Quantum magnetostriction oscillations in a two-dimensional antiferromagnet with spin-phonon interaction in a magnetic field

The ground state of a two-dimensional antiferromagnet with $S=1/2$ interacting with acoustic phonons in a magnetic field was studied by the quantum Monte Carlo method in the nonadiabatic approximation. Oscillations of the amplitude of the root-mean-square displacement of ions and the average phonon occupation number in a magnetic field were found. Local maxima were revealed in the distribution functions of site magnetic moments and ion displacements. The saturation magnetization was calculated as a function of the spin-phonon coupling constant.