# Fermi Liquid Study of Exotic Modes in Magnetically Ordered Systems

## Abstract

The Landau Fermi liquid theory is a very successful theory in condensed matter physics. It provides a phenomenological framework for describing thermodynamics, transport and collective modes of itinerant fermionic systems. In 1957, Silin described the spin waves in polarized Fermi liquids based on Landau Fermi liquid theory, which are related to series of components of the spherical harmonic expansion of the fermi surface. It has been proved by Pomeranchuck that for the Fermi surface to be stable, the Landau parameters should satisfy the relation: $F_l^{s,a}>-(2l+1)$. Whenever the relation is violated, there will exist an instability of the Fermi surface known as a Pomeranchuck instability, such as the Stoner ferromagnetism when $F_0^a→ -1^+$, or phase separation when $F_0^s→ -1^+$. In 1959, Abrikosov and Dzyaloshinskii developed a ferromagnetic Fermi liquid theory(FFLT) of itinerant ferromagnetism based on Landau Fermi liquid theory, whose microscopic foundations were established later by Dzyaloshiskii and Kondratenko. Further studies had been made of this state using a generalized Pomeranchuck instability based on the FFLT of Blagoev, Engelbrecht and Bedell and Bedell and Blagoev. In this thesis, I study a magnetically ordered system with spin orbit magnetism, where the order parameter has a net spin current and no net magnetization in both two dimension and three dimension. Starting from a Fermi liquid theory, similar to that for a weak ferromagnet, I have shown that this excitation emerges from an exotic magnetic Fermi liquid state that is protected by a generalized Pomeranchuck condition. I derive the propagating mode using the Landau kinetic equation, and find that the dispersion of the mode has a $sqrt q$ behavior in leading order in 2D. I also find an instability toward superconductivity induced by this exotic mode, and a further analysis based on the forward scattering sum rule strongly suggests that this superconductivity has triplet pairing symmetry. I perform similar studies in the 3D case, with a slightly different magnetic system and find that the mode leads to a Lifshitz-like instability most likely toward an inhomogeneous magnetic state in one of the phases. I also study the collective modes in itinerant ferromagnetic system, which is related to the $F_0^a$ pomeranchuck instability. Using FFLT, I obtained the well-known magnon (Nambu-Goldstone) mode and a gapped mode that was first found by Bedell and Blagoev. I have identified this mode as the Higgs boson (amplitude mode) of a ferromagnetic metal. This is identified as the Higgs since it can be shown that it corresponds to a fluctuation of the amplitude of the order parameter. I use this model to describe the itinerant-electron ferromagnetic material MnSi. By fitting the model with the existing experimental results, I calculate the dynamical structure function and see well-defined peaks contributed from the magnon and the Higgs. From my estimates of the relative intensity of the Higgs amplitude mode I expect that it can be seen in neutron scattering experiments on MnSi.