Micromagnetic calculation of dynamic susceptibility in ferromagnetic nanorings

Abstract

Dynamic magnetic susceptibilities of high-aspect-ratio permalloylike nanorings (outer diameter 20 nm, inner diameter 12 nm, length (L) range 12–500 nm) are studied using three-dimensional micromagnetic simulations. The investigated systems show two major resonance modes associated with volume and shape resonance modes, corresponding to low and high resonance frequencies, respectively. When L is below 40 nm, only the shape resonance mode is seen with a frequency predicted using the Kittel’s equation and demagnetization factor calculated for a ring. At sufficiently large L, the frequency of the volume mode converges to that of the Kittel prediction. For other lengths, however, neither the low resonance frequency nor the high resonance frequency agrees with the Kittel’s equation. A weighted average resonance frequency fa(i) that contains two major modes is introduced and shows the same trend as the results predicted by the Kittel’s equation for all lengths. The frequencies of volume and shape resonance modes have also been investigated by changing the exchange stiffness constant (A) and the saturation magnetization (Ms).