Experimental exploration of the vector nature of the dynamic order parameter near dynamic magnetic phase transitions

Abstract

We have devised an experimental study to explore the vector nature of the dynamic order parameter $Q$ and the corresponding dynamic fluctuation ${\mathbit{\ensuremath{\sigma}}}^{Q}$ and susceptibility ${\mathbit{\ensuremath{\chi}}}^{Q}$ tensors in the vicinity of the dynamic phase transition (DPT). For this purpose, we have fabricated epitaxial Co and CoRu thin films with ($10\underline{1}0$) surface orientation and associated in-plane uniaxial anisotropy to mimic the behavior of an anisotropic Heisenberg model in the absence of magnetostatic interactions. Specifically, we measured the time-dependent magnetization component parallel to the externally applied magnetic field for different orientations of the magnetic easy axis (EA) while exploring the dynamic phase space defined by the applied oscillatory field amplitude ${H}_{0}$ and an additionally applied time-independent bias field ${H}_{b}$. The magnetization dynamics was hereby observed by utilizing an ultrasensitive transverse magneto-optical Kerr effect setup that allowed for real-time observations of the magnetic state evolution. Our experimental results demonstrate that while the position of the critical point changes upon rotating the EA away from the field axis, all qualitative aspects of the dynamic phase diagram close to the critical point are unchanged and the DPT can be universally observed. Also, metamagnetic anomalies occur for all measurement conditions. All our results are in agreement with a domain nucleation initiated magnetization reversal process and indicate that the overall dynamic state is dominated by the magnetization component parallel to the EA, so that a change in orientation in between the field axis and EA leads to a rather trivial rotation of the $Q$ vector, which simply follows the EA.