We successfully synthesized a verdazyl-based charge-transfer salt $[$$o$-MePy-V-($p$-Br)$_2]$FeCl$_4$, which has an $S_{rm{V}}$=1/2 on the radical $o$-MePy-V-($p$-Br)$_2$ and an $S_{rm{Fe}}$=5/2 on the FeCl$_4$ anion. $Ab$ $initio$ molecular orbital calculations indicate the formation of an $S_{rm{V}}$=1/2 honeycomb lattice composed of three types of exchange interaction with two types of inequivalent site. Further, the $S_{rm{V}}$=1/2 at one site is sandwiched by $S_{rm{Fe}}$=5/2 spins through antiferromagnetic (AF) interactions. The magnetic properties indicate that the dominant AF interactions between the $S_{rm{V}}$ = 1/2 spins form a gapped singlet state, and the remaining $S_{rm{Fe}}$ = 5/2 spins cause an AF order. The magnetization curve exhibits a linear increase up to approximately 7 T, and an unconventional 5/6 magnetization plateau appears between 7 T and 40 T. We discuss the differences between the effective interactions associated with the magnetic properties of the present compound and ($o$-MePy-V)FeCl$_4$. We explain the low-field linear magnetization curve through a mean-field approximation of an $S_{rm{Fe}}$ = 5/2 spin model. At higher field regions, the 5/6 magnetization plateau and subsequent nonlinear increase are reproduced by the $S_{rm{V}}$ = 1/2 AF dimer, in which a particular internal field is applied to one of the spin sites. The ESR resonance signals in the low-temperature and low-field regime are explained by conventional two-sublattice AF resonance modes with easy-axis anisotropy. These results demonstrate that exchange interactions between $S_{rm{V}}$ = 1/2 and $S_{rm{Fe}}$ = 5/2 spins in $[$$o$-MePy-V-($p$-Br)$_2]$FeCl$_4$ realize unconventional magnetic properties with low-field classical behavior and field-induced quantum behavior.
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