We report magnetic optical second-harmonic generation (SHG) polarimetry and imaging on $\mathrm{Sr}{}_2\mathrm{Cu}{}_3\mathrm{O}{}_4\mathrm{Cl}{}_2$, which allows direct visualization of the mesoscopic antiferromagnetic (AFM) structure of a parent cuprate. Temperature- and magnetic-field-dependent SHG reveals large domains with ${90}^{\circ }$ relative orientations that are stabilized by a combination of uniaxial magnetic anisotropy and the Earth's magnetic field. Below a temperature $T_{\mathrm{R}}$ $\sim$ 97 K, we observe an unusual ${90}^{\circ }$ spin-reorientation transition, possibly driven by competing magnetic anisotropies of the two copper sublattices, which swaps the AFM domain states while preserving the domain structure. This allows deterministic switching of the AFM states by thermal or laser heating. Near $T_{\mathrm{R}}$, the domain walls become exceptionally responsive to an applied magnetic field, with the Earth's field sufficient to completely expel them from the crystal. Our findings unlock opportunities to study the mesoscopic AFM behavior of parent cuprates and explore their potential for AFM technologies.

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• Antiferromagnetism
• Magnetic anisotropy
• Micromagnetism
• Spintronics
• High-temperature superconductors
• Optical second-harmonic generation