Spin-wave dispersion in two-layer magnetic films

Zyuzin, A. M.; Sabaev, S. N.; Kulyapin, A. V.

doi:10.1134/1.1635504

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…) This reduction is not correct in the vicinity of the sample boundary ∂ V . The linearized Landau-Lifshitz equations (21) with differential operators Ê± ( r , ω) given by relation (30) are used in [8,9,[32][33][34][35]. For solvability of these equations the exchange boundary conditions are imposed:…”

Section: Dispersion Relations and Exchange Boundary Conditionsmentioning

confidence: 99%

“…Taking into account the forms of Pand ˆ -matrices (35), (36), we perform the polynomial decomposition of the determinant (37) with respect to ¯ C D . Then, neglecting higher orders and holding linear terms containing ¯ C D in the decomposition, we obtain that the term with ¯ (1+)(1−) , which is determined by two diagrams in figure 5(a), makes a major contribution to the pole singularity of the P ( ) -matrix.…”

Section: Approximation Of Small Longitudinal Wavevectors: Q Qmentioning

confidence: 99%

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Landau–Lifshitz equations and relaxation of spin wave modes in the Heisenberg model with dipole–exchange interaction

Lutsev¹

2005

J. Phys.: Condens. Matter

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Landau-Lifshitz equations and spin wave damping are derived from first principles by the spin operator diagram technique for the Heisenberg model with magnetic dipole and exchange interactions. It is found that spin excitations, which are determined by poles of effective Green functions, are given by solutions of the linearized pseudodifferential Landau-Lifshitz equations and the equation for the magnetostatic potential. For a normal magnetized ferromagnetic film the spin wave damping has been calculated in the oneloop approximation for a diagram expansion of the Green functions at low temperature. In the framework of the Heisenberg model the magnetic dipole interaction makes a major contribution to the long-wavelength spin wave relaxation in comparison with the exchange interaction. It is found that the damping decreases with increasing film thickness and applied magnetic field and increases directly proportionally to the temperature. For modes of high orders the damping is higher than for the first spin wave mode.

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