The field of highly frustrated magnetism harbors a wide variety of exotic phases that sustain interest in the field with no end in sight. Competing interactions yield models that often remain highly fluctuating down to zero temperature, have long-range entangled ground states, or exhibit fractionalized excitations. The study of these frustrated models presents a challenge for experimental and theoretical methods alike, driving their development in the process. As a contribution to the field, this thesis both further develops the pseudo-fermion functional renormalization group and applies the method in collaborative studies involving complementary methods to reveal low-temperature properties of a selection of frustrated spin models with relevance to spin compound families of recent interest.
In the first chapters of the thesis, the pseudo-fermion functional renormalization group is extended to enable the treatment of spin models with broken time-reversal symmetry. Newly accessible applications include models with finite magnetic fields in the form of site-dependent Zeeman terms. While previous formulations of the method could investigate magnetically ordered models only in their paramagnetic regime, often achieved by a finite renormalization group parameter in the model, the new scheme further allows the study of magnetic phases in absence of this parameter. In an exploratory study across a selection of Heisenberg and XXZ models, magnetic order parameters and magnetization plateaus will be compared with literature results to reveal for which newly accessible applications the method is best suited.
In addition to method development, a major emphasis of the thesis is placed on the study of nearest-neighbor spin models on the pyrochlore lattice. It is argued that the S = 1/2 and S = 1 Heisenberg models assume nematic ground states that break either only C3, or both C3 and lattice inversion symmetry. Quantum and classical phase diagrams of the model with Heisenberg and Dzyaloshinskii-Moriya interactions, and of non-Kramers pyrochlores are computed as well. In this context, an in-depth study of the so-called Γ5 phase will resolve subtle order-by-disorder selections from quantum or thermal fluctuations at both zero and critical temperatures. Furthermore, a model contained in both phase diagrams will be presented that exhibits a temperature-dependent spin liquid to spin liquid transition driven by entropic selections between ground state submanifolds in the case of classical spins. While the intermediate-temperature spin liquid can be described by coexisting vector and matrix gauge fields, spin degrees of freedom associated with the matrix gauge field depopulate as the temperature is lowered, realizing a spin-ice phase in the process. Emphasis is put on the study of the corresponding quantum model and its vicinity in the phase diagrams. This model is found to be best described in analogy to the intermediate-temperature classical spin liquid.
In the last part of the thesis, the pseudo-fermion functional renormalization group is applied in collaboration with classical Monte Carlo and inelastic neutron scattering to resolve the low-temperature behavior and magnetic order of the three-dimensional tetra-trillium compound and spin liquid candidate K2Ni2(SO4)3. The phase diagram of a Heisenberg model on the tetra-trillium lattice contextualizes the strongly fluctuating behavior of K2Ni2(SO4)3 by hosting a large paramagnetic region close to the density functional theory model of K2Ni2(SO4)3. In a broader scope, this region establishes compounds of the langbeinite family, which are described by Heisenberg models on the tetra-trillium lattice, as a promising platform in the future search for three-dimensional quantum spin-liquid phases.
