"We have explored the collective phenomena of correlated electrons in two different transition-metal oxides, Ruddlesden-Popper type ruthenates (Sr,Ca)n+1RunO3n+1 and inverse-trirutile chromates Cr2MO6 (M = Te, Mo and W), using neutron scattering in combination with various material characterization methods. (Sr,Ca)n+1RunO3n+1 are 4d transition-metal oxides exhibiting competing magnetic and electronic tendencies. The delicate balance among the competing states can be readily tuned by perturbations, such as chemical doping and magnetic field, which gives rise to emergent phenomena. We have investigated the effects of 3d transition-metal doping on the magnetic and electronic properties of layered ruthenates. For instance, the single-layer (n = 1) Sr2RuO4 is an unconventional superconductor possessing an incommensurate spin density wave instability with a wave vector = (0.3 0.3 L) driven by Fermi surface nesting. Upon Fe substitution, we have unveiled an unexpected commensurate spin density wave order with a propagation vector = (0.25 0.25 0) in Sr2Ru1-xFexO4 (x = 0.03 and 0.05), despite the magnetic fluctuations persisting at . The latter feature is corroborated by the first principles calculations, which show that Fe doping barely changes the nesting vector of the Fermi surface. These results suggest that in addition to the known incommensurate magnetic instability, Sr2RuO4 is also in proximity to a commensurate magnetic tendency that can be stabilized via Fe doping. We have also studied the effects of a magnetic field. For example, the bilayer (n = 2) Ca3(Ru1-xTix)2O7 (x = 0.03) is a G-type antiferromagnetic Mott insulator. We have revealed that a modest magnetic field can lead to colossal magnetoresistance arising from an anomalous collapse of the Mott insulating state. Such an insulator-to-metal transition is accompanied by magnetic and structural transitions. These findings call for deeper theoretical studies to reexamine the magnetic field tuning of Mott systems with magnetic and electronic instabilities, as a magnetic field usually stabilizes the insulating ground state in Mott-Hubbard systems. Cr2MO6 (M = Te, W and Mo) are spin dimer systems with the magnetic ions Cr3+ structurally dimerized favoring a singlet ground state. However, all three compounds investigated exhibit long-range antiferromagnetic orders at low temperature owing to the inter-dimer interactions. We have shown that the inter-dimer exchange coupling can be tuned from antiferromagnetic in Cr2TeO6 to ferromagnetic in Cr2WO6 and Cr2MoO6, by altering the degree of d-p orbital hybridization between W(Mo) and O atoms. The tunability of the inter-dimer interactions without introducing additional complexities such as structural distortions and carrier doping offers a rare opportunity to drive the system toward the quantum critical point (QCP) separating the dimer-based quantum disordered state and the classical long-range antiferromagnetic order. Moreover, we have unraveled Higgs amplitude modes in the magnetic excitation spectra of Cr2TeO6 and Cr2WO6, which are generally believed to survive only in systems close to the QCP where the ordered moment is suppressed significantly from its fully saturated value by quantum fluctuations. However, these two compounds are away from the QCP with the ordered moment reduced only by 240303%. This study suggests that Higgs amplitude modes are not the privilege of ordered systems in the vicinity of the QCP, but may be common excitation modes in ordered spin dimer systems."--Pages ii-iii.
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