Title: Spin-mechanical coupling in 2D antiferromagnet CrSBr

Abstract: Spin-mechanical coupling is vital in diverse fields including spintronics, sensing and quantum transduction. Two-dimensional (2D) magnetic materials provide a unique platform for investigating spin-mechanical coupling, attributed to their mechanical flexibility and novel spin orderings. However, studying spin-mechanical coupling in 2D magnets presents challenges in probing mechanical deformation and thermodynamic properties change at nanoscale. Here we use nano opto-electro-mechanical interferometry to mechanically detect the phase transition and magnetostriction effect in multilayer CrSBr, an air-stable antiferromagnets with large magnon-exciton coupling. The transitions among antiferromagnetism, spin-canted ferromagnetism and paramagnetism are visualized by optomechanical frequency anomalies. Nontrivial magnetostriction coefficient 2.3x10^(-5) and magnetoelastic coupling strength on the order of 10^6 J/m^3 have been found. Moreover, we demonstrate the substantial tunability of the magnetoelastic constant by nearly 50% via gate-induced strain. Our findings demonstrate the strong spin-mechanical coupling in CrSBr and paves the way for developing sensitive magnetic sensing and efficient quantum transduction at atomically thin limit.