Macrospin reversals and spin wave softening in isolated nodes of Kagome-like structures: statics and ‎dynamics‎

In complex networks of ferromagnetic macrospins, like artificial spin ices or artificial quasi-crystals, much ‎interest has focused on the dynamics of Dirac strings, i.e. the apparently irregular path followed by ‎macrospin reversals, producing a magnetic charge drift across the network. The understanding and ‎control of these strings is currently the subject of intense study, and has numerous potential applications: ‎the different paths followed by the magnetic charge can, depending on the applied magnetic field and its ‎direction, be used, e.g., as spin wave guides or for magnetic bead delivery [1]. Depending on the ‎symmetry of the ferromagnetic network, and the possible presence of geometric and magnetic defects, ‎the string can be continuous or discontinuous (the extreme situation is found in aperiodic artificial quasi-‎crystals), but in any case follows a definite, reproducible sequence, which can change with the applied ‎field and direction. In ref.[2], it was shown how the origin of the string almost always starts from the ‎network edges and can be interpreted within a soft mode framework; in addition the resulting sequence ‎of macrospin reversals is correlated with the behavior of the low frequency spin-wave dynamics.‎ In this work, we experimentally explore many features of this mechanism, in a special system, which is a ‎key geometrical element of many networks: a three-macrospin node, interacting with each other either ‎by dipole-only interaction or dipole-exchange interaction. The macrospins consist of 15 nm thick ‎elongated ellipses (aspect ratio 2.5), made of Permalloy. The sample was fabricated using lift-off e-beam ‎lithography. DC magnetization curves were obtained using SQUID magnetometry. These curves show ‎different discontinuities corresponding to different macrospin reversals (Fig. 1). Broad band FMR ‎measurements were obtained using a meanderline or strip line antenna [3] ‎and clearly show mode ‎softening preceeding the magnetization discontinuities. The experimental results are interpreted within ‎the dynamical matrix method [4], and show some correlation between the measured FMR signal and the ‎calculated soft mode profile (Fig. 2). Symmetry arguments are used to examine the connection between ‎the soft mode profile and the order of reversal of the macrospins as a function of the applied field. We have also investigated the role of asymmetry on the order of reversal. Here we considered a three-‎macrospin node with an asymmetric geometry in which one arm has a reduced aspect ratio (e.g., 1.25). ‎We studied the effects of this special asymmetry with the goal of finding general criteria, valid for other ‎asymmetries (or irregularities due to e.g. defects). Asymmetry has direct consequences on the order of ‎macrospin reversals and we will discuss its effect on the DC magnetization curves, particularly ‎discontinuities, together with the characteristics of the specific macrospin that is reversing (involving its ‎angle relative to the applied field direction, total macrospin magnetic moment, etc.). We will also discuss ‎the corresponding effects seen in the FMR curves and correlate them with the (changed) soft mode ‎profile. We can extend the above results to the analysis of actual complex networks, made up of many nodes ‎similar to those studied. As an example, consider what happens when a sequence of reversals (and the ‎associated magnetic current) lead to a Dirac string that reaches a given network node. If one macrospin of ‎that node is “preferred” over another the resulting “decision” will be a consequence of the asymmetry (in ‎our case, of geometric origin), and will be accompanied by specific soft mode dynamics of that node. Such ‎phenomena should be detectable both statically (in the DC magnetization) and dynamically (by FMR). This research paves the way to tailoring complex ferromagnetic networks in which different lines are ‎tailored by the patterning of specific macrospin aspect ratios, so that they undergo magnetization reversal ‎at a specific, predetermined, field only: the magnetic field value (together with its angle) would then act ‎as a switch, allowing the magnetic charge signal to go along one chosen path or another, at will.