One-dimensional (1D) structures provide a unique platform to study the correlated quantum interactions and phase transitions such as unconventional magnetism and superconducting states. Here, we report that iron chalcogenide ${\mathrm{K}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_4$ exhibits an unusual block-type canted antiferromagnetic (AFM) order with a clear single chain quasi-1D structure, which is structurally different from the two-leg ladder ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$, through both experimental measurements and density matrix renormalization group (DMRG) calculations. The narrow bandgap semiconductor ${\mathrm{K}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_4$ has a quasi-1D edge-shared ${\mathrm{FeSe}}_4$ tetrahedra chain structure and orders antiferromagnetically below 110 K. The magnetic moments couple antiferromagnetically along the quasi-1D chain direction of the $b$ axis and form an up-down-down-up ($\uparrow \text{−}\downarrow \text{−}\downarrow \text{−}\uparrow$)–like spin structure with a commensurate propagation vector $\mathit{k}=(0,0,0)$, where block-type spin $\uparrow \text{−}\uparrow$ or $\downarrow \text{−}\downarrow$ coupling are between the longer Fe-Fe bonds of the quasi-1D chain. DMRG results show that block antiferromagnetic state is stable in ${\mathrm{K}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_4$ and reveal that the block-ordered arrangement of ${\mathrm{Fe}}^{2.5+}$ ions spins arise from the competition between ferromagnetic and AFM interaction in the presence of strong electronic correlation. Our research results not only report the discovery of a clear block-type canted antiferromagnetic structure in a real quasi-1D chain material but also provide a theoretical approach to understand the block-type antiferromagnetism in quasi-1D iron chalcogenides.

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• Antiferromagnetism
• Density matrix renormalization group
• Exchange interaction
• Magnetic order
• Magnetic phase transitions