Embedding non-collinear two-component electronic structure in a collinear quantum environment

Spin-containing materials are important for spintronic applications. In this work, we present a computational framework to embed nonrelativistic, two-component calculations in a one-component environment. In this framework, both embedding scalar potential and magnetic field can be included to describe the interaction between quantum subsystems. In this current development, a generalized Kohn-Sham density functional theory electronic structure is embedded in unrestricted Kohn-Sham density functional theory. Two test systems are studied: a Li₃ on a closed-shell He lattice and a Li₃ on a He lattice containing a Li atom defect. The noncollinearity of Li₃ is unaffected upon embedding in a closed-shell environment through the scalar potential embedding. However, the open-shell nature of the Li atom defect introduces an effective magnetic field that couples to the magnetic components of the generalized Kohn-Sham Hamiltonian. These results show that noncollinear quantum embedding in an open-shell collinear environment may modify the spin structure of the embedded system. The formalism developed herein may serve as a useful tool in the modeling of inhomogeneous magnetic fields in two-component calculations.