How to deal with f-electrons in rare-earth nitrides: a critical review of existing approaches

Abstract

The $f$-electrons in the lanthanides form an open shell with localized atomic-like orbitals. The traditional approach to study such systems uses atomic multiplet theory, crystal field theory and accounts well for the magnetic moments and shape of X-ray absorption and emission spectra.[1,2] However, it does not tell us anything about how these electrons affect the other electrons in the system, such as the lanthanide $d$-orbitals or the nitrogen $p$ orbitals in their nitrides. These are important to understand whether these materials are semiconductors or semimetals, to understand the hybridization effects of $f$-electrons with delocalized electrons in the system. The problem of how to reconcile band structure theory with the localized treatment of the $f$-electrons in a many-electron framework is not trivial. We review some of the existing approaches with a critical hindsight and discuss their successes and failures. One approach is to treat the open $f$-shell as core electrons [3,4] but which induce a spin-polarization on the other orbitals via the exchange effect. Relatedly, there are model approaches, in which the localized magnetic moments of the $f$-electrons are treated simply as localized spins with exchange interactions to the conduction electrons. [5] The self-interaction correction (SIC) approach is one attempt to make an orbital dependent Hamiltonian with the framework or density functional theory. [6] Another is the L(S)DA+U approach [7] in which the strong Coulomb interactions U and exchange interactions J of f-electrons are treated in a parametrized Hartree-Fock mean field treatment. But in this approach,[8-10] is the solution unique or does it depend on the initial choices of the density matrix for the f-electrons? Yet another approach is the quasi-particle self-consistent GW method, [11-15] which supposedly should describe the U and J effects via the self-energy and has no free parameters. Dynamic mean field theory using the Hubbard-I approximation[16-19] is perhaps the most sophisticated approach to bring together the atomic and band physics used so far. We will review these methods and illustrate some of their successes and shortcomings.