Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B2L-A

Session:

Number:360

Nonlinear Dynamics and Orbital Instabilities of a Magnetic Resonance Force Microscope Operating in Ultra-High Vacuum

O. Gottlieb,  E. Hacker,  F. R. Ruiz-Oliveras,  

pp.360-362

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.360

PDF download (335.2KB)

The focus of this paper is on the nonlinear dynamics of a micro-cantilever resonator model proposed for measurement of electron spin via magnetic resonance force microscopy. The resonator model, augmented by the Bloch equations for the magnetization, is analyzed numerically and compared to asymptotic results derived for a low order asymmetric adiabatic limit. Orbital instabilities include coexisting solutions and lengthy chaotic transients that occur below a homoclinic jump-to-contact threshold. A multiple-scales analysis of the limiting adiabatic model enables estimation of the threshold for bistable solutions, and prediction of the frequency shift that enables spin detection. A numerical investigation of the dynamical system reveals a global stability threshold beyond which solutions jump-to-contact with the sample. Below the threshold system response is primarily periodic with the exception of distinct solutions that exhibit lengthy nonstationary transients.

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