Spin-wave non-reciprocity in magnetization-graded ferromagnetic films

Abstract

A theoretical approach has been developed to study the spin-wave dynamics of magnetization-graded ferromagnetic films, where the magnetic properties change along the film thickness. The theory is based on a multilayer approach, where the influence of both long-range dipolar interactions and interlayer exchange coupling between sublayers is included. This allows for instance to describe films with a continuous variation of the saturation magnetization along the thickness. A systematic study is carried out in order to analyze different profiles of the saturation magnetization, which is checked through a test of convergence. It is found that the spin-wave dispersion is significantly modified when the strength of the magnetization changes in the bulk film, where a notable frequency non-reciprocity of two counter propagating spin waves is predicted. This is associated with heterosymmetric mode profiles and a modification of the conventional quantization condition associated to perpendicular standing spin-wave modes. Micromagnetic simulations have been carried out to validate the model, where a perfect agreement is reached between both methods. These results show that magnetizationgraded ferromagnetic films can be used to channel and control spin waves, thus promoting different kinds of functionalities for magnon-based devices.

Slow-Wave-Based Nanomagnonic Diode

“…change of sign of is expected at the particular value |k * | = {(l/2)[3 + l 2 /( π ) 2 ]} −1 , which indeed amounts to a few radians per micrometer for magnetic materials with 4 nm and thickness l in the 40-50-nm range. Such a change of sign has also been predicted for films where breaking of the top-bottom magnetic symmetry is not obtained through a blockwise variation of M S , like here, but rather by a grading of saturation magnetization across the thickness [22]. In contrast, it has not been observed for bilayers where the two magnetic materials, being separated by a nonmagnetic spacer, are coupled only through longrange dipole interactions [41,42].…”

“…This configuration is specific in that a dipolar coupling exists between the two (in-plane and out-of-plane) components of the dynamic magnetization [17], which happens to be nonreciprocal. In the presence of top or bottom magnetic asymmetry, this coupling does not average out to zero and translates into counterpropagating surface waves with a given wave number having different frequencies [18][19][20][21][22]. As demonstrated at the millimeter scale with relatively thick films in which symmetry was broken either by addition of a nonmagnetic conductor to one side of the film [23] or by use of a magnetic bilayer stack [24], one can even reach an extreme situation in which, at some frequencies, propagation is possible only in one direction.…”

Chiral magnonic resonators: Rediscovering the basic magnetic chirality in magnonics

“…This could enable one to enhance the radiative linewidths' chirality by non-reciprocally slowing done the propagating modes, e.g. using DMI, 4-8 thickness-asymmetry in the DESW geometry [10][11][12][13][14] or electric field. [69][70][71] One should note however that the reduced group velocity can slow down the device overall.…”

“…By breaking the reflection symmetry of the medium, 10 the amplitude asymmetry can be converted into non-reciprocity of the DESW dispersion relation. [11][12][13][14] Yet, there are both practical and fundamental reasons to widen the search for chiral spin wave phenomena and devices beyond the DESW geometry. For instance, the backward volume spin wave (BVSW) geometry (the wave vector is parallel to the in-plane static magnetisation, Fig.…”

Control of Dynamics in Weak PMA Magnets

“…While the first two possibilities do not apply to our simulations (as they imply the existence of other kinds of materials) the three later ones are possible candidates. It is known that Ni-Al and Co-Al alloys form at room temperature, so the Al diffusion in Permalloy and NdCo x cannot be neglected [44,45]. Interdiffusion will decrease the actual magnetic volume of the layers and/or promote the creation of different magnetic parameters at interfaces.…”