The linear magnetoelectric (ME) coupling effect is of particular interest due to its role in hosting fascinating off-diagonal magnetoelectricity and toroidal moments. In this work we present a systematic investigation of successive metamagnetic transitions by high-field study up to 55 T and switching of the off-diagonal ME state of the spin-chain antiferromagnet $\mathrm{CoS}{\mathrm{e}}_2{\mathrm{O}}_5$ single crystal. When the magnetic field is applied along the easy $a$-axis, in addition to the low-field spin-flop transition at $H_{a1}=6.1$ T, two other metamagnetic transitions occur at $H_{a2}=8.8$ T and $H_{a3}=11.2$ T, corresponding to the appearance of 1/2 and 4/5-like plateaus, respectively. For the hard $c$-axis, there are two successive upturns in the magnetization at $H_{c1}=10.7$ T and $H_{c2}=13.9$ T, corresponding to 1/2 and 4/5 of the saturation magnetization. In contrast, only one metamagnetic magnetic transition is revealed for $b$-axis magnetization, highlighting a strongly anisotropic feature. Furthermore, the selection and switching between two magnetoelectric states have been realized via the combination of electric and magnetic fields. The switching field of the ME state exhibits a temperature dependence that can be explained by a phenomenological model for ME antiferromagnets. We corroborated our experimental results with density-functional theory calculations, thereby determining the magnetic ground-state and field-induced electric polarization, both of which align well with our experimental results. The strong hybridization between O-$p$ and Co-$d$ orbitals, coupled with the reduced symmetry of the octahedral environment, may act as one of the spin-driven mechanisms underlying the observed ME properties. Furthermore, the calculation shows that the net ionic displacement along the $b$ axis is extremely small, demonstrating that the ferroelectric polarization in $\mathrm{CoS}{\mathrm{e}}_2{\mathrm{O}}_5$ is primarily driven by electronic rather than ionic contributions. Our results suggest that $\mathrm{CoS}{\mathrm{e}}_2{\mathrm{O}}_5$ is a compelling candidate for investigating potential toroidicity and collinear spins, with the toroidal moment expected to be parallel to spins.

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• Magnetic anisotropy
• Magnetoelectric effect
• Antiferromagnets
• Multiferroics
• Single crystal materials
• Crystal growth
• First-principles calculations
• Magnetization measurements