General existence and determination of conjugate fields in dynamically ordered magnetic systems

We investigate experimentally as well as theoretically the dynamic magnetic phase diagram and its associated order parameter Q upon the application of a non-antisymmetric magnetic field sequence composed of a fundamental harmonic component H_{0}, a constant bias field H_{b}, and a second-harmonic component H_{2}. The broken time antisymmetry introduced by the second-harmonic field component H_{2} leads to an effective bias effect that is superimposed onto the influence of the static bias H_{b}. Despite this interference, we can demonstrate the existence of a generalized conjugate field H^{*} for the dynamic order parameter Q, to which both the static bias field and the second-harmonic Fourier amplitude of the field sequence contribute. Hereby, we observed that especially the conventional paramagnetic dynamic phase is very susceptible to the impact of the second-harmonic field component H_{2}, whereas this additional field component leads to only very minor phase-space modifications in the ferromagnetic and anomalous paramagnetic regions. In contrast to prior studies, we also observe that the critical point of the phase transition is shifted upon introducing a second-harmonic field component H_{2}, illustrating that the overall dynamic behavior of such magnetic systems is being driven by the total effective amplitude of the field sequence.