Negative permeability due to exchange spin-wave resonances in thin magnetic films with surface pinning

Abstract

We report a theory of the effective permeability of multilayered metamaterials containing thin ferromagnetic layers with magnetization pinned on either one or both surfaces. Because of the pinning and small film thickness, the lowest frequency magnetic resonances are due to nonuniform exchange spin waves with frequencies far above those expected for uniform ferromagnetic resonance in known magnetic materials. Yet, the coupling of the nonuniform spin-wave modes to the electromagnetic field is shown to be strong enough to lead, for magnetic parameters characteristic for conventional transition metal alloys, to negative values of the effective permeability at frequencies of several hundred gigahertzs. The permittivity of metals is already negative in this frequency range. Hence, this system represents a negative refractive index metamaterial at subterahertz frequencies. The ways by which to maximize the frequency and the strength of the negative magnetic response are analyzed.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics

“…For plasmonics, the characteristic length scales of features are in the millimetre to micrometre range. One important area to be explored is the incorporation of magnetically polarisable elements in a plasmonic array in order to tune different properties such as negative refraction with external applied fields [91,[190][191][192]. Further directions include laser induced switching [193], coupling light to charge and spin currents for information encoding and transfer, optical trapping and manipulation, nanoplasmonics and imaging, to name just a few, with the potential to generate and steer spinwaves in an all optical set-up [194].…”

Magnonic Metamaterials

“…The age of nanotechnology therefore sets an intriguing quest for additional benefits to be gained by structuring natural magnetic materials into so called magnonic metamaterials, in which the frequency and strength of resonances based on spin waves (magnons) 8 are determined by the geometry and magnetization configuration of meta-atoms. Spin waves can have frequencies of up to hundreds of GHz (in the exchange dominated regime) [6][7][8][9] and have already been shown to play an important role in the high frequency magnetic response of composites [10][11][12][13][14] . Moreover, in view of the rapid advances in the field of magnonics 9,15,16, , which in particular promises devices employing propagating spin waves, the appropriate design of magnonic metamaterials with properties defined with respect to propagating spin waves rather than electromagnetic waves acquires an independent and significant importance.…”

“…The negative permeability could be obtained via geometrical control of high frequency currents, e.g. in arrays of split ring resonators 5 , or alternatively one could rely on spin resonances in natural magnetic materials 6,7 , as was suggested by Veselago in Ref. 2.…”

Generation of Propagating Spin Waves From Edges of Magnetic Nanostructures Pumped by Uniform Microwave Magnetic Field

“…At the same time, the possibility of spin-wave excitation at boundaries with a finite pinning is well known [25][26][27] and is general indeed. The role of the dynamic demagnetizing field in generating the pinning can also be inferred from analytical calculations from Ref.…”

“…The role of the dynamic demagnetizing field in generating the pinning can also be inferred from analytical calculations from Ref. 27, from which it follows that zero-pinning disables excitation of spin waves with a finite wave number in the exchange approximation.…”