Материал: Маслов ИНТРОДУЦТИОН ТО ПХЫСИЦС ОФ СЕЦОНД-ОРДЕР МАГНЕТИЦ 2015

where u and v are constants, p is the whole number, k is the wave vector and a is the lattice constant. Upon substitution of Eqs. (30.8) to Eqs. (30.7), we obtain

These equations have the nontrivial solution if

This determinant defines the spin wave dispersion ω(k ). It has the following form

From the solution obtained one can see that v = −iu , i.e., the solution describes the spin precession relative to the z-axis.

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Literature

1.Kittel C. Introduction to Solid States Physics. 8th ed. John Wiley

&Sons, 2004.

2.Kittel C. Quantum Theory of Solids. Second Revised Printing. John Wiley & Sons, 1987.

3.Landau L.D., Lifshitz L.M. Quantum Mechanics: NonRelativistic Theory (Volume 3). 3rd ed. Butterworth-Heinemann, 1981.

4.Landau L.D., Lifshitz L.M. Statistical Physics (Volume 5). 3rd ed. Butterworth-Heinemann, 1980.

5.Aharoni A. Introduction to the Theory of Ferromagnetism. 2nd ed. Oxford University Press, 2001.

6.Miyazaki T., Jin H. The Physics of Ferromagnetism. Springer,

2012.

7.Kronmüller H., Fähnle M. Micromagnetism and the Microstructure of Ferromagnetic Solids. 1st ed. Cambridge University Press, 2009.

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