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Main Authors: Pisani, Federico, Spitz, Leonie, Vojáček, Libor, Santos, Flaviano José dos, Carta, Alberto, Piazza, Bastien Dalla, Nikitin, Stanislav E., Krämer, Karl W., Fåk, Björn, Nakajima, Taro, Ueta, Daichi, Saito, Hiraku, Soh, Jian-Rui, Marzari, Nicola, Rønnow, Henrik M.
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.13751
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author Pisani, Federico
Spitz, Leonie
Vojáček, Libor
Santos, Flaviano José dos
Carta, Alberto
Piazza, Bastien Dalla
Nikitin, Stanislav E.
Krämer, Karl W.
Fåk, Björn
Nakajima, Taro
Ueta, Daichi
Saito, Hiraku
Soh, Jian-Rui
Marzari, Nicola
Rønnow, Henrik M.
author_facet Pisani, Federico
Spitz, Leonie
Vojáček, Libor
Santos, Flaviano José dos
Carta, Alberto
Piazza, Bastien Dalla
Nikitin, Stanislav E.
Krämer, Karl W.
Fåk, Björn
Nakajima, Taro
Ueta, Daichi
Saito, Hiraku
Soh, Jian-Rui
Marzari, Nicola
Rønnow, Henrik M.
contents 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.
format Preprint
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institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Probing the real-space density of spin-entangled electrons
Pisani, Federico
Spitz, Leonie
Vojáček, Libor
Santos, Flaviano José dos
Carta, Alberto
Piazza, Bastien Dalla
Nikitin, Stanislav E.
Krämer, Karl W.
Fåk, Björn
Nakajima, Taro
Ueta, Daichi
Saito, Hiraku
Soh, Jian-Rui
Marzari, Nicola
Rønnow, Henrik M.
Strongly Correlated Electrons
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.
title Probing the real-space density of spin-entangled electrons
topic Strongly Correlated Electrons
url https://arxiv.org/abs/2604.13751