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Model for the envelopes of spin waves in magnetic film feedback rings, A
Anderson, Justin Carr, Lincoln D. Wu, Mingzhong
Anderson, Justin
Carr, Lincoln D.
Wu, Mingzhong
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2010
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Abstract
Experimental observation of spin wave envelopes(SWE) in magnetic thin films necessarily occurs in non-conservative systems. The generation of time-stable results is realized by approximating conservation through active feedback, or otherwise driving the system into equilibrium with its major linear loss mechanisms. A rich variety of SWE nonlinear dynamics have successfully been observed in "conservative" systems of this form, including chaos, soliton formation, and more recently, a chaotic modulation of solitary wave train envelopes. The dynamics of these "conservative" systems have often been modeled by a 1D Ginzburg-Landau Equation (GLE) of the general form, -d_t Phi=(Dd_xx+N|Phi|^2)Phi, where D and N are real parameters corresponding to the system's inherit dispersion and nonlinearity, respectively, and Phi is the SWE wavefunction. Extension to multiple dimensions is the trivial introduction of a Lapacian operator in place of the spatial derivative. The GLE is a fully conservative equation which has succeeded in modeling SWE solitons in these dissipative systems. However, the cubic GLE does not yield chaos and the severity of the nonlinear term, which is a function of the wavefunction normalization, exhibits time dependence in any dissipative system due to loss and gain. A driven damped model is proposed to overcome the shortcomings of the traditional GLE and is studied numerically in the context of the chaotic modulation of solitary waves. The model is a cubic, quintic complex GLE (CGLE) with constant gain, -d_t Phi=(Dd_xx+(N+iG) |Phi|^2-iL-(Q+iS)|Phi|^4)Phi, where all constants, D, N, G, L, Q, S, are real. This modification of the GLE introduces higher order nonlinearity and a gain/loss mechanism at linear, cubic, and quintic orders. A preliminary investigation of the CGLE is reported and a qualitative agreement of simulations with experimental observation is demonstrated. A saturation of cubic nonlinearity, of the four-wave process, is suggested as the driving force behind the chaotic modulation of magnetic SWE solitary waves, and predictions of experimentally achievable chaotic domains are presented. This work is supported by the U.S. National Science Foundation.
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