Magnetic Exchange Interaction in the Spin Polarized Electron Gas

Abstract

The exchange interaction between two magnetic moments embedded in a host metal is fundamental to the description of the magnetic behavior of solids. In the standard spin-degenerate electron gas, it leads to the well known Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, which is of the Heisenberg form $J{\vec{S}}_1\cdot {\vec{S}}_2$, where the interaction strength $J$ oscillates and falls off with the distance between the moments in a characteristic way. Here, we study the more general case of the spin-polarized electron gas both in two and three dimensions, by evaluating the interaction strength as an integration over the product of the host Green's functions. We find that in addition to the Heisenberg term, an additional Ising-like term appears in the magnetic interaction, so that the net interaction for the spin-polarized gas is of the form $J_1{\vec{S}}_1\cdot {\vec{S}}_2+J_2{S}_{1z}{S}_{2z}$. The interactions show a beating pattern as a function of distance, caused by the two different Fermi momenta for the two spins.

References in corpus (8)

• Robust formation of skyrmions and topological Hall effect in epitaxial thin films of MnSi
• RKKY Interaction in Graphene from Lattice Green's Function
• Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling
• Indirect exchange interaction between magnetic adatoms in a monolayer MoS2
• RKKY interaction in a disordered two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings
• Anisotropic RKKY interaction in spin polarized graphene
• Dynamical exchange interaction between localized spins out of equilibrium
• RKKY Interaction for the Spin Polarized Electron Gas

Cited by in corpus (2)

• Effect of Rashba splitting on RKKY interaction in topological insulator thin films
• RKKY interaction in Rashba altermagnets