In the quest for high-spin building blocks to form covalently bonded 1D or 2D materials with controlled magnetic interactions, $π$-electron magnetism provides an ideal framework to engineer large ferromagnetic interactions between nanographenes. As a first step in this direction, we investigate the spin properties of ferromagnetically coupled triangulenes, triangular nanographenes with spin $S = 1$. Combining in-solution synthesis of rationally designed molecular precursors and on-surface synthesis, we achieve covalently bonded $S = 2$ triangulene dimers and $S = 3$ trimers on Au(111). Starting from the triangulene dimer, we thoroughly characterize its low-energy magnetic excitations using inelastic electron tunneling spectroscopy (IETS). IETS reveals conductance steps identified as a quintet to triplet excitation, and a zero-bias peak stemming from higher-order spin-spin scattering of the 5-fold degenerate ferromagnetic ground state. The Heisenberg picture captures the relevant parameters of inter-triangulene ferromagnetic exchange, and its successful extension to the larger $S = 3$ system confirms the model's accuracy. We expect that the addition of ferromagnetically coupled building blocks to the toolbox of magnetic nanographenes opens new opportunities to design carbon materials with complex magnetic ground states.
Exchange interactions and intermolecular hybridization in a spin-1/2 nanographene dimer
Department of Chemistry, University of Zurich（苏黎世大学化学系）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Universidad del País Vasco UPV/EHU（巴斯克国立大学先进聚合物与材料系：物理、化学与技术）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）；Integrated Systems Laboratory, ETH Zürich（苏黎世联邦理工学院集成系统实验室）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学化学、生物化学与药学系）
Learning Inhomogeneous Heisenberg Hamiltonians in Nanographene Spin Chains
Aalto University（阿尔托大学）；Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技与检测局）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微结构物理研究所）；Technische Universität Dresden（德累斯顿工业大学）
Identification and optimization of accurate spin models for Fermi-Hubbard ladders using matrix product states
Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基奎，巴斯克科学基金会）
Prediction of two-dimensional $π$-electron half-metallic ferrimagnets
International Iberian Nanotechnology Laboratory（伊比利亚纳米技术国际实验室）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Universidad de Alicante（阿利坎特大学）；University of Minho（米尼奥大学）
Engineering Ferrimagnetic Interactions in Molecular Quantum Systems
Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技研究院）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子科技与卡弗里纳米科学研究所）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微观结构物理研究所）；Center for Advancing Electronics Dresden (cfaed) & Faculty of Chemistry and Food Chemistry, Technische Universität Dresden（德累斯顿工业大学先进电子中心及化学与食品化学学院）；Department of Chemistry, University of Zurich（苏黎世大学化学系）；College of Materials Science and Optoelectronic Technology & Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院及材料科学与工程中心）；Beijing National Laboratory for Molecular Science, CAS Key Laboratory for Organic Solids, Institute of Chemistry, Chinese Academy of Sciences（中国科学院化学研究所有机固体院重点实验室及北京分子科学国家实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学生物化学与药学系化学部）
