Dipole-exchange propagating spin-wave modes in metallic ferromagnetic stripes

Kostylev, Mikhail; Gubbiotti, G.; Jia, Hu; Carlotti, G.; Ono, Teruo; Stamps, R. L.

doi:10.1103/physrevb.76.054422

Cited by 98 publications

(70 citation statements)

References 24 publications

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“…4,9,23 Consequently, the mode numbers are expected to be larger for the x-direction than for the y-direction of the same pillar, and possibly different for easy and hard axis applied field.…”

Section: Quantization Of In-plane Wavevectormentioning

confidence: 99%

Quantized spin-wave modes in magnetic tunnel junction nanopillars

et al. 2010

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We present an experimental and theoretical study of the magnetic field dependence of the mode frequency of thermally excited spin waves in rectangular shaped nanopillars of lateral sizes 60 × 100, 75 × 150, and 105 × 190 nm 2 , patterned from MgO-based magnetic tunnel junctions. The spin wave frequencies were measured using spectrally resolved electrical noise measurements. In all spectra, several independent quantized spin wave modes have been observed and could be identified as eigenexcitations of the free layer and of the synthetic antiferromagnet of the junction. Using a theoretical approach based on the diagonalization of the dynamical matrix of a system of three coupled, spatially confined magnetic layers, we have modeled the spectra for the smallest pillar and have extracted its material parameters. The magnetization and exchange stiffness constant of the CoFeB free layer are thereby found to be substantially reduced compared to the corresponding thin film values. Moreover, we could infer that the pinning of the magnetization at the lateral boundaries must be weak. Finally, the interlayer dipolar coupling between the free layer and the synthetic antiferromagnet causes mode anticrossings with gap openings up to 2 GHz. At low fields and in the larger pillars, there is clear evidence for strong non-uniformities of the layer magnetizations. In particular, at zero field the lowest mode is not the fundamental mode, but a mode most likely localized near the layer edges.

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Section: Quantization Of In-plane Wavevectormentioning

confidence: 99%

Quantized spin-wave modes in magnetic tunnel junction nanopillars

et al. 2010

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“…The theoretical description of the observed phenomena is based on concepts developed in Refs. [9] and [10]. The ingredients of the model are (i) effective dipole pinning of magnetization, which results in a tri-linear interaction as the initial interaction for development of the transverse instability of the wave packet profile, (ii) the widthmode group velocity matching, and (iii) the nonlinear extension of spectrum of width modes.…”

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confidence: 99%

“…In Ref. [9], we theoretically studied linear propagating eigenwaves of a magnetic stripe. The eigenwaves represent guided modes with discrete transverse wavenumbers.…”

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confidence: 99%

Formation of Guided Spin-Wave Bullets in Ferrimagnetic Film Stripes

2008

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The formation of quasi-2D nonlinear spin-wave eigenmodes in longitudinally magnetized stripes of a ferrimagnetic film, so-called guided spin-wave bullets, was experimentally observed by using timeand space-resolved Brillouin light scattering spectroscopy and confirmed by numerical simulation. They represent stable spin-wave packets propagating along a waveguide structure, for which both transversal instability and interaction with the side edges of the waveguide are important. The experiments and the numerical simulation of the evolution of the spin-wave excitations show that the shape of the formed packets and their behavior are strongly influenced by the confinement conditions. The discovery of these modes demonstrates the existence of quasi-stable nonlinear solutions in the transition regime between one-dimensional and two-dimensional wave packet propagation.PACS numbers: 75.30. Ds, 76.50.+g, 85.70.Ge Stable two-dimensional localized nonlinear spin-wave excitations, so-called spin-wave bullets, have been previously observed in thin ferrimagnetic films of yttriumiron-garnet (YIG) magnetized along the propagation direction [1,2,3]. These films were practically unbounded in both in-plane directions compared to the transversal size of the spin-wave packets and the wavelength of the carrier spin wave. In contrary, in a one-dimensional waveguide structure, where the width is comparable to or smaller than the spin-wave wavelength, only quasi onedimensional nonlinear spin-wave objects were observed, which are spin-wave envelope solitons. [4,5]. Both for solitons and bullets linear pulse spreading in the direction of propagation (so called longitudinal direction) due to wave dispersion is compensated by longitudinal nonlinear compression. As for the transverse in-plane direction, solitons are meant to have a stable transverse distribution of their dynamic magnetization coinciding with the profile of the lowest linear spin-wave eigenmode of the waveguide. On the contrary, bullets show transverse nonlinear instability of attractive type which overcompensates transverse diffraction broadening of the wave packet. The nonlinear compression would lead to a wave packet collapse if the medium is lossless. Weak magnetic losses in a real magnetic film ensure a fine balance of nonlinear narrowing of the packet and of its diffraction spreading for some distance of propagation [1]. This results in a quasi-2D spatially localized bell-shaped waveform which is stable during the lifetime of the bullet.Here we report on the experimental observation of a stable spin-wave packet propagating along a waveguide structure, for which both transversal instability and interaction with the side edges of the film waveguide are crucial. The structure can be considered as a transitional case between the 2D case of a continuous film and the quasi-1D case of a narrow stripe. We show that in this case the nonlinear wave dynamics is distinctively different from both the soliton and the bullet cases, and can be considered as efficient coherent nonlin...

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“…2 it is well seen that any averaging by thickness, used by authors in Refs. [6][7][8] is impossible in the case of an arbitrary magnetized magnonic waveguide. In this case the full account of two-dimensional distribution of the internal magnetic field have to be done in order to describe correctly the conditions of spinwaves propagation.…”

Section: Static Problemmentioning

confidence: 99%

“…[6][7][8], our exact tensorial Green's function have all nine nonzero components and describes the nonuniform dipole field in the arbitrary magnetized magnonic waveguide with any width-thickness aspect ratio (even equal unity).…”

Section: Theoretical Modelmentioning

confidence: 99%

Some peculiarities of spin-wave propagation in magnonic waveguides

Grigoryeva

Popov

Kalinikos

2013

EPJ Web of Conferences

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Abstract.A normal-mode theory for the dipole-exchange spin-wave spectrum in the finite-width ferromagnetic waveguide is presented. The theory takes into account a nonuniform character of the demagnetizing field in the waveguide cross section and, therefore, can be applied to any infinitely long, rectangular rod, even with square cross section. The inhomogeneity of static and dynamic dipole fields is taken into account using the same tensorial Green's function, obtained from Maxwell equations, this fact allows to simplify the spectrum calculation procedure. According to the elaborated theory the spin-wave spectrum in the finite-width ferromagnetic waveguide can be calculated with simultaneous account of the dipole-dipole and exchange interaction, surface anisotropy, arbitrary direction of the external bias magnetic field and for any possible width-thickness aspect ratio of the magnonic waveguide. It is shown that the previously used analytical methods of the accounting of the finite width of the magnetic waveguides give unsuitable results for nanometer-size waveguides.

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Dipole-exchange propagating spin-wave modes in metallic ferromagnetic stripes

Cited by 98 publications

References 24 publications

Quantized spin-wave modes in magnetic tunnel junction nanopillars

Quantized spin-wave modes in magnetic tunnel junction nanopillars

Formation of Guided Spin-Wave Bullets in Ferrimagnetic Film Stripes

Some peculiarities of spin-wave propagation in magnonic waveguides

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