Observation of anisotropic energy transfer in magnetically coupled magnetic vortex pair

Abstract

We have experimentally investigated the energy transfer and storage in the magnetostatically coupled vortices in a pair of disks. By measuring the frequency dependence of the rectified dc voltage, we observed a specific gyrating motion due to anomalous energy storage at the off-resonant frequency for anti-parallel polarities. Micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation qualitatively reproduce the experimental results and reveal that the behavior arises from the anisotropic energy transfer, i.e., the modulation of effective damping constant of the pair disks, originating from the phase difference between coupled vortex cores. These findings can be of use in magnetic vortex based logic operations. The magnetic vortex has been drawing much attention as one of the fundamental structures confined in a nanometer scaled ferromagnetic disk.1,2 It is characterized by two degrees of freedom, the in-plane curling magnetization direction, “chirality” (c=±1 ), and the out of core magnetization, “polarity” (p=±1 ). The core of a magnetic vortex is known to behave as a quasiparticle in a harmonic potential.3 In the low energy excitation (or gyration) mode, the core continuously gyrates along an equipotential line. The resonant frequency for a single vortex can be determined by the potential shape which depends on the aspect ratio (thickness/radius) of the magnetic disk4 and not on polarity or chirality. When two magnetic vortices are placed sufficiently close to each other, the dynamic dipolar interaction serves as a binding force. In the two-coupled vortices system, the resonant frequency splits into two branches and the split-width depends on the strength of the dipolar interaction.5,6 By arranging magnetic vortices in a two-dimensional array, it forms a so-called magnonic crystal, where the band structure can be tuned by polarity.7 Thus, its band structure has been intensively studied for several cases such as a one-dimensional chain,8–10 a two-dimensional array7,11 and a carbon flake.12 In these systems, properties of the energy transfer and storage in each disk are also important for actual applications.13,14 The interesting properties of the energy transfer and storage within a group of magnetic vortices have recently been examined in a theoretical study;15 however, no experimental observation has been reported. Here, we observed the specific gyrating motion due to anomalous energy storage, for a coupled vortices system by using the electrical detection method. Samples were fabricated on a silicon substrate by means of electron beam lithography on polymethyl-methacrylate resist and a subsequent lift-off process after electron beam deposition. We fabricated two 30 nm thick disks 500 nm in radius of Permalloy (Py: Ni80Fe20) aligned along the x axis with a 100 nm gap between their nearest edges. By attaching Cu electrodes in each Py disk, we can apply different ac currents IacL and IacR, where the subscripts “L” and “R” represent the left and right Py disks, respectively. The Cu electrodes were patterned at the same distance from the disk center and deposited by thermal evaporation. Before the Cu deposition, a careful Ar ion beam etching (600 V beam voltage) was carried out for 30 s in order to clean the Py surface. In Fig. 1(a), we show a scanning electron microscope (SEM) image of the two Py disks as well as a schematic image of the measurement circuit. Here, anti-parallel polarities were prepared by applying relatively large ac current16 and confirmed it by measuring the splitting intensity of resonant frequencies as reported in Ref. 6.