Ferromagnetic resonance of a magnetic dimer with dipolar coupling

Abstract

We develop a general formalism for analyzing the ferromagnetic resonance characteristics of a magnetic dimer consisting of two magnetic elements (in a horizontal or vertical configuration) coupled by dipolar interaction, taking account of their finite-size and aspect ratio. We study the effect on the resonance frequency and resonance field of the applied magnetic field (in amplitude and direction), the inter-element coupling, and the uniaxial anisotropy in various configurations. We obtain analytical expressions for the resonance frequency in various regimes of the interlayer coupling. We (numerically) investigate the behavior of the resonance field in the corresponding regimes. The critical value of the applied magnetic field at which the resonance frequency vanishes may be an increasing or a decreasing function of the dimer's coupling, depending on the anisotropy configuration. It is also a function of the nanomagnets aspect ratio in the case of in-plane anisotropy. This and several other results of this work, when compared with experiments using the standard ferromagnetic resonance with fixed frequency, or the network analyzer with varying frequency and applied magnetic field, provide a useful means for characterizing the effective anisotropy and coupling within systems of stacked or assembled nanomagnets.Comment: 22 Pages, 13 Figure

Single-Particle Phenomena in Magnetic Nanostructures

“…In fact, the shape anisotropy is much stronger than the magnetocrystalline anisotropy, as was remarked in Ref. [273]. In this work, the FMR characteristics were obtained for a pair of (vertical or horizontal) nanodisks coupled by dipolar interaction (beyond the dipole-dipole approximation), taking account of their finite size [274].…”

Variable variance Preisach model for multilayers with perpendicular magnetic anisotropy

“…However, due to external factors, the magnetic moments could prefer a direction that is not parallel to the connecting vector, and the dipolar interaction tends to align the two magnetic moments in an antiparallel state, as shown in Fig. 6 and multilayers [71], and experimentally in arrays of elliptical nanomagnets [72]. In our samples, the external factor inducing the antiparallel state is the PMA.…”

Ferromagnetic resonance of magnetostatically coupled shifted chains of nanoparticles in an oblique magnetic field

“…This approach extends the so-called point-dipole approximation which consists in replacing the magnetic elements (here the chains) by point dipoles. In fact, this assumption fails for finite-size elements with a too small separation between them and this is why one has to extend the magnetostatic interaction by including adequate geometrical factors [11][12][13] , as is done in Eqs. (3,4).…”

“…(37) after a rotation of the frame axes and noting that for point dipoles δ = L/d becomes small and that the quantity µ0 4π (λL) 2 /d 3 is the DI coefficient in Ref. 13.…”

“…In particular, these authors show that the DI are no longer negligible in such systems with respect to the usual prevalence of the exchange coupling in classical materials. In order to account for the effects of all a) Electronic mail: roland.bastardis@univ-perp.fr b) Electronic mail: dejardin@univ-perp.fr c) Electronic mail: francois.vernay@univ-perp.fr d) Electronic mail: hamid.kachkachi@univ-perp.fr these parameters, we shall consider here the more general formalism of DI [11][12][13] between finite-size magnetic elements of cylindrical shape. From the applied physics standpoint, this investigation is of interest in the context of magnetic recording.…”