Magnetodynamical response of large-area close-packed arrays of circular dots fabricated by nanosphere lithography

Abstract

We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic excitations in large-area arrays of NiFe nanodisks forming a hexagonal lattice with the lattice constant of 390 nm. Arrays were fabricated by patterning a 20-nm-thick NiFe film using the etched nanosphere lithography. We have studied a close-packed (edge-to-edge separation between disks dcp = 65 nm) and an ultraclosed packed (ducp = 20 nm) array. Hysteresis loops for both arrays were qualitatively similar and nearly isotropic, i.e., independent on the in-plane external field orientation. The shape of these loops revealed that magnetization reversal is governed by the formation and expulsion of vortices inside the nanodisks. When we assumed that the nanodisks’ magnetization significantly decreases near their edges, micromagnetic simulations with material parameters deter-mined independently from continuous film measu-rements could satisfactorily reproduce the hysteresis. Despite the isotropic hysteresis, significant in-plane anisotropy of the dynamic response of the ultraclose-packed array was found experimentally by the all-electrical spin-wave spectroscopy and Brillouin light scattering. Dynamical simulations could successfully reproduce the difference between excitation spectra for fields directed along the two main symmetry axes of the hexagonal lattice. Simulations revealed that this difference is caused by the magnetodipolar interaction between nanodisks, which leads to a strong variation of the spatial distribution of the oscillation power both for bulk and edge modes as a function of the bias field orientation. Comparison of simulated and measured frequencies enabled the unambiguous identification of experimentally observed modes. Results of this systematic research are relevant both for fundamental studies of spin-wave modes in patterned magnetic structures and for the design of magnonic crystals for potential applications as, e.g., spin-wave guides and filters

Theoretical formalism for collective spin-wave edge excitations in arrays of dipolarly interacting magnetic nanodots

“…Together, equations (27) and (37) are the central result of this paper. Using these equations one can calculate the distribution of the internal magnetic field (B i )in the array, equilibrium directions of the magnetic moments in each dot (μ i ), and the spectrum of collective spin wave edge excitations in a semi-infinite array of magnetic nanodots with a complex primitive cell.…”

“…Although the recent progress in the electron and ion beam lithography has made possible the fabrication of arrays of magnetic nanoelements (nanodots) on a large scale 9,[11][12][13]20,22,[25][26][27] , the fabrication of arrays of elements with high aspect ratios (height substantially larger than the radius), which is necessary for the effective dipolar interaction between the elements 22 , still remains a challenging technological problem. Nonetheless, we believe that materials with uniaxial crystallographic anisotropy 28 , like multi-layered composites of CoPt, Co 3 Pt, FePt, CoPd 29 , which exhibit strongly perpendicular static magnetization in the absence of a bias magnetic field, will make possible the physical realization of the magnetic nanodot arrays for signal processing applications in the near future.…”

“…Although equations (27) and (37) were obtained using purely analytical methods, further analytical solution of these equations (e.g., using the nearest neighbor approximation 60 ) is tedious and does not allow one to obtain qualitative analytical results in a closed form. The internal structure of the tensorsÊ κ (n) is complicated, and, moreover, the dispersion equation (27) leads to a generalized eigenvalue problem with an infinite block "Toeplitzlike" matrix, in which blocks standing on the main diagonal are not equal, becauseB n =B m when n = m in (28).…”

“…Therefore, equation (34) allows one to calculate the components of the block-matrixÊ κ (n) that are necessary for the solution of the equation (27).…”

Asymmetry of spin wave dispersions in a hexagonal magnonic crystal

“…34 However, a detailed investigation of the SEM images at different magnification revealed that the orientation of the symmetry axis suffers a decrease of 25 over the distance of 5.0 mm. 35 The BLS experiments were performed in the Voigt configuration, where the in-plane transferred wave-vector (k) was perpendicular to the external magnetic field applied in the sample plane. The SW dispersion was measured for two different orientations of the magnetic field of l 0 H ¼ 40 mT, as indicated in Figs.…”