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When electrons in a metal become correlated with each other, new cooperative behavior can arise. This correlation is magnified when the metal has magnetic ions embedded in it. These atomic magnets try to line up with each other, but in doing so actually create a correlation between the motions of conduction electrons. In turn, these correlated electron motions prevent the magnetic ions from aligning, even at zero Kelvin. When this competition is strongest (at the so-called quantum critical point-QCP) the response of the system can no longer be described using the text book theory for metals. In addition, a range of new phenomena has been seen to emerge in the vicinity of a QCP, such as heavy-fermion superconductivity, coexistence of magnetism and superconductivity and hyper-scaling. The main goal of our research is to try to unravel the details of the feedback mechanism between electron motion and magnetism that lies at the heart of this new physics. We have chosen lithium-based spinel structures as the most promising family of systems to achieve our goal. Known lithium-based spinels Li{sub x}M{sub 2}O{sub 4} [M=V, Ti and Mn] show a variety of ground states: heavy-fermion, superconducting, or geometrically frustrated local moment systems. Li{sub x}M{sub 2}O{sub 4} should be ideal systems for studying QCPs since their properties can easily be fine-tuned, simply by extracting some Li [which can be done without introducing disorder in the immediate surroundings of the magnetic ions]. The premise of the proposal was that since this Li-extraction can be done both in the metallic as well as in insulating compounds, that we can expand the types of quantum phase transitions that can be studied to beyond transitions in magnetic metals. The project called for developing a better understanding of quantum phase transitions by measuring all aspects of the electronic response of Li{sub x}M{sub 2}O{sub 4} by means of neutron scattering, giving microscopic information about the behavior of the individual magnetic moments and their interactions, as well as by macroscopic measurements. In addition, the aim was to synthesize new lithium-based spinel compounds by using other transition metals that exhibit both 3{sup +} and 4{sup +} valencies. Here we report on the progress we have made during the course of this grant both towards the stated goals and on new avenues that developed as a direct result of the data we collected during this grant

designer phase transitions in lithium-based spinels