Tunable microwave properties of a skyrmion in an antidot nanodisk structure

Abstract

Chiral interactions between magnetic moments in ferromagnetic systems with broken inversion symmetry has attracted lots of attention in the recent years. Dzyaloshinskii-Moriya interaction[1] (DMI) present in these systems leads to an ordering of the spins that forms various exotic spin configurations such as chiral domain walls[2] and skyrmion[3]. DMI is an anti-exchange interaction which prefers to cant the neighbouring spins orthogonal to each other that forms whirling structures such as skyrmions. A magnetic skyrmion is a topological object having particle-spin like configuration, which can be stabilized in ferromagnetic systems with DMI. Recently magnetic skyrmions are proposed as promising candidates for non-volatile memory and logic applications due to their nanoscale size, high stability, high density and small driving currents required for their motion. Besides memory applications, skyrmions also hold great potential in the emerging area of magnonics where collective spin excitations (magnons) are used as a medium of information processing. In addition, observation of skyrmions on low Gilbert damping materials may allow the use of the skyrmions for manipulations of magnon transport. Recently skyrmion generation at an antidot is demonstrated using micromagnetic simulations[4].In this work, we present the various routes for obtaining giant tunability in microwave properties based on skyrmion dynamic via micromagnetic simulations using Mumax3. We have investigated microwave properties of magnetic skyrmions in a circular nanodisk having antidot at the centre. An in-plane ac magnetic field excites gyrotropic dynamics with a clockwise and a counter-clockwise mode. We have systematically investigated skyrmion resonant modes as a function of DMI and perpendicular magnetic anisotropy (K). Large variation of resonant modes as a function of small out-of-plane bias magnetic field has been demonstrated.Simulated microwave spectrum of this Néel type skyrmion in an antidot nanodisk has been shown in figure 1(a) and it is compared with an antidot nanodisk having uniform OOP magnetization without any skyrmions. It is to be noted that there is no external bias field applied for these results in fig 1(a). Microwave responses are found in 13-22 GHz frequency range. The most prominent modes are found at 13 GHz and 17 GHz for the disk with a skyrmion and no skyrmion, respectively. Therefore, the modes at 13.1 GHz can be associated to the skyrmion resonances whereas the other higher frequency modes arise from the bulk magnetization (OOP) of the disk. Next, we demonstrate the tunability of the skyrmion resonance modes by applying a small bias field (Hext) along the OOP direction of the nanodisk with a single skyrmion. We have varied the polarity and the magnitude of the OOP field. The results are shown in fig 1(b) where the microwave resonance spectra are shown at different external fields: 0 to 35 mT. A relatively large frequency shift of 3.3 GHz has been observed for a change of 35 mT bias field.To further explore the functionalities, we have investigated skyrmion stabilization with various combinations of the parameters, DMI and K. Néel skyrmion is found to be stabilized at K = 0.25×106 J/m3 and DMI = 1.8×10-3 J/m2. Next, we have varied the K from 0.22 to 0.34 (×106) J/m3 for a fixed value of DMI = 1.8 mJ/m2 and we have varied the parameter DMI from 1.6 mJ/m2 to 1.9 mJ/m2, for a fixed value of K = 0.25×106 J/m3 shown in fig 2(a & b) respectively. Furthermore, a broad microwave tunability of 9.8 GHz has been shown with a variation of magnetic anisotropy of 1×105 J/m3. The manifestation of inertial mass of the skyrmion, its dependence on the resonance responses and the size of the skyrmion are explained by using Thiele’s equation. The inertial mass of the skyrmion is estimated to be in the order of 10-23 kg. We believe these results will have potential implications in the area of skyrmion based nano-scale reconfigurable microwave devices. **