituted with specific amounts of A = Sr, Ca, and Ba to achieve commensurate charge order, are investigated using broadband dielectric spectroscopy up to GHz frequencies. The transition temperatures of the samples are characterized by additional specific heat and magnetic susceptibility measurements. We find colossal magnitudes of the dielectric constant for all three compounds and strong relaxation features, which partly are of Maxwell-Wagner type arising from electrode polarization. Quite unexpectedly, the temperature-dependent colossal dielectric constants of these materials exhibit distinct anomalies at the charge-order transitions.

Abstract:
Guided by experiment and band structure, we introduce and study a phenomenological Landau theory for the unusual charge and spin ordering associated with the Mott transition in the perovskite nickelates, with chemical formula RNiO$_3$, where R=Pr, Nd, Sm, Eu, Ho, Y, and Lu. While the Landau theory has general applicability, we show that for the most conducting materials, R=Pr, Nd, both types of order can be understood in terms of a nearly-nested spin density wave. Furthermore, we argue that in this regime, the charge ordering is reliant upon the orthorhombic symmetry of the sample, and therefore proportional to the magnitude of the orthorhombic distortion. The first order nature of the phase transitions is also explained. We briefly show by example how the theory is readily adapted to modified geometries such as nickelate films.