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Magnetostatic spin waves

The key feature doing CB unique, is their variance (drawing 1.3) which can be strongly aeolotropic depending on prevailing interaction between moments of magnet [1,2]. There are two basic interactions.

The first - kvantovomehanicheskoe the exchange interaction responsible for magnetic streamlining which prevails in nanometrovom a wave band and leads to the isotropic parabolic variance so-called. Exchange CB (OCB). In a gamut of lengths of waves from hundreds nanometrov and above CB are termed magnetostatic as in their variance aeolotropic prevails magnitodipolnoe interaction. In the intermediate gamut of lengths of waves, it depends exchange, and dipole energies considerably influence a variance, say, that CB have obmenno-DIPOLE character. In any case CB dvizhutsja with the characteristic velocities in some kilometres per second i.e. - are slow enough. However it also means, that on the same frequency they have much shorter wave length in comparison with electromagnetic waves that leads to idea of miniaturization of devices.

Spectrum MCB is by joint solution ULL (1.1), and combined equations of Maxwell for a degaussing field. As a rule approach of relative malosti velocities of distribution CB in comparison with a velocity of light in vacuo so homogeneity of an external field in the explored sample is not broken by retardation is thus used. In this case it is possible to neglect arising vortex electric field CB and to write down Maxwell equations in a view:

To zero of the right part second from the equations (1.10) the field hпотенциальным gives the chance to consider equality and to enter corresponding scalar function ι∕> for which h = ∖7τJjи the equation is valid

Termed Walker's as equation [7]. In it uravneniiopredeljaetsja from solution ULL (1.1).

Solutions of the equation of Walker (Lll) in bezobmennom magnetostatic approach, also are MCB [7]. Their amplitudes are spotted "sshivkoj" solutions of the equation of Walker (1.10) in different fields by means of continuity boundary conditions f and normal to boundary of a component of a vector of an induction of a magnetic field

For a finding of spectrum MCB in a film [2,4] equation of a magnetostatics (1.11) is solved taking into account dynamic communication between magnetisation and a degaussing field created to it, following of Landau-Lifshits's equation (1.1). As a rule, are thus restricted bezobmennym to approach, valid for not too small lengths of waves that allows to neglect a spatial dispersion in a dynamic tensor of a susceptibility. The relation between them also is used in (1.11).

Drawing 1.1. () Variance MCB constructed in one quadrant of return space for a film in a plane ug with magnetisation in a plane lengthways z. () the Curves of isofrequencies characterising distribution MCB, where

() the Curves of isofrequencies characterising distribution obmennodipolnyh SV,]

In various magnetic structures monographies [7,13] have been devoted a problem of distribution MCB. At distribution MCB a number of interesting effects is observed. One of them, featured in [14] and realised in [15] consists in equality to degaussing field zero on one leg of a film on which it is spread MCB with circular polarisation. Features nevzaimnosti distributions obmennodipolnyh waves in two-layer wave guides have been explored in operations [16,17].

Frequency CB with the perpetual wave length (to = 0) is termed as frequency of the ferromagnetic resonance (FMR), that corresponds to an energy gap in a spectrum of magnons. The incident wave on this frequency will be strongly related to a magnetisation precession in the sample, raising its homogeneous precessional mode. The constant magnetic field enclosed to the sample, shifts frequency FMR together with a dispersion curve. The direction and velocity of transmission of energy CB is spotted by their group velocity as a lapse rate of cyclic frequency in return space. Except an exterior magnetic field, group velocity CB essentially depends on a corner between BB and magnetisation. In particular - group velocity is subzero (is strictly antiparallel BB) for return volume SV, i.e. for a case of their distribution parallelly magnetisation. On the contrary - for CB Damon - Eshbaha with a direction, perpendicular magnetisations, group velocity is plus. Generally the direction of group velocity is convenient for spotting, using isofrequencies (curve constant frequency) [18]. Group velocity is always orthogonal to the isofrequency curves in return space the same as an electric field always orthogonally curve constant potential - in real. Dispersion anisotropy is stronger for MCB, and promptly decreases at wave length reduction.

1.3

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A source: Pojmanov Vladislav Dmitrievich. DISTRIBUTION, DISPERSION And GENERATION of SPIN WAVES To the NONUNIFORM MAGNETIC STRUCTURES. The dissertation on competition of a scientific degree of the candidate of physical and mathematical sciences. Donetsk - 2018. 2018

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  11. Pojmanov Vladislav Dmitrievich. DISTRIBUTION, DISPERSION And GENERATION of SPIN WAVES To the NONUNIFORM MAGNETIC STRUCTURES. The dissertation on competition of a scientific degree of the candidate of physical and mathematical sciences. Donetsk - 2018, 2018
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