Standing spin waves in perpendicularly magnetized circular dots at millimeter waves

Abstract

Spin wave spectra of 40-nm thick perpendicularly magnetized circular Permalloy dots of 250 nm radius were measured using ferromagnetic resonance technique in 70-80 GHz range at 4.2 K and in 10 GHz at room temperature. The five sharp resonance peaks were observed for both frequency ranges. The resonance fields can be well described by a magneto-exchange dispersion relation, implying that the observed resonances correspond to circular “drumhead” modes with Bessel-function profiles. The relative distances between neighbor peaks for different frequency ranges were almost the same, while the absolute interpeak distances in millimeter range were ∼30% bigger than at 10 GHz, as predicted by the theory.

Using rf voltage induced ferromagnetic resonance to study the spin-wave density of states and the Gilbert damping in perpendicularly magnetized disks

“…The second effect -the increased frequency spacing between the modes at small diameters -is the expected effect of the confinement of the spin waves and the resulting increase of the exchange contribution to the mode frequencies 17 . The eigenmodes of perpendicularly magnetized circular disks are well understood and can be described analytically in a semi-quantitative manner 21,[24][25][26][27][28] . The frequency spacing between the lowest frequency modes scales with γ 0 H J where H J = 2Ak 2 µ0M S is a generalized exchange field with A the exchange stiffness.…”

Spin wave spectra in perpendicularly magnetized permalloy rings

“…13,14 Recently, there has been an increasing research interest on fundamental understanding of the dynamic properties of perpendicularly magnetized dot arrays using ferromagnetic resonance (FMR) spectroscopy. 15,16 With the field applied out of plane, high in-plane symmetry is preserved, and therefore, it is easier to interpret theoretically with regards to the observed spin wave (SW) modes. 17 To date, multiple spin wave modes were observed in perpendicularly magnetized submicron dot arrays in saturated field range.…”

“…17 To date, multiple spin wave modes were observed in perpendicularly magnetized submicron dot arrays in saturated field range. [16][17][18] Dipole-exchange theory of in-plane spin wave spectra 17 has been utilized to explain this phenomenon. It shows that a high static magnetic field is necessary to excite high frequency SWs in dots.…”

Role of boundaries in micromagnetic calculations of magnonic spectra of arrays of magnetic nanoelements

“…As before, the pulsed field is uniform and applied in the plane of the disks perpendicular to the bias magnetic field. The spectrum and mode profiles of isolated magnetic elements in the quasiuniform ground state of various, e.g., rectangular, 37 elliptical, 48,49 stadiumlike, 50 and round, 36,[51][52][53] shapes were extensively studied by experimental, numerical, and analytical means. For rectangular elements, it is possible to use the mode classification scheme derived in Ref.…”