Physica B 343 (2004) 200–205 Magnetostatic spin waves in nanoelements J. Fidler*, T. Schrefl, W. Scholz, D. Suess, V.D. Tsiantos, R. Dittrich, M. Kirschner Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10/138, A-1040 Vienna, Austria Abstract The relaxation of magnetostatic spin waves in a square NiFe nano-element (100  100  20nm 3 ) has been simulated by micromagnetic finite element modeling after the excitation by a rotational field of m 0 H ¼ 0:2 T with various frequencies between 1 and 16 GHz. The micromagnetic simulations are based on the Landau–Lifshitz–Gilbert equation of motion with a Gilbert damping parameter a ¼ 0:02: The relaxation after switching off the external field led to a damped oscillation of the magnetization, which is related to changes of the exchange and magnetostatic field energies of the system. Finally, depending on the frequency of the rotating field ‘‘C-’’ and ‘‘S-’’ domain configurations were observed after approximately 10 ns. The different inhomogeneous magnetostatic and exchange field strength values inside the square for the ‘‘C-’’ and ‘‘S-’’ state lead to different frequencies of the magnetostatic spin-wave modes, such as about 4.5 GHz for the C-state and 3 GHz for the S-state, respectively. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 75.60.Jk; 75.50.Bb; 75.75.+c Keywords: Numerical micromagnetics; Precessional switching; Magnetostatic spin waves; Rotational fields 1. Introduction Fast magnetization reversal processes play an important role in magnetic recording applications. They impose physical limits on data rates, areal storage densities, and signal to noise ratio, which makes their understanding fundamental for the design of novel ultrahigh density magnetic storage applications [1]. Recent advances in the fabrication and experimental investigation of thin films and patterned media have shown the influence of edge effects and inhomogeneous internal fields on the excitation of spin wave modes [2]. Magnetization reversal in quasi-single-domain magnetic particles by nonlinear spin-wave-like excitations has been explored using numerical micromagnetic simula- tions with limited discretization [3]. These non- linear spin-wave excitations have been shown to transfer excess Zeeman energy to uniaxial aniso- tropy and exchange energies, allowing the average magnetization to reverse [4]. Micromagnetic simu- lations revealed precessional oscillation effects of the magnetization in NiFe- and Co nanoelements during and after fast switching processes. Preces- sional effects in NiFe nanoelements can lead to a ‘‘bounce back’’ effect, which reduces the possible data rates in MRAM and perpendicular recording applications [5]. The magnetization distribution of the remanent state in small square magnetic elements can attain so-called ‘‘C-’’ and ‘‘S-states’’, ARTICLE IN PRESS *Corresponding author. Tel.: +43-1-58801-13714; fax: +43- 1-58801-13899. E-mail address: fidler@tuwien.ac.at (J. Fidler). 0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.08.094