The family of monolayer two-dimensional (2D) materials hosts a wide range of interesting phenomena, including superconductivity, charge density waves, topological states and ferromagnetism, but direct evidence for antiferromagnetism in the monolayer has been lacking. Nevertheless, antiferromagnets have attracted enormous interest recently in spintronics due to the absence of stray fields and their terahertz resonant frequency. Despite the great advantages of antiferromagnetic spintronics, controlling and detecting Neel vectors have been limited in bulk materials. In this work, we developed a sensitive second harmonic generation (SHG) microscope and detected long-range Neel antiferromagnetic (AFM) order and Neel vector switching down to the monolayer in MnPSe$_3$. Temperature-dependent SHG measurement in repetitive thermal cooling surprisingly collapses into two curves, which correspond to the switching of an Ising type Neel vector reversed by the time-reversal operation, instead of a six-state clock ground state expected from the threefold rotation symmetry in the structure. We imaged the spatial distribution of the Neel vectors across samples and rotated them by an arbitrary angle irrespective of the lattice in the sample plane by applying strain. By studying both a Landau theory and a microscopic model that couples strain to nearest-neighbor exchange, we conclude that the phase transition of the XY model in the presence of strain falls into the Ising universality class instead of the XY one, which could explain the extreme strain tunability. Finally, we found that the 180{deg} AFM domain walls are highly mobile down to the monolayer after thermal cycles, paving the way for future control of the antiferromagnetic domains by strain or external fields on demand for ultra-compact 2D AFM terahertz spintronics.
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