Spatially dependent f-π exchange interaction within a single-molecule magnet TbPc2

Xin Liao; Yun Chen; Tao Xie; Rui-Jing Sun; Lian-Zhi Yang; Chao-Fei Liu; Rui Wang; Svetlana Klyatskaya; Mario Ruben; Wenhao Zhang; Ying-Shuang Fu

doi:10.1038/s41467-025-61594-4

Spatially dependent f-π exchange interaction within a single-molecule magnet TbPc₂

Nat Commun. 2025 Jul 7;16(1):6263. doi: 10.1038/s41467-025-61594-4.

Authors

Xin Liao^#¹, Yun Chen^#², Tao Xie¹, Rui-Jing Sun¹, Lian-Zhi Yang¹, Chao-Fei Liu¹, Rui Wang^{2

3

4}, Svetlana Klyatskaya⁵, Mario Ruben^{5

6

7}, Wenhao Zhang^{8

9}, Ying-Shuang Fu^{10

11}

Affiliations

¹ School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, China.
² National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, China.
³ Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
⁴ Jiangsu Physical Science Research Center, Nanjing, China.
⁵ Institute of Nanotechnology, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
⁶ Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
⁷ Centre Européen de Sciences Quantiques, Institut de Science et d'Ingénierie Supramoléculaires, Strasbourg Cedex, France.
⁸ School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, China. wenhaozhang@hust.edu.cn.
⁹ Wuhan Institute of Quantum Technology, Wuhan, China. wenhaozhang@hust.edu.cn.
¹⁰ School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, China. yfu@hust.edu.cn.
¹¹ Wuhan Institute of Quantum Technology, Wuhan, China. yfu@hust.edu.cn.

^# Contributed equally.

Abstract

Electrically probing the spin state of localized f electrons in a rare-earth-based single-molecule magnet, along with understanding its intramolecular magnetic coupling, is of crucial importance for applications in quantum information and advanced spintronics, yet it remains experimentally challenging. Herein, within a single-molecule magnet terbium(III) bis(phthalocyaninato) (TbPc₂) double-decker molecule adsorbed on a bilayer graphene epitaxially grown on a SiC(0001) substrate, we experimentally demonstrate a spatially dependent exchange interaction between the magnetic moment of the localized Tb 4f electron and the unpaired spin of the Pc π-radical. The magnetic state of TbPc₂, associated with the f-π interaction, is evidently detected through the spectroscopic Kondo resonance and a zero-field Kondo splitting, which can be reversibly switched in a charge/discharge process triggered by the tip-molecule distance. Furthermore, we theoretically describe how the Kondo resonance evolves at the molecular scale, which is mediated by the f-π exchange interaction with its strength varying spatially in a radial decay fashion. Our spatially resolved Kondo characteristics offer a quantitative understanding of the many-body spin correlation, which is coupled with the charge states in a nonuniform and spatially extended system.