Band structure of collective modes in permalloy/cobalt magnonic crystals - Presentazione orale by Roberto Zivieri - Conferenza internazionale

The band structure of the most representative collective modes in four different permalloy/cobalt periodic systems consisting of cylindrical cobalt (Co) nanodots etched into a continuous permalloy (Py) film are studied. The investigation is performed according to a micromagnetic approach, called dynamical matrix method (DMM), generalized to study the dynamical properties of periodic binary magnetic systems and the eigenvalue problem is recast in the form of a complex generalized Hermitian problem. An external magnetic field H having intensity H = 500 Oe is applied along the y -axis and the Bloch wave vector K is along the x -axis . The lattice constant is a = 600 nm, the Co circular nanodot has a diameter d = 310 nm and the thickness is L = 16 nm for every system. The Co circular dot is totally embedded into the Py film only in system 1. In system 2 it is partially embedded into Py film with a thickness L Co = 8 nm. In system 3 the thickness of the Co circular nanodot is L Co = 16 nm, but it is etched only 8 nm into Py film, while in system 4 it is above the Py film (L Co = 8 nm). The binary ferromagnetic systems studied are twodimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. Magnonic modes have Damon- Eshbach-like (DE) character with nodal planes parallel to the local direction of the magnetization. According to the mode classification, we denote the two families of collective modes with DEn BZ and DEn BZHR with n =1,2,... labeling the n th Brillouin zone. The DEn BZHR modes are mainly localized along the horizontal rows (HRs) containing Co cylindrical nanodots with a much lower degree of localization in the Co cylindrical nanodots, but their amplitude can be rather large also along the horizontal channels. Instead, the DEn BZ modes have amplitudes spreading mainly inside the Py film with maxima in the horizontal channel, but with appreciable amplitude also in the horizontal rows containing cobalt cylindrical dots. The dispersion curves of magnonic modes for system 2 are slightly downshifted with respect to the corresponding ones calculated for system 1. The same behavior is exhibited by dispersion of system 4 compared to that of system 3. This small downshift of the dispersion is due to larger demagnetizing effects on mode frequencies. The surface magnetic charges created by the static magnetizations are of opposite sign, but of different magnitude at the interface between Py and Co leading to the formation of effective “surface magnetic charges” that take the sign of the ones due to MCo.As a result, the static demagnetizing field is parallel to H in the Py horizontal channels and antiparallel to in the Co cylindrical nanodots and in the HRs . Also band gaps (BGs) appearing at edges of n BZs with n = 1,2,.. are determined up to the 5th BZ. For both families of collective modes the BG amplitude is about 0.5 GHz at the border of the 1BZ. We have found that the perturbation which produces the band gaps is proportional to the quantity of Co which acts like a BG resonator. A quantitative comparison with band gaps estimated via an analytical method based on a perturbation approach is also performed. According to this approach it is assumed that the unperturbed collective mode frequencies of the lower bands are perturbed by the demagnetizing field created by the Co cylindrical dots. Band gaps calculated with DMM are also compared with the ones determined by means of an approximated version of another analytical approach called the plane wave method. It is also shown that the interchange between Co and Py does not lead in all cases to an interchange of the corresponding mode dispersion. This is in turn due to the demagnetizing effects that are different in every system investigated. In every system, localized modes minaly along HRs have their largest amplitude in the regions filled by Py. The degree of localization of localized modes is expressed by means of a concentration factor in analogy to electromagnetic waves in two-dimensionale photonic crystals. The obtained results could stimulate the reseach on technological applications for tailoring band structure in magnonic crystals in a way similar to what was done for electronic and photonic crystals. This work was partially supported by MIUR-PRIN 2010-11 Project2010ECA8P3 “DyNanoMag”.