Between Quantum and Classical: Evolution of Electron Magnetic Resonance with Growth of a Spin System Size
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Between Quantum and Classical: Evolution of Electron Magnetic Resonance with Growth of a Spin System Size Brittany Bates1, James Hilton2, Carl Bonner1, and Natalia Noginova1 1 2
Norfolk State University, Norfolk, Virginia, USA Cornell University, Ithaca, New York, USA
ABSTRACT Systems with a single or several coupled electron spins are commonly described with the quantum approach while ferromagnetic domains with millions of coupled spins are classical systems. Large spin clusters and superparamagnetic nanoparticles contain hundreds of coupled electron spins, and are on the boundary between classical and quantum behavior. Electron magnetic resonance observed in ultra-fine iron oxide nanoparticles (~ 5 nm size) reveals several features which are typical for paramagnetic spins and absent in macroscopic systems, including multiple quantum transitions observed at H0/n, where n = 2, 3, 4 and H0 is the field of the main resonance. In order to better understand the transition from quantum to classical behavior and magnetization dynamics at the nanoscale, we study the evolution of the EMR signal with increase of the particle size in suspensions of magnetite nanoparticles. The experimental data are compared with numerical simulations. INTRODUCTION Systems with small number of electron spins, such as individual spins of paramagnetic impurity or several coupled spins are well described with quantum approach. By increasing a number of coupled spins, one can expect a transition from purely quantum to classical behavior, with strongly different thermodynamics and different shape of electron magnetic resonance (EMR) spectrum [1]. Magnetic nanoparticles containing hundreds or thousands of coupled spins are on the boundary between quantum and classical regimes. Commonly, magnetization dynamics and magnetic resonance in superparamagnetic nanoparticles are described from the classical point of view [2-4]. Recently, it was shown that the quantal approach based on “giant spin model” [5-7] can satisfactory describe the EMR lineshape and its temperature dependence in small magnetic nanoparticles [8-12]. In addition, this approach explains the presence of additional features in EMR spectra of nanoparticles, including the narrow component at H0 and transitions at H0/n, n=2, 3,4, where H0 is the field of the main resonance [10]. Such features are typical for small paramagnetic systems, where they are discussed in terms of multiple quantum resonance transitions [13] but have not been observed in classical ferromagnetic resonance (FMR). The goal of this work was to experimentally study the evolution of the EMR spectra as the function of the particle size and compare the results with the predictions of the “giant spin” model. Particular attention was paid to the evolution of “quantal” features with the increase in the particle size, in particular, a narrow central component and double quantum transition signals observed at the half of the main resonance field.
EXPERIMENTAL In our experiments we used iron oxide nanoparticles (NP) with sizes r
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