Magnetic resonance of nanoparticles in a ferrofluid: evidence of thermofluctuational effects

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Abstract

Ferromagnetic resonance (FMR) experiments on non-interacting maghemite (γ-Fe2O3) nanoparticles in ferrofluids, are performed in X- and Q-bands as a function of the particle diameter (4.8–10 nm) and the temperature (3.5–300 K). The colloidal stability and grain size are controlled through a chemical synthesis, the polydispersity being reduced by a phase separation method. The dependencies of spectral characteristics with temperature T, particle volume V and experimental frequency ω, reveal a generic behavior of the FMR lines due to the effect of thermal fluctuations. Their scaling with the Langevin parameter ξ0=MVω/γkBT is explained in the framework of the theory of FMR for an assembly of independent single-domain anisotropic particles.

Introduction

Two main mechanisms specifically affect the magnetic behavior of nanosize particles [1], [2], viz. (i) their enhanced sensitivity to thermal fluctuations [3], [4], [5] and (ii) the importance of surface and interface effects [6], [7]. Indeed, due to their small size, the magnetic anisotropy energy Ea, being proportional either to the volume or to the surface of the particle, may become comparable with the thermal energy kBT. The global magnetic moment μ in a single-domain particle is then subjected to orientational fluctuations, including those which reverse its direction. This thermally activated effect, called superparamagnetism, was first predicted by Néel [3], [4]. Magnetodynamics of fine particle systems have been studied through AC susceptibility measurements [8], magnetization measurements [9], Mössbauer spectroscopy [10], [11], [12] and inelastic neutron scattering [7], [13]. Beside these, ferromagnetic resonance (FMR) is a standard method to study magnetodynamics in presence of the distribution of the internal anisotropy barriers [14]. This technique is directly sensitive to the local fields experienced by μ. A consistent theory of FMR in a suspension of single-domain particles has been developed recently [15], [16], [17], [18]. However, experiments on FMR in fine particles [19], [20], [21], [22], [23], [24], [25], [26], [27], [28] are yet far from being numerous and have never been compared to the improved theory insofar. In a previous paper [28], the FMR behavior of chemically synthesized γ-Fe2O3 nanoparticles dispersed in a ferrofluid has been investigated and discussed in the low-temperature range. The size dependencies of spectral characteristics point out from one side that the anisotropy energy is proportional to the particle surface and from the other side that magnetic disorder at the particle surface plays a significant role in the low-temperature dynamics. However, above some specific temperature and depending on the particle size, complex FMR line shapes were observed revealing thermofluctuational effects. The purpose of the present paper is to focus on the effects of thermal fluctuations on the FMR behavior of maghemite nanoparticles.

In Section 1, we describe our system of size-selected and isolated γ-Fe2O3 particles in a ferrofluid. In Section 2, the influence of thermal fluctuations on the FMR behavior is experimentally evidenced through the correlated action of three parameters, namely, temperature T, particle diameter d and excitation frequency ω. Finally in Section 3, the generic scaling of FMR in nanosize particles with the dimensionless parameter ξ0=MVω/γkBT is shown. The experimental manifestations of thermal fluctuations are compared with the predictions of the FMR theory for an ideal superparamagnet.

Section snippets

Presentation of the samples

We study anionic ferrofluids [29] composed of γ-Fe2O3 (maghemite) chemically synthesized particles, dispersed in glycerol. The synthesis parameters such as temperature, initial molar ratio Fe3+/Fe2+ and pH allow to control the mean size of the magnetic grains. The particles are also macro-ions with a negative superficial density of charge. Thus screened electrostatic repulsions between particles ensure the colloidal stability. The isolated character of the grains is indeed confirmed by SANS [30]

Experimental setup and procedure

FMR experiments are performed with a Varian E102 spectrometer at 9.26 GHz and a Bruker spectrometer at 34.2 GHz. The modulation field has the frequency 100 kHz and amplitude 10 Oe. The first derivative dW/dH of the power absorption W is recorded as a function of the applied field H in the range 0–20 kOe. Very small quantities (microliters) of highly dilute ferrofluids (Φ=10−3–1%) are used in order to prevent the radio-frequency field lines distortion. Sample cooling is performed with the aid of

Discussion

The magnetodynamics of the system is governed by the anisotropy energy Ea=KSS [28] and the magnetic energy MVH, where H is the external field. The dimensionless parameters σ=KSS/kBT and ξ=MVH/kBT account for the strength of thermal orientational fluctuations.

The values of σ and ξ0 are given in Table 2 for the particle sizes and for a set of temperatures of the experiment. The σ values are evaluated with the constant KS=2.2×10−2 erg/cm2 deduced from the FMR angular variations at T=200 K; the ξ0

Conclusions

We show that well-understood features prove the sensitivity of the Larmor precession of the magnetic moment to fluctuations, which make the internal fields vanish at elevated temperatures. The relevant parameter to describe the linewidth and the resonance field is ξ0=MVω/γkBT. In the FMR spectra of γ-Fe2O3 particles we observe a superparamagnetic isotropic line existing only for σ=KSS/kBT⩽2 and ξ0⩽15. Angular variations performed on FC samples demonstrate that anisotropy does not affect this

Acknowledgements

We are grateful to B. Boizot, from the Laboratoire de Minéralogie-Cristallographie de Paris, for his kind help in the Q-band measurements. We also thank J.L. Dormann and M. Rivoire for fruitful discussions and J. Lannuza and P. Lepert for their technical assistance. This work was supported by `Le Réseau Formation-Recherche’ No. R0933 of Menesrip and from the Russian side–by the grant No. 96-02-16716 of RFBR.

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