INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 34 (2001) 1612–1616 www.iop.org/Journals/jd PII: S0022-3727(01)19222-3 The estimation of the signal-to-noise ratio of a nanoparticle P C Fannin 1 and Y L Raikher 2 1 Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland 2 Laboratory of Complex Fluids, Institute of Continuous Media Mechanics, Ural Division of RAS, Perm 614013, Russia Received 21 November 2000 Abstract The quality of a single-domain nanoparticle as a signal processing device is estimated with the aid of the signal-to-noise ratio (SNR) characteristic. In the absence of an external field, the magnetic moment of a uniaxial particle flips spontaneously between two anti-parallel equilibrium positions ensuing customary superparamagnetism. On imposition of an external ac field, it, together with random noise, influences the magnetic switching and the SNR can be found in the framework of micromagnetic theory. The main material parameters essentially involved in the resulting expression are, the N´ eel relaxation time, τ N , the precessional decay time, τ 0 , and also the magnetic viscosity coefficient, η m . In the paper we find these quantities by measuring the complex magnetic susceptibility as a function of frequency and polarizing field. Using these data, we estimate the SNR for the nanometre-size grains of a cobalt ferrofluid. 1. Introduction In recent years considerable advances have been made in the theory of field-driven fluctuating oscillatory systems, giving rise to the so-called stochastic resonance (SR) theory, which by now has a number of specific variants and modifications, both linear and nonlinear [1]. This line of research is distinguished by a high extent of universality and, consequently, a tremendous diversity of applications. The main model object in the SR theory is an overdamped bistable oscillator in a thermal (or other fluctuation-producing) bath. As is often the case, a new line of research creates its own thesaurus. In particular, in this context, even the notion as fundamental as resonance has been transformed, and no longer can be described as being just a drastic increase of the oscillation amplitude upon coincidence of the frequency of the driving force with some eigenfrequency. In fact, in the modern scientific parlance stochastic resonance refers to the maximization of the response of a fluctuating oscillatory system in response to increasing noise intensity. One of the best definitions has been given by Fox [2], who describes SR as ‘noise-induced signal-to-noise ratio enhancement’. Unfortunately, with the passing of time, considerable confusion with the terms has arisen. For example, the development of SR theory has brought in the effect dubbed noise-induced resonance (NIR) [3, 4], which is totally different from what is conventionally understood to be SR. Indeed, the precise meaning of NIR is as follows. Due to nonlinearity of the system, the spectrum of its response to a periodic excitation contains multiple harmonics. It turns out that the amplitudes of the higher harmonics behave in a non-monotonic way with the growth of the fluctuation intensity D. Namely, they decrease to zero (or pass a minimum) at certain values of D. This ability of the harmonic amplitude (or its spectral power density) to undergo a minimum when D is increased is what is actually called NIR. In other words, the NIR effect is not at all a selective enhancement of a response at some eigenfrequency but a way to selectively suppress any given harmonic in the response spectrum by changing the level of noise, such as by heating the system. Notwithstanding all the theoretical achievements, there are very few real systems where the conditions for the occurrence of the effects of the SR family can be easily created and verified experimentally. Of those, ring lasers and Josephson junctions are referred to, but a great majority of scholars either restrict themselves to numerical simulations or, at best, perform modelling with the aid of ad hoc constructed analogue electric schemes. Meanwhile, single- domain superparamagnetic particles (in both fluid or solid matrices) are an important class of real physical systems, where the SR effect should manifest itself straightforwardly. Consider a fine particle of the volume V with the magnetization M S and uniaxial magnetic anisotropy characterized by the energy volume density K and the easy 0022-3727/01/111612+05$30.00 © 2001 IOP Publishing Ltd Printed in the UK 1612