Order-by-frustration: emergent condensed states of frustrated magnets

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NON-TECHNICAL SUMMARYThis award supports theoretical research and education on new states of magnetic insulators, in which there is a competition between different kinds of interactions between localized spins, the microscopic magnetic components that contain electrons orbiting around atomic nuclei. The interactions between spins can drive them into magnetically ordered states, such as ferromagnetism, in which the spins of the electrons are aligned along the same common axis, or anti-ferromagnetism, in which neighboring spins point in opposite directions. The focus of this research is on a wide class of materials in which magnetic order appears to be altogether absent as a consequence of competing interactions between spins. However, closer examination reveals a kind of "hidden" order, in which not the individual spins but rather small groups of them are correlated over large distances far exceeding the typical size of a small group of spins. These types of order are known as multi-polar, and this project is devoted to classifying and understanding their static and dynamic properties, as well as understanding the conditions necessary for their realization. This research advances fundamental understanding of quantum mechanics and magnetism, particularly in materials with different competing magnetic interactions. It may contribute to the discovery of new states of electronic matter within a wide range materials that may have technological application. This award also supports graduate students in theoretical solid state physics. Students involved in the research will be trained in modern theoretical techniques. In addition, the PI is planning to organize a department-wide Physics Olympiad for undergraduate students. The Olympiad will consist of a set of short but non-trivial problems which requires good understanding of general physics to solve. Its purpose is to promote student interest in physics, to identify particularly talented students and to provide them with early contacts with professional researchers.TECHNICAL SUMMARYThis award supports theoretical investigation and education focused on frustrated magnetic materials with unusual multi-particle condensates as well as on systems with "hidden" frustration which emerges due to strong and mutually competing spin-orbital interactions.The research brings together several outstanding topics of condensed matter physics - the multiplicity of competing orders in correlated systems, quantum phase transitions among them, and identification of the mechanism behind the appearance of "hidden" orders.Unlike the well-understood case of the usual, single particle, Bose condensates, the two (or more)- particle condensates are characterized by short-ranged spin correlations and unusual nematic-type order parameters. The case in point is represented by a frustrated ferromagnet, the phase diagram of which is controlled by a quantum critical point of Lifshitz type with dynamical critical exponent z=4. The PI proposes to construct a field theory description of this critical point, and to investigate the conditions needed for the emergence of multi-polar spin-nematic phases. In the course of this study the PI intends to explore analogies between boson systems with two-magnon condensates and fermion superconductors or charge density waves.Metallic frustrated magnets, in which itinerant electrons are exchange-coupled to localized spins, constitute another major research direction which the PI intends to pursue. These materials allow for the interesting possibility of probing magnetic phases and transitions via electron transport measurements. The PI plans to theoretically analyze the resistivity of a magnet undergoing a magnon Bose-Einstein condensation transition, and also to extend this analysis to novel experimental systems with topologically non-trivial band structures.The theory developed here will be applied to real magnetic materials. By combining a field theory approach with a semi-classical spin wave expansion, the PI plans to describe the physics of the recently discovered one-third magnetization plateau in the kagome material volborthite, and to analyze its possible instabilities. The PI will also study novel spin-chain insulators with competing spin-orbit interactions, which, by forcing opposite helical correlations in the neighboring chains, effectively promote an Ising-like longitudinal spin-density wave state that is an insulating analogue of a charge-density wave order in itinerant electron systems.This award will support graduate students in theoretical solid state physics. Students involved in the research will be trained in modern theoretical techniques such as bosonization, renormalization group, quantum field and diagrammatic many-body theories. In addition, the PI is planning to organize a department-wide Physics Olympiad for undergraduate students. The Olympiad will consist of a set of short but non-trivial problems which requires good understanding of general physics to solve. Its purpose is to promote student interest in physics, to identify particularly talented students and provide them with early contacts with professional researchers.