Pushing down the lateral dimension of single and coupled magnetic dots to the nanometric scale: Characteristics and evolution of the spin-wave eigenmodes

Abstract

Planar magnetic nanoelements, either single-or multi-layered, are exploited in a variety of current or forthcoming spintronic and/or ICT devices, such as read heads, magnetic memory cells, spin-torque nano-oscillators, nanomagnetic logic circuits, magnonic crystals and artificial spin-ices. The lateral dimensions of the elemental magnetic components have been squeezed down during the last decade to a few tens of nanometers, but they are still an order of magnitude larger that the exchange correlation length of the constituent materials. This means that the spectrum of spin-wave eigenmodes, occurring in the GHz range, is relatively complex and cannot be described within a simple macrospin approximation. On the other hand, a detailed knowledge of the dynamical spectrum is needed to understand or to predict crucial characteristics of the devices.With this focused review we aim at the analysis and the rationalization of the characteristics of the eigenmodes spectrum of magnetic nanodots, paying special attention to the following key points: (i) Consider and compare the case of in-plane and out of-plane orientation of the magnetization, as well as of single-and multi-layered dots, putting in evidence similarities and diversities, and proposing a unifying nomenclature and labelling scheme; (ii) Underline the evolution of the spectrum when the lateral size of magnetic dots is squeezed down from hundreds to tens of nanometers, as in current devices, with emphasis given to the occurrence of soft modes and to the change of spatial localization of the fundamental mode for in-plane magnetized dots; (iii) Extend the analysis from isolated elements to twins of dots, as well as to dense arrays of dipolarly interacting dots, showing how the discretized eigenmodes distinctive of the single element transform in finite-width frequency bands of spin waves propagating through the array.

Higher-order ferromagnetic resonances in periodic arrays of synthetic-antiferromagnet nanodiscs

“…With respect to the position of L m , lines L e1 and L e2 are observed at higher resonance fields. A similar higher-field mode, along with the main mode, was reported previously [11] for arrays of single-layer nanodiscs and was attributed to the edge-mode resonance. For our arrays of SAF nanodiscs, we observe two higher-field modes, both of which we associate with higher-order edge-mode resonances in the SAF nanostructure -the interpretation supported by our micromagnetic simulations, detailed below.…”

“…Relatively simple periodic arrays of single-layer ferromagnetic nanodiscs exhibit anisotropic spin wave modes (commonly, with four-fold in-plane anisotropy) affected by the inter-element dipolar interactions [9][10][11]. The properties become more intriguing for arrays of multilayered elements such as SAF's, which are of interest in antiferromagnetic spintronics [12] as well as magnonics [13].…”

Controlling the three dimensional propagation of spin waves in continuous ferromagnetic films with an increasing out of plane undulation

“…We see how the increase in the undulation amplitude causes a frequency increase for all 4, 6, and 8-stripe system, but not for the 12-stripe system, which shows a different behavior in both cases. This diversity occurs because the width of the elemental stripe is too small 45 (i.e., w = 60 nm) and the corresponding dipolar fields are very stronger. For this reason, in both Figures the curve relevant to the 12-stripe system departs from the others.…”

Effect of the Interfacial Dzyaloshinskii–Moriya Interaction on the Spin Waves Eigenmodes of Isolated Stripes and Dots Magnetized In-Plane: A Micromagnetic Study

“…Let us now consider the more complicated case of elliptical nanodots, which, different from the wires discussed above, are laterally confined in both in-plane directions. For such case, we adopt the classification and the labelling scheme of the eigenmodes of magnetic nanodots that have been described in a recent review paper [30]: each mode is labelled with two integer indices (n x ,n y ) whose values correspond to the number of nodal lines perpendicular or parallel to the direction of the magnetization (x axis), respectively. In Figure 3 one can see the results of our simulations relative to the smallest dots considered in this study, having lateral dimensions 100 × 50 nm 2 .…”