${\tilde{J}}$-pseudospin states and the crystal field of cubic systems

TL;DR

This paper develops a theory for $ ilde{J}$-pseudospin states in cubic systems, allowing for a more comprehensive description of crystal-field effects and interactions in $f$-element ions, including covalency and $J$-mixing.

Contribution

The paper introduces a symmetry-consistent framework for $ ilde{J}$-pseudospin states that extends traditional models by incorporating higher-rank tensor effects and connecting with ab initio calculations.

Findings

Derived $ ilde{J}$-pseudospin states for Nd$^{3+}$ and Np$^{4+}$ ions.

Unified description including covalency and $J$-mixing effects.

Framework validated through combination with ab initio methods.

Abstract

Theory of $\tilde{J}$-pseudospin for $f$ element in cubic environment is developed. By fulfilling the symmetry requirements and the adiabatic connection to atomic limit, the crystal-field states are uniquely transformed into $\tilde{J}$-pseudospin states. In terms of the pseudospin operators, both the total angular momentum and the crystal-field Hamiltonian contain higher-rank tensor terms than the traditional ones do, which means the present framework naturally include the effects such as the covalency and $J$-mixing beyond the $f$-shell model. Combining the developed theory with {\it ab initio} calculations, the $\tilde{J}$-pseudospin states for Nd$^{3+}$ and Np$^{4+}$ ions in octahedral sites of insulators are derived.