Probing the real-space density of spin-entangled electrons

TL;DR

This paper demonstrates how inelastic neutron scattering can be used to extract the real-space density of spin-entangled electrons in magnetic materials, validated by DFT calculations.

Contribution

It introduces a method to determine magnetic electron density and form factors from INS data, validated against DFT calculations, for magnetic materials.

Findings

Measured 3D magnetic structure factor of Cu(II) acetate monohydrate.

Deduced real-space density of spin-entangled electrons from experimental data.

Validated DFT broken-symmetry spin densities against full 3D INS data.

Abstract

On the textbook example of an isolated antiferromagnetic Heisenberg dimer, we demonstrate that the magnetic form factor and the magnetic electron density distribution can be extracted from the momentum-dependence of the inelastic neutron scattering (INS) intensity of a magnetic excitation. We measure the three-dimensional (3D) magnetic structure factor of the singlet-to-triplet excitation in Cu(II) acetate monohydrate with INS. Using a minimal parametrization of the magnetic electron density, we deduce the real-space density of the spin-entangled electrons and the transfer of magnetic electron density between metal and ligand atoms from the experimental data. Density functional theory (DFT) calculations reproduce the measured structure factor quantitatively, providing a direct validation of DFT broken-symmetry spin densities against full 3D INS data. The quantitative agreement between experiment, parametrization, and theory establishes a robust framework for determining magnetic form factors and the magnetic electron density in a broad range of magnetic materials and demonstrates INS as a probe of the envelope of spatial electronic wavefunctions.