Hartman effect for spin waves in exchange regime

Abstract

Hartman effect for spin waves tunnelling through a barrier in a thin magnetic film is considered theoretically. The barrier is assumed to be created by a locally increased magnetic anisotropy field. The considerations are focused on a nanoscale system operating in the exchange-dominated regime. We derive the formula for group delay τgr of a spin wave packet and show that τgr saturates with increasing barrier width, which is a signature of the Hartman effect predicted earlier for photonic and electronic systems. In our calculations, we consider the general boundary conditions which take into account different strength of exchange coupling between the barrier and its surrounding. As a system suitable for experimental observation of the Hartman effect we propose a CoFeB layer with perpendicular magnetic anisotropy induced by a MgO overlayer.

An anomalous refraction of spin waves as a way to guide signals in curved magnonic multimode waveguides

“…By implantation of Ga ions, we can locally reduce the magnetization and create the distribution of magnetization saturation of high spatial resolution 32,44,45 . From the other side, when the sufficiently thin layer of the CoFeB is deposited on the MgO, the surface-induced outof-plane anisotropy can force the perpendicular orientation of the magnetization 31,46 . The effective anisotropy field (including both the shape and surface, magnetocrystalline anisotropy) can be controlled by the annealing in the fabrication process or by the application of the electric field [47][48][49] .…”

“…Except for the changes in the phases of refracted waves, the GRIN element should not introduce significant changes to their amplitudes. The interplay between the material parameters of the slab and its sizes determines the conditions for the resonanant transmission 31,32 . Therefore, we need to design a system to work in the conditions close to the resonant transmission.…”

Spin- and Angle-Resolved Spectroscopy and Spin Waves in Biogenic Magnonic Systems

“…the lengthening of barrier width causes saturation of group delay. The Hartman effect was demonstrated in [12], where exchange spin waves of GHz frequency tunnelling through a barrier in a thin film of perpendicular magnetic anisotropy showed saturation for group delay after expanding the thickness of the barrierthis was calculated using the transmissivity of the spin waves (which the group delay depends on)…”

Voltage controlled on-demand magnonic nanochannels

“…Numerous strategies have been adopted for excitation, manipulation, channeling, and amplification of SWs, as well as the development of MCs and logic gates ( 7 ). Recently, SW tunneling, through a narrow magnetic barrier formed by local increase in magnetic anisotropy and the ensuing Hartman effect, has been demonstrated ( 28 ). On the other hand, the electrically controlled dynamic crystal has been presented in a magnetic insulator–based SW waveguide comprising a metallic meander structure situated close to its surface ( 29 ).…”