Visualization of spin-orbit entangled 4f electrons in crystalline materials

TL;DR

This paper introduces a novel visualization method combining high-energy X-ray diffraction and valence electron density analysis to observe the anisotropic distribution of 4f electrons in lanthanide-containing materials, revealing ground-state wavefunction parameters.

Contribution

It presents a new approach for directly visualizing 4f electron distributions in real space using core differential Fourier synthesis, advancing understanding of spin-orbit coupled electrons in crystals.

Findings

VED distributions reveal ground-state wavefunction parameters

Results roughly agree with point-charge calculations

Method enables studying 4f states in various materials

Abstract

Lanthanide 4f electrons are strongly influenced by spin-orbit coupling, resulting in well-defined J multiplets, which are further split by the crystalline electric field in condensed matter. While the anisotropy of 4f electrons is closely linked to material properties, direct experimental observation of the 4f electron distribution in real space remains a significant challenge. Here, we present an approach for visualizing the anisotropic distribution of lanthanide 4f electrons in pyrochlore oxides by combining high-photon-energy X-ray diffraction and valence electron density (VED) analysis based on the core differential Fourier synthesis (CDFS) method. The observed VED distributions around the lanthanide site reveal the parameters of the ground-state wavefunction, which roughly agree with point-charge calculations for the trigonal crystal electric field under the LS coupling scheme. This CDFS-based VED observation method not only provides insights into the anisotropic nature of 4f electrons but also opens a pathway for studying the 4f states in a wide range of crystalline materials.