Standard model of the rare-earths, analyzed from the Hubbard I approximation

Abstract

In this work we examine critically the electronic structure of the rare-earth elements by use of the so-called Hubbard I approximation. From the theoretical side all measured features of both occupied and unoccupied states are reproduced, without significant deviations between observations and theory. We also examine cohesive properties like the equilibrium volume and bulk modulus, where we find, in general, a good agreement between theory and measurements. In addition we have reproduced the spin and orbital moments of these elements, as they are reflected from measurements of the saturation moment. We have also employed the Hubbard I approximation to extract the interatomic exchange parameters of an effective spin Hamiltonian for the heavy rare earths. We show that the Hubbard I approximation gives results which are consistent with calculations where $4f$ electrons are treated as core states for Gd. The latter approach was also used to address the series of the heavy/late rare-earths. Via Monte Carlo simulations we obtained ordering temperatures which reproduce measurements within about $20\%$. We have further illustrated the accuracy of these exchange parameters by comparing measured and calculated magnetic configurations for the heavy rare earths and the magnon dispersion for Gd. The Hubbard I approximation is compared to other theories of the electronic structure, and we argue that it is superior. We discuss the relevance of our results in general, and how this makes it possible to treat the electronic structure of materials containing rare-earth elements, such as permanent magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological insulators, and molecular magnets.