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.
Macrospin reversals and spin wave softening in isolated nodes of Kagome-like structures: statics and dynamics
MONTONCELLO, Federico;GIOVANNINI, Loris;
2017
Abstract
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.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
