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We successfully synthesized ($p$-Py-V)[Cu(hfac)$_2$], a verdazyl-basedcomplex. Molecular orbital calculations revealed five types of intermolecularinteractions between the radical spins and two types of intramolecularinteractions between the radical and the Cu spins, resulting in a spin-1/2distorted honeycomb-based lattice. Additionally, competing ferromagnetic andantiferromagnetic (AF) interactions induce frustration. The magnetization curvedisplayed a multistage increase, including a zero-field energy gap. Consideringthe stronger AF interactions that form dimers and tetramers, the magneticsusceptibility and magnetization curves were qualitatively explained. Thesefindings demonstrated that the quantum state, based on the dominant AFinteractions, was stabilized due to the effects of frustration in the lattice.Hence, the exchange interactions forming two-dimensional couplings decoupled,reducing energy loss caused by frustration and leading to frustration-induceddimensional reduction.

Quantum gapped state in a spin-1/2 distorted honeycomb-based lattice with frustration