Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions

TL;DR

This paper investigates the unique momentum-dependent spin structures and Fermi surface deformations in an itinerant Fermi system with magnetic dipolar interactions, revealing novel entanglement of spin and orbital degrees of freedom.

Contribution

It introduces the concept of momentum-dependent spin states and analyzes the resulting magnetic structures and self-energy in dipolar Fermi systems, expanding understanding of unconventional magnetism.

Findings

Spin states depend on momentum, entangling spin and orbital degrees.

Fermi surfaces for different spins are not well-defined.

Magnetic moments are renormalized by interactions.

Abstract

We study the magnetic structure of the ground state of an itinerant Fermi system of spin-\nicefrac{1}{2} particles with magnetic dipole-dipole interactions. We show that, quite generally, the spin state of particles depend on its momentum, i.e., spin and orbital degrees of freedom are entangled and taken separately are not ``good'' quantum numbers. Specifically, we consider a uniform system with non-zero magnetization at zero temperature. Assuming the magnetization is along $z$-axis, the quantum spin states are $\v{k}$-dependent linear combinations of eigenstates of the $\sigma_z$ Pauli matrix. This leads to novel spin structures in \textit{momentum space} and to the fact that the Fermi surfaces for ``up'' and ``down'' spins are not well defined. The system still has a cylindrical axis of symmetry along the magnetization axis. We also show that the self energy has a universal structure which we determine based on the symmetries of the dipolar interaction and we explicitly calculated it in the Hartree-Fock approximation. We show that the bare magnetic moment of particles is renormalized due to particle-particle interactions and we give order of magnitude estimates of this renormalization effect. We estimate that the above mentioned dipolar effects are small but we discuss possible scenarios where this physics may be realized in future experiments.