Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 8
ContentsFull text in Russian (pdf)
DOI https://doi.org/10.30898/1684-1719.2020.8.
2UDC 537.874; 537.624
EXCITATION OF SPIN-WAVE RESONANCE IN THIN MAGNETIC FILMS IN THE ABSENCE OF SURFACE ANISOTROPY
V. I. Shcheglov
Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia
The paper is received on June 16, 2020
Abstract. The main result of this work is the interpretation of spin-wave resonance excitation by uniform alternating field in the case of the absence of surface anisotropy but on the basis of hardness of spin chain which is brought by non-uniform exchange interaction. In the geometry of normal magnetized film we investigated the classic variant of spin-wave resonance excitation on the basis of vibrations of change consisted from spins which are connected by exchange interaction. The task is solved about the vibrations of this chain in connection with the boundary conditions which consist of equality to zero of amplitude of vibrations on the film surfaces. These conditions correspond to attachment on spins on these surfaces. Based on the analysis of the overlap integral, it is shown that excitation is possible only of those modes for which an odd number of half-waves of oscillations fit over the film thickness. The insufficiency of the surface anisotropy model for the interpretation of a number of experimental results is noted. It is noted that in all versions of this model, there is no account of the hardness of the spin chain due to the exchange interaction. A model of spin chain vibrations is proposed, based on taking into account the hardness of the spin chain without introducing surface anisotropy. As a simplified analogy, a mechanical model of vibrations of a hard string is presented. It was found that the manifestation of string hardness consists in the emergence of a straighten force opposing the bending of the string. It is shown that the rectifying force is proportional to the second derivative of the displacement of the string along the coordinate along its main direction. A wave-type equation is obtained for the vibrations of a hard string, which contains the second-order coordinate and time derivatives in combination with a third-order derivative of the string displacement along the coordinate. It is noted that the third-order derivative corresponds to a straighten force that prevents the string from bending. The solution of the obtained third-order equation is performed by the method of separation of variables. Boundary conditions are proposed, which consist in the absence of a straighten force, that is, in the equality to zero of the second derivative of the coordinate displacement at the ends of the string. It is shown that taking into account the proposed boundary conditions leads to a solution that is a discrete set of modes, similar to that for a string with fixed ends, the main difference being the absence of such a fixation. The results obtained on the mechanical model were applied for analyzing vibrations of a chain of spins coupled by exchange interaction in a normally magnetized thin film. It is established that the field of non-uniform inhomogeneous exchange interaction is proportional to the second derivative of the transverse component of the magnetization along the coordinate along the chain. It was found that such a field is a mechanism for the generation of a force that straightens the spin chain during its bending. Boundary conditions are proposed, consisting in the absence of a straighten force, that is, in the equality to zero on the film surfaces of the second derivative of the transverse magnetization. Taking into account the boundary conditions, a discrete spectrum of vibration modes was found, similar to that obtained using the surface anisotropy model with the main difference being the absence of spin pinning on the film surfaces. Some recommendations are given for the further development of the hard spin chain model.
Key words: spin-wave resonance, exchange interaction, curvature hardness.
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For citation:
Shcheglov V.I. Excitation of spin-wave resonance in thin magnetic films in the absence of surface anisotropy. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 8. https://doi.org/10.30898/1684-1719.2020.8.2 (In Russian)