This award supports theoretical and computational research and educational activities aimed at advancing our understanding of quantum systems, in which spin and orbital degrees of freedom are strongly coupled. Relevant materials are transition metal oxides on frustrated lattices.
The research has two parts. The first part is devoted to the study of the fundamental properties of strongly interacting electron systems with coupled spin and orbital fluctuations. Vanadates are perhaps the most prominent examples of spin-orbital systems. The research in this part is motivated by recent experiments on several vanadates including spinel ZnV2O4 and quasi one-dimensional CaV2O4, in which reduced dimensionality appears because of a particular structure of orbital interactions. The PI will study relevant one-dimensional spin-orbital systems. The vanadium chains in these compounds are characterized by frustrated magnetic interactions, Ising-like orbital exchanges, and a large relativistic spin-orbit interaction. Corresponding one-dimensional spin-orbital systems are in many aspects different from the famous one-dimensional SU(4) model. The PI intends to investigate these models using both analytical and numerical theoretical techniques, including bosonization and density matrix renormalization group.
The second part of the proposal is devoted to the development of the theory of two-magnon and two-orbiton Raman scattering in coupled spin-orbital systems. This is a challenging but rewarding project as the theory can be readily applied to understanding a variety of existing experimental data in correlated materials with coupled spin and orbital degrees of freedom. Special emphasis will be given to the study of Raman scattering from antiferromagnets, orbitally ordered states, and spin-orbital liquids on frustrated lattices.
The PI will be engaged in educational activities at the graduate level aimed at refining and enhancing courses in solid state, statistical and many-body physics. She will develop an advanced course in strongly correlated phenomena in complex systems with special emphasis on new trends in magnetism and transport phenomena. A graduate student will be involved in the research activity. The PI will organize, in collaboration with other faculty from UW-Madison, a Wisconsin Winter School on Modern Condensed Matter and Quantum Information, which will introduce young researchers to various problems in the field and will also improve collaboration between faculty, students, and postdocs from all campuses of the University of Wisconsin system.
NONTECHNICAL SUMMARY
This award supports theoretical and computational research and educational activities aimed at advancing our understanding of materials, in which the electron spin, an intrinsic quantum mechanical property of electrons, and the motion of the electron strongly interact with each other. The relevant materials are oxides that include transition metals, for example vanadium or zinc, with certain spatial arrangements of atoms leading to spin or spatial distribution of electrons which can occur in many nearly equivalent and hence, competing ways. Achieving a theoretical understanding of the properties of these strongly correlated materials is challenging. Interest in these systems stems in part from the richness of their novel properties: the unexpected variety of ordered states, like various forms of magnetism, the transformations among them, and their sensitivity to stresses, such as applied electric or magnetic fields. The PI will use state-of-the-art analytical as well as computational tools to investigate the physical properties of such transition metal oxides, predict new effects in these materials, and contribute to understanding of experiments.
The PI will be engaged in educational activities at the graduate level aimed at refining and enhancing courses in solid state, statistical and many-body physics. She will develop an advanced course in strongly correlated phenomena in complex systems with special emphasis on new trends in magnetism and electron transport phenomena. A graduate student will be involved in the research activity. The PI will organize, in collaboration with other faculty from UW-Madison, a Wisconsin Winter School on Modern Condensed Matter and Quantum Information, which will introduce young researchers to various problems in the field and will also improve collaboration between faculty, students, and postdocs from all campuses of the University of Wisconsin system.
The main goal of this project was to improve our understanding of properties of materials with strong spin-orbit coupling and orbital degeneracy from fundamental microscopic basis.In particular, we have focused on theoretical descriptions of novel phenomena that emerge in complex electronic systems from a strong interplay between charge, spin, and orbital degrees of freedom, and geometric frustration. During the time of project, several important findings have been made. They were published in 9 high profile publications and presented in many international conferences. We have studied and understood ground state properties and the excitation spectra of several spinels: ZnV2O4, MgV2O4, MnV2O4, LiV2O4 and CdCr2O4. These studies helped us to understand the phase diagram of these materials and a number of experimental results obtained in these systems. Particularly important was understanding of peculiar spin and orbital structure of the ground state in vanadium spinel MnV2O4, which for quite a long time remained an open issue. We have also performed a general study of quantum phase transitions in spin-orbital chains strongly entangled by spin-orbit coupling. We have understood the nature of quantum phase transitions in this spin-orbital chain model based on the comparison of our field theoretical description and numerical simulations based on the density-matrix renormalization group technique. We showed that the role of the spin-orbit coupling term is two-fold: firstly it introduces anisotropy to the spin-1 subsystem, and secondly it endows quantum dynamics to the otherwise classical Ising chain. We also computed the phase diagram of this model, which despite of simplicity of the model, is very rich. We have also achieved much better understanding of the low-energy physics of the quasi two-dimensional iridates, Na2IrO3 and Li2IrO3. We have shown that the Kitaev-Heisenberg model describing these systems undergoes two phase transitions as a function of temperature. At low temperatures, thermal fluctuations induce magnetic long-range order by order-by-disorder mechanism. We showed that magnetically ordered state persists up to a certain critical temperature, but the system doesn't become fully disordered above this temperature -- we found that there is an intermediate phase between the low-temperature ordered phase and the high-temperature disordered phase. We obtained Monte Carlo data, performed the finite-sized scaling analysis, and demonstrated that the intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We argue that the intermediate phase has been actually observed above the low-temperature magnetically ordered phase in Na2IrO3 and Li2IrO3. The project provided possibility for the first research experience for three PhD students, three undergards and one master student. Both PI and PhD students have presented the results of this research in various international conferences. The students also participated in various summer schools, where they were trained by the world class specialists in the field of strongly correlated electron systems and frustrated magnetism. The PI gave several colloquia, some of them were particularly targeted for undergraduate students. PI also co-organize two international workshops. PI has organized weekly condensed matter seminar for PhD students and postdocs at Physics Department of the University of Wisconsin and ran for three consequtive years.
