Stopping field for collective spin waves at the edge of magnetization reversal

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[1]. 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[2]. Actually, it has been recently demonstrated[3] that the bandwidth of the mode that softens at the critical field, undergoes dramatic variations even when just approaching this critical field. This fact can result either in a band broadening of modes usually non-dispersive (like some end modes), or, vice versa, in a strong band reduction for modes with usually a large bandwidth (as the fundamental mode). In some cases, it is possible to design the magnonic crystal to be characterized by one or another soft mode with the desired symmetry in order to use its bandwidth variation close to the transition field for a specific purpose. We apply this concept to a rectangular array of interacting elliptical dots of Permalloy (i.e., a 2-D magnonic crystal), magnetized along the major axis, and, by calculations with the dynamical matrix method, find out the behavior of the soft mode dispersion at the edge of magnetization reversal. We discuss the correlation among different curves characterizing the magnetic system close to reversal: the magnetization curve, the soft mode frequency vs. field curve, and the frequency vs. wavevector curve. We investigate different aspect ratios for the ellipses, and different magnetic configurations. We show how 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 non-dispersive (stationary). We believe that this feature can be used to design versatile devices, in which information can be stored or delivered at the energy costs of a small magnetic field variation. [1] F. Montoncello, L. Giovannini, F. Nizzoli, P. Vavassori, and M. Grimsditch, Phys. Rev. B 77, 214402 (2008). [2] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, M. P. Kostylev, V. S. Tiberkevich, and B. Hillebrands, Phys. Rev. Lett. 108, 257207 (2012). [3] F. Montoncello and L. Giovannini, Applied Physics Letters 104, 242407 (2014).