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Condensed matter exhibits diverse magnetic properties depending on the connectivity of magnetic elements and the lattice geometry. Frustrated lattices, competing interactions, and bond-direction-dependent interactions driven by spin–orbit coupling can give rise to nontrivial quantum states, including spin liquids and Kitaev magnetism [1,2]. Although transition-metal inorganic compounds have been central platforms for such studies, it remains difficult to independently control interaction strength, anisotropy, exchange pathways, and lattice geometry. In this presentation, I focus on metal–organic frameworks (MOFs) as a new platform for quantum magnetism, where organic ligands offer a route to designing magnetic interactions and three-dimensional magnetic networks. In particular, gyroid MOFs provide a three-dimensional analogue of the honeycomb lattice and are promising for exploring frustration, bond-direction-dependent interactions, and Kitaev-type magnetism [3-5]. I will discuss how MOFs may overcome limitations of inorganic magnets [6] and introduce the background and current status of magnetic studies on gyroid MOFs [3-5].

[1] H. Takagi et al., Nat. Rev. Phys. 1 264 (2019).

[2] Y. Motome and J. Nasu, J. Phys. Soc. Jpn. 89, 012002 (2020).

[3] A. Mizuno et al., Bull. Chem. Soc. Jpn. 92, 1068 (2019).

[4] H. Ishikawa et al., Phys. Rev. Lett. 132, 156702 (2024).

[5] S. Imajo et al., Chem. Mater. 37, 297 (2025).

[6] M. Yamada et al., Phys. Rev. Lett. 119, 057202 (2017).

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