A theoretical study on critical phenomena of magnetic soft modes

Below a threshold magnetic field, domain structures in ferromagnetic samples may start to nucleate from the initially saturated state via either continuous or discontinuous phase transitions. Such processes are usually accompanied by the occurrence of soft spin-wave modes at the critical point. In this paper, we present a theoretical study on the critical phenomena of uniform soft modes in a macrospin model and spatially non-uniform ones in ferromagnetic thin films. The critical exponents of the mode frequency and its polarization are derived. The value is found to be equal to one half, which is directly related to the breaking of a reflection-symmetry in the phase transition. At the critical point, the soft mode becomes linearly polarized, which provides an additional measurable effect of the critical phenomena.