Antiferromagnetic Spin Orientation and Magnetic Domain Structure in Epitaxially Grown MnN Studied Using Optical Second-Harmonic Generation

$\mathrm{Mn}\mathrm{N}$ is a centrosymmetric collinear antiferromagnet belonging to the transition-metal-nitride family with a high N\'eel temperature ($660\phantom{\rule{0.2em}{0ex}}\mathrm{K}$), a low anisotropy field, and a large magnetic moment ($3.3{\ensuremath{\mu}}_{B}$ per $\mathrm{Mn}$ atom). Despite several recent experimental and theoretical studies, the spin symmetry (magnetic point group) and magnetic domain structure of the material remain unknown. In this work, we use optical second-harmonic generation (SHG) to study the magnetic structure of thin epitaxially grown single-crystal (001) $\mathrm{Mn}\mathrm{N}$ films. Our work shows that spin moments in $\mathrm{Mn}\mathrm{N}$ are tilted away from the [001] direction and the components of the spin moments in the (001) plane are aligned along one of the two possible in-plane symmetry axes ([100] or [110]), resulting in a magnetic-point-group symmetry of 2/m1'. Our work rules out magnetic-point-group symmetries 4/mmm1' and mmm1' that have been previously discussed in the literature. Four different spin domains consistent with the 2/m1' magnetic-point-group symmetry are possible in $\mathrm{Mn}\mathrm{N}$. A statistical model based on the observed variations in the polarization-dependent intensity of the second-harmonic signal collected over large sample areas puts an upper bound of $0.65\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$ on the mean domain size. Our results show that SHG can be used to probe the magnetic order in metallic antiferromagnets. This work is expected to contribute to the recent efforts in using antiferromagnets for spintronic applications.