From micro- to nanomagnetic dots: evolution of the eigenmode spectrum on reducing the lateral size

Brillouin light scattering experiments and micromagnetic simulations have been exploited to investigate the spectrum of thermally excited magnetic eigenmodes in 10 nm-thick elliptical Permalloy dots, when the longer axis D is scaled down from about 1000 to 100 nm. It is shown that for D larger than about 200 nm the characteristics of the spin-wave eigenmodes are dominated by dipolar energy, while for D in the range of about 100 to 200 nm exchange energy effects cause qualitative and quantitative differences in the spin-wave spectrum. In this 'mesoscopic' regime, the usual classification scheme, involving one fundamental mode with large average magnetization and many other modes collected in families with specific symmetries, no longer holds. Rather, one finds the simultaneous presence of two modes with 'fundamental' character, i.e. with a significant and comparable value of the average dynamical magnetization: the former is at larger frequency and has its maximum amplitude at the dot's centre, while the latter occurs at lower frequency and is localized at the dot's edges. Interestingly, the maximum intensity swaps from the higher frequency mode to the lower frequency one, just when the dot size is reduced from about 200 to 100 nm. This is relevant in view of the exploitation of nanodots for the design of nanomagnetic devices with lateral dimensions in the above interval, such as memory cells, logic gates, reading heads and spin-torque oscillators. (paper)