Bandwidth variation of collective spin waves at the edge of magnetic transitions‎

Similarly to other magnetic systems, even magnonic crystals are characterized by soft modes with a vanishing frequency at the critical field of any given magnetic transition. The profile of these modes has a symmetry that depends on the symmetry change between the initial and final magnetic configurations. The knowledge of the soft mode is not a theoretical-only issue, but can have technological implications, especially in the field of magnonic- and spin-logic devices, where collective spin waves are used for information storage and delivery. Actually, it has been recently demonstrated that the bandwidth of the mode that softens at the critical transition field, undergoes dramatic variations even when just approaching this critical field. This fact can result in a band broadening also for modes usually non-dispersive (like some end modes). In some cases, it is possible to design the magnonic crystal to be characterized by a soft mode with the desired symmetry, in order to use its bandwidth variation close to the transition field for a specific purpose. We show this concept as emerging from calculations within the dynamical matrix method: first, for square arrays of disks in the saturated and also in the vortex state, then for rectangular arrays of interacting elliptical dots, magnetized along the minor and also major axis, and find out the behavior of the soft mode dispersion close to different magnetic transitions. We discuss the correlation among: the magnetization curve, the soft mode frequency vs. field curve, and the frequency vs. wavevector curve. In the vortex-to-saturated transition the soft mode is characterized by a bandwidth that goes to zero at a magnetic field quite distinct from the critical transition field, and we call this field stopping field, because at this field the collective soft mode turns into nondispersive (stationary). We believe that this features might be used to design versatile devices, in which information can be stored or delivered at the energy costs of a small magnetic field variation