Effects of the Dzyaloshinskii-Moriya interaction on the Fermi-Pasta-Ulam behavior in a magnetic system

We study the behavior of nonlinear spin motion in one-dimensional magnetic chain models. We explore how the various parameters affect the phase transitions between linear and nonlinear behaviors both with and without the Dzyaloshinskii-Moriya interaction (DMI). A Fourier analysis method is employed to investigate the modes in the structure with DMI. In all cases, we find that uniaxial anisotropy is necessary for the Fermi-Pasta-Ulam effect to appear. We investigate the DMI influence through the use of phase diagrams that examine the transitions between the three fundamental states: linear, Fermi-Pasta-Ulam, and ergodic. The DMI does make significant changes in these phase diagrams because it allows for additional routes for the distribution of energy.