Non-Langevin high-temperature magnetization of nanoparticles in a weak magnetic field
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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS
Non-Langevin High-Temperature Magnetization of Nanoparticles in a Weak Magnetic Field M. A. Chuev Institute of Physics and Technology, Russian Academy of Sciences, Moscow, 117218 Russia e-mail: [email protected]; [email protected] Received July 10, 2008
Abstract—Experimental evidence and theoretical substantiation are presented for the asymptotic behavior of high-temperature magnetization of an ensemble of nanoparticles in a weak magnetic field, which was predicted earlier and which differs qualitatively from the “Langevin” limit for ideal superparamagnetic particles. It is shown that the physical reason for the new asymptotic behavior is the temperature-independent “positive” tilt of the uniform magnetization vector at local energy minima in the direction of the field; this asymptotic behavior is associated with the nonstandard thermodynamics of single-domain particles, which depends on the ratio of characteristic frequencies of regular precession and random diffusion of this vector. An alternative approach is proposed for describing the magnetic dynamics of an ensemble of nanoparticles in a magnetic field, and the precession orbits of the magnetization vector are considered as stochastic states of each particle, whereas each state is characterized by the trajectory-averaged value of magnetization. PACS numbers: 61.46.-w, 75.50.Tt, 75.60.Ej, 61.05.Qr DOI: 10.1134/S1063776109020071
1. INTRODUCTION Systematic investigations of the structural and magnetic properties of materials containing magnetic particles or clusters of small size (on the order of a few nanometers) are mainly necessitated by the wide range of their application in nanotechnology for magnetic and magnetooptical data recording systems, ferroliquids, NMR tomography, chemical catalysis, color image devices, biotechnologies, etc. Naturally, such investigations are based on the previously established fundamental regularities of magnetism observed in ensembles of nanometer-size magnetic particles. Quantitative analysis of experimental data measured on specific materials requires a model of magnetic dynamics to describe the magnetic properties of this material with the help of a certain number of physical parameters. In developing such a phenomenological model of magnetic dynamics [1] suitable for numerically analyzing a large body of experimental data on the temperature dependences of magnetization for various systems of small particles or nanoclusters, a nontrivial fundamental dependence (namely, asymptotic high-temperature behavior of magnetization and susceptibility in a weak magnetic field, which differs qualitatively from the classical Langevin limit for ideal superparamagnetic particles [2]) has been obtained recently in addition to a qualitative description of the form of experimental dependences. In this model, the resultant magnetization of an
ensemble of particles in a weak external field H at a high temperature T is expressed as [1] 1 M ( T ) = --- M 0 ( T ) [ 2h + x ( T ) ] 3 M 0 ( T )H ⎛ KV - 1
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