Observation of Biradical Spin Coupling through Hydrogen Bonds

Yang He, Na Li, Ivano E. Castelli, Ruoning Li, Yajie Zhang, Xue Zhang, Chao Li, Bingwu Wang, Song Gao, Lianmao Peng, Shimin Hou, Ziyong Shen, Jing-Tao Lü, Kai Wu, Per Hedegård, and Yongfeng Wang

Phys. Rev. Lett. 128, 236401 – Published 6 June 2022

Abstract

Investigation of intermolecular electron spin interaction is of fundamental importance in both science and technology. Here, radical pairs of all-trans retinoic acid molecules on Au(111) are created using an ultralow temperature scanning tunneling microscope. Antiferromagnetic coupling between two radicals is identified by magnetic-field-dependent spectroscopy. The measured exchange energies are from 0.1 to 1.0 meV. The biradical spin coupling is mediated through $O ─ H \dots O$ hydrogen bonds, as elucidated from analysis combining density functional theory calculation and a modern version of valence bond theory.

Received 16 September 2019
Revised 9 February 2022
Accepted 3 May 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.236401

Physics Subject Headings (PhySH)

Electronic structure of atoms & molecules Exchange interaction Kondo effect Molecular magnetism

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yang He¹, Na Li ¹, Ivano E. Castelli², Ruoning Li¹, Yajie Zhang¹, Xue Zhang¹, Chao Li¹, Bingwu Wang³, Song Gao³, Lianmao Peng¹, Shimin Hou¹, Ziyong Shen¹, Jing-Tao Lü ^4,*, Kai Wu^3,†, Per Hedegård^5,‡, and Yongfeng Wang ^1,6,§

¹Center for Carbon-Based Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, Beijing 100871, China
²Department of Energy Conversion and Storage, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
³Beijing National Laboratory for Molecular Science, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
⁴School of Physics, Institute for Quantum Science and Engineering, and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074 Wuhan, China
⁵Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
⁶Beijing Academy of Quantum Information Sciences, Beijing 100193, China

^*Corresponding author. jtlu@hust.edu.cn
^†Corresponding author. kaiwu@pku.edu.cn
^‡Corresponding author. hedegard@nbi.ku.dk
^§Corresponding author. yongfengwang@pku.edu.cn

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Issue

Vol. 128, Iss. 23 — 10 June 2022

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Images

Figure 1
Formation and characterization of a hydrogen-bonded ReA radical pair. (a) Chemical structure of a ReA dimer. (b)–(d) STM images showing the formation process of a ReA radical pair. The molecular nonmagnetic, spin-carrying, and spin-coupled states are denoted by U, A, and A’A”, respectively. Imaging parameters: (b) $V = - 4 mV$ , $I = 16 pA$ ; (c) $V = - 10 mV$ , $I = 16 pA$ ; (d) $V = - 10 mV$ , $I = 16 pA$ . The sizes of all three STM images are $4.5 \times 4.5 {nm}^{2}$ . (e) $d I / d V$ spectra measured over the centers of molecular bulky heads of different states (U, A, A’, A”). The STM is operated at $V = 11 mV$ and $I = 0.5 nA$ before opening the current feedback loop when taking constant-height spectroscopic measurements. (f) Magnetic-field-dependent $d I / d V$ spectra recorded on the head group of state A” with the set point of $- 5.7 mV$ and 1.2 nA. In both (e) and (f), all black dotted curves were experimentally obtained and solid color curves represent fits of the spectra. All plots are vertically shifted for clarity. (g) Illustration of spin transitions between singlet and triplet states in magnetic fields. (h) Extracted Zeeman splitting as a function of magnetic field. A linear fit yields the $g = 1.7$ .
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Figure 2
Experimental confirmation of spin coupling through hydrogen bonds. (a) STM image comprising two A-state ReA molecules packed side by side with their molecular bulky heads higher than others ( $- 11 mV$ , 0.10 nA; $4.1 \times 2.4 {nm}^{2}$ ). (b) $d I / d V$ spectra taken over the 16 white-dotted positions in (a). (c) STM image of A-state ReA molecule. ( $- 11 mV$ , 0.10 nA; $2.3 \times 1.5 {nm}^{2}$ ). (d) $d I / d V$ spectra measured over the 11 white-dotted positions along the line in (c). For all spectra, the STM is operated at $- 11 mV$ and 0.53 nA before opening the feedback loop.
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Figure 3
Mechanism of biradical spin coupling through hydrogen bonds. (a) Optimized structures of a ReA molecule on Au(111) and that after removing the purple H atom. (b) A model of ReA radical formed by removing one H atom at dotted position. (c) Calculated spin distribution of the ReA radical on Au(111). The spin density is represented by red arrows with different lengths. (d) Optimized structure of a ReA radical pair.
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Figure 4
VBT analysis of biradical spin coupling through hydrogen bonds. (a) One resonant structure of the ReA radical shown in Fig. 3. (b) Simplified molecular model of the ReA radical for VBT analysis. (c) Nine valence bond states of (b), which reveal that the spin polarity of oxygen atoms is the same as that of the ReA radical. (d) One of the six exchange processes, where two spins on oxygen $2 p_{z}$ orbitals on separate molecules are being exchanged. The amplitudes of the hops are denoted by $t_{i j}$ , and the intermediate energies are $E_{i}$ .
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