Magnetic Spin-Wave Properties of Ferromagnetic Nanosystems of Various Shapes. Peculiarities of the Border Conditions Accounting in the Process of the Wavenumber Values Spectrum Finding




Spin waves, Nanomagnetism, Dipole-exchange theory, Boundary conditions


Background. The paper continues the investigation of linear dipole-exchange spin waves in ferromagnetic nanosystems started by the author in previous papers. The known papers investigating dipole-exchange spin waves obtain their spectral characteristics only for a narrow range of special cases. In the presented paper, an approach that allows expanding substantially this range of cases is described and applied.

Objective. The aim of the paper is to develop a method – based on the use of boundary conditions – for obtaining the spectral characteristics of dipole-exchange spin waves in a number of nanosystems’ configurations as well as an application of this method to specific configurations.

Methods. A method for obtaining a values’ spectrum of the wavenumbers for dipole-exchange spin waves in ferromagnetic nanosystems of a series of typical configurations is proposed. The method does not require specific assumptions, e.g. the absence of transverse spin excitations or the presence of a high-conductivity metal outside the ferromagnet. The method uses imposition of boundary conditions for the magnetic field and the magnetization on the boundary of the ferromagnetic medium for a linear spin wave in the magnetostatic approximation. This method allows obtaining the above-mentioned spectral characteristics for a wider range of cases compared to the known previous papers.

Results. The results of the paper are conditions for the magnetic potential – that imply from the above-mentioned boundary conditions – of a linear spin wave on the boundary of a ferromagnetic nanosystem as well as the spectrum of the wavenumbers’ values of such wave for the investigated nanosystems (in the implicit form). In particular, for a ferromagnetic nanosystem of an arbitrary cross section with a one-dimensional translational symmetry, the conditions specifying this spectrum are found. Such conditions are specified – and an implicit expression for this spectrum is obtained – for the case when such nanosystem is a nanotube with a circular cross section. The analysis of the obtai­ned results is carried out.

Conclusions. The obtained expressions for the spectrum of the values of the investigated spin waves’ wavenumbers can be used for a wider range of cases than the ones obtained in the previous papers dedicated to the investigated configurations of nanosystems. For a nanotube of the circular cross-section with small (compared to the inverse characteristic size of the nanotube cross-section) values of the longitudinal wave number, the dependence of the latter on the transverse wave number is weak, as well as for the big longitudinal to transverse wavenumber component ratio. The obtained dependence is also represented graphically.









M. Madami et al., “Direct observation of a propagating spin wave induced by spin-transfer torque”, Nature Nanotechnol., vol. 6, pp. 635–638, 2011. doi: 10.1038/nnano.2011.140

T. Schneider et al., “Realization of spin-wave logic gates”, Appl. Phys. Lett., vol. 92, 022505, 2008. doi: 10.1063/1.2834714

V.V. Kruglyak et al., “Magnonics”, J. Phys. D: Appl. Phys., vol. 43, 264001, 2010. doi: 10.1088/0022-3727/43/26/260301

S.D. Bader and S.S.P. Parkin, “Spintronics”, Annu. Rev. Condens. Matter Phys., vol. 1, pp. 71–88, 2010. doi: 10.1146/annurev-conmatphys-070909-104123

M. Bauer et al., “Observation of spatiotemporal self-focusing of spin waves in magnetic films”, Phys. Rev. Lett., vol. 81, 3769, 1998. doi: 10.1103/PhysRevLett.81.3769

R. Arias and D.L. Mills, “Theory of spin excitations and the microwave response of cylindrical ferromagnetic nanowires”, Phys. Rev. B., vol. 63, 134439, 2001. doi: 10.1103/PhysRevB.63.134439

F.G. Aliev et al., “Spin waves in circular soft magnetic dots at the crossover between vortex and single domain state”, Phys. Rev. B., vol. 79, 174433, 2009. doi: 10.1103/PhysRevB.79.174433

Y.I. Gorobets and V.V. Kulish, “Dipole-exchange spin waves in a periodically layered ferromagnetic nanotube”, Functional Materials, vol. 20, pp. 516–522, 2013. doi: 10.15407/fm20.04.516

Yu.I. Gorobets and V.V. Kulish, “Dipole-exchange spin excitations in a thin ferromagnetic nanoshell”, Cent. Eur. J. Phys., vol. 3, pp. 375–379, 2013. doi: 10.2478/s11534-013-0172-x

V.V. Kulish, “Spin waves in an arbitrary ferromagnetic nanosystem with a translational symmetry. Nano-tube with a round cross-section. Nanotube with an elliptic cross-section”, Zhurnal Nano- ta Elektronnoyi Fizyky, vol. 6, 02021, 2014 (in Ukrainian).

V.V. Kulish, “Spin waves in a ferromagnetic film with a periodic system of antidots”, Zhurnal Nano- ta Elektronnoyi Fizyky, vol. 7, 01020, 2015 (in Ukrainian).

Yu.I. Gorobets and V.V. Kulish, “Spin excitations in ‘nanorice’-type ferromagnetic nanoshell”, Metalofizyka ta Novitni Tekhnologii, no. 8, pp. 1023–1033, 2014 (in Ukrainian).

/* Style Definitions */


{mso-style-name:"Обычная таблица";





mso-padding-alt:0cm 5.4pt 0cm 5.4pt;





font-family:"Times New Roman";