Splitting of standing spin-wave modes in circular submicron ferromagnetic dot under axial symmetry violation.

S A Bunyaev,A V Chumak,N A Sobolev,V O Golub,A A Serga,G N Kakazei,N M Santos,B Hillebrands,O Yu Salyuk,A A Timopheev,E V Tartakovskaya

doi:10.1038/srep18480

Abstract

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades. On the one hand, this interest is generated by new physics that can be explored in such structures. On the other hand, with the development of nanolithography, patterned nanoelements and their arrays can be used in many practical applications (magnetic recording systems both as media and read-write heads, magnetic random access memory, and spin-torque oscillators just to name a few). In the present work the evolution of spin wave spectra of an array of non-interacting Permalloy submicron circular dots for the case of magnetic field deviation from the normal to the array plane have been studied by ferromagnetic resonance technique. It is shown that such symmetry violation leads to a splitting of spin-wave modes, and that the number of the split peaks depends on the mode number. A quantitative description of the observed spectra is given using a perturbation theory for small angles of field inclination from the symmetry direction. The obtained results give possibility to predict transformation of spin wave spectra depending on direction of the external magnetic field that can be important for spintronic and nanomagnetic applications.

Highlights

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades
The good agreement between analytical calculations and experimental data was found for only few cases of simplest symmetry, for example, infinite stripes magnetized along two principal directions[1,2] and axially magnetized circular dots[3]
A square array of circular Py dots was prepared on a Si wafer with an oxidized surface Since the distance between the neighbour resonance peaks of standing spin waves in a perpendicularly magnetized circular dot is inversely proportional to the dot radius R3, we selected R to be 250 nm

Summary

Introduction

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades. The good agreement between analytical calculations and experimental data was found for only few cases of simplest symmetry, for example, infinite stripes magnetized along two principal directions[1,2] and axially magnetized circular dots[3] In the former case, it was natural to assume that the eigenfunctions of the stripes would have an almost sinusoidal form, analogous to the form of spin wave resonance modes in a perpendicularly magnetized continuous homogeneous film. In this paper we study, both experimentally and theoretically, the modification of such spectra for circular Permalloy (Ni81Fe19) dots in external magnetic fields slightly inclined from the perpendicular direction For this orientation the most efficient experimental techniques are either cavity-based[3,5,6,7,8] or broadband[9] ferromagnetic resonance (FMR) spectroscopy as well as FMR force microscopy[10,11]. The well established cavity-based X-band FMR was applied, that allows to probe the millimeter-size samples and to use sample holder with both in-plane and out-of-plane angular rotations

Methods

Results

Conclusion