| This work deals with a state of matter known as the orbital antiferromagnet or the flux state, and its close relative the quantum spin liquid. The orbital antiferromagnet is characterized by ordered magnetic moments associated with circulating electron currents on the order of a lattice spacing, and not the magnetic moments associated with electron spin as in a traditional spin antiferromagnet.; In this work, the theory of orbital antiferromagnetism is extended to cover three-dimensional systems. It is shown that the three-dimensional orbital antiferromagnet requires a four-fold multiplication of the unit cell. The mean-field phase diagram for the orbital antiferromagnet is calculated, demonstrating that this state is energetically favorable with respect to a large class of mean-field states. Additionally, it is shown that the three-dimensional orbital antiferromagnet can explain the peak observed in the optical conductivity of strontium ruthenate. The theory can be experimentally tested by neutron diffraction; calculations of the neutron diffraction spectra are reported that show the system produces scattering at wave vectors not present in the spectra of a spin antiferromagnet.; It is shown how the susceptibility to orbital antiferromagnetic order depends on the electronic band structure of the material, demonstrating that the band structure particular to strontium ruthenate pushes the material toward such a transition. Strontium ruthenate has multiple bands crossing the Fermi surface and the effect of coupling between these bands on the orbital antiferromagnetic state is calculated. The results demonstrate that the system chooses its configuration such that the current loops in each of the bands add maximally.; The work concludes with a discussion of the quantum spin liquid, a state of matter closely related to the orbital antiferromagnet. It is shown that the only known exact solution for such a state is in fact incorrect, and how this error arises from a non-commutativity of certain lattice sums. The problem of finding an exact solution for the quantum spin liquid in dimensions greater than one is therefore still an open one. |
