Fermi liquid instabilities in the spin channel

Abstract

We study the Fermi-surface instabilities of the Pomeranchuk type [Sov. Phys. JETP 8, 361 (1959)] in the spin-triplet channel with high orbital partial waves $[{F}_{l}^{a}(l>0)]$. The ordered phases are classified into two classes, dubbed the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases by analogy to the superfluid $^{3}\mathrm{He}$ A and B phases. The Fermi surfaces in the $\ensuremath{\alpha}$ phases exhibit spontaneous anisotropic distortions, while those in the $\ensuremath{\beta}$ phases remain circular or spherical with topologically nontrivial spin configurations in momentum space. In the $\ensuremath{\alpha}$ phase, the Goldstone modes in the density channel exhibit anisotropic overdamping. The Goldstone modes in the spin channel have a nearly isotropic underdamped dispersion relation at small propagating wave vectors. Due to the coupling to the Goldstone modes, the spin-wave spectrum develops resonance peaks in both the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases, which can be detected in inelastic neutron-scattering experiments. In the $p$-wave channel $\ensuremath{\beta}$ phase, a chiral ground-state inhomogeneity is spontaneously generated due to a Lifshitz-like instability in the originally nonchiral systems. Possible experiments to detect these phases are discussed.