Nanoscale physics
Phenomenological theory of a spin wave damping in long-periodic structures
Bar’yakhtar V.G.1, Danilevich A.G.1, 2, Krivoruchko V. N.3
1 Institute of Magnetism NAS of Ukraine and MES of Ukraine, 36-b Vernadsky Str., 03142, Kyiv, Ukraine 
E-mail: alek_tony@ukr.net
2 National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37 Prosp. Peremohy, 03056, Kyiv, Ukraine

3 Donetsk Institute for Physics and Engineering named after O.O.Galkin NAS of Ukraine, 46 Nauki Ave., 03680, Kyiv, Ukraine

Spin waves in long-period structures demonstrate the so-called nonreciprocity properties, i.e., a non-invariance of dynamic characteristics when the sign of the wave vector is replaced with opposite. Motivated by recent experiments [1], we studied spin waves relaxation distinctive features in inhomogeneous long-period magnetic structures. 
Spiral magnetic structures with a large helicity step caused by the competitive exchange interactions or by the exchange-relativistic interactions are considered and related dissipative functions are constructed for such crystals of different symmetry. Within a general phenomenological approach [2], it is demonstrated that nonreciprocity not only leads to a difference in the phase velocities of spin waves with a given energy and opposite wave vectors relative to the selected direction, but also manifests itself in a different damping of these spin waves. It is shown that the non-invariance of dynamic characteristics of long-period magnetic structures should be taken into account when constructing the dissipation function for such systems.
Such nonreciprocity features of long-period magnetically ordered structures are fundamental to the creation of functional elements of quantum information processing based on the ideas of magnonics and magnetic spintronics.

1.	Seki S., Okamura Y., Kondou K., Shibata K., Kubota M., Takagi R., Kagawa F., Kawasaki M., Tatara G., Otani Y., Tokura Y. Magnetochiral nonreciprocity of volume spin wave propagation in chiral-lattice ferromagnets// Phys. Rev. B.-2016.-93.-P. 235131-1-235131-9.
2.	Bar’yakhtar V. G., Danilevich A. G. The phenomenological theory of magnetization relaxation// Low Temp. Phys.-2013.-39, N. 12.-P. 993-1007.