[en] 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

[en] The effect of a deterministic behavior of the molecular angular momentum between molecular collisions on the shapes of the resonance absorption spectra and the curves of synchrotron-radiation-based perturbed angular correlations (SRPAC) is considered and taken into account for description of the chaotic reorientation of 'molecular' axes in fluids, in contrast to the standard statistical approaches employed previously for the interpretation of data of Moessbauer spectroscopy and recently developed SRPAC techniques. A general formalism is proposed for the calculation of the Moessbauer spectra and SRPAC curves in the presence of time-dependent hyperfine interactions. This formalism is used to describe the fluctuating quadrupole interaction within the framework of two models of the deterministic behavior of the principal axis of the electric field gradient tensor, which either rotates or oscillates (at an arbitrary angle) about some axis. Nontrivial transformation of the Moessbauer spectra and SRPAC curves depending on the parameters in both models is demonstrated, which describes the qualitatively different physical natures of the rotational dynamics and the corresponding resonance effects in fluids. In some limiting cases, simple analytical expressions are obtained that describe the Moessbauer spectra and SRPAC curves in terms of the effective constants of the quadrupole interaction and the rotational splitting of the main spectral lines. The revealed features of the hyperfine structure formation should be taken into account in developing models used for the analysis and interpretation of experimental data

[en] A multi-level stochastic model taking into account the magnetic anisotropy, precession and diffusion of the uniform magnetization of single-domain particles is developed in order to describe the Moessbauer absorption spectra of an ensemble of magnetic nanoparticles in the presence of quadrupolar hyperfine interaction with an arbitrary orientation of its principal axes. This model allows one to take into account physical mechanisms for forming the hyperfine structure in a real situation and can be easily realized even on a personal computer. In particular, now one can numerically describe qualitative features of temperature evolution of the Moessbauer spectral shape from a 'symmetric' magnetic sextet to a quadrupolar doublet of lines, which has been observed in a large number of experimental spectra of ⁵⁷Fe nuclei in magnetic nanoparticles for almost half a century. (paper)

[en] A theory is developed for the Mössbauer absorption spectra of an ensemble of single-domain particles in a magnetic field. This theory is based on the generalization of a relaxation model with a quantummechanical description of the stationary states of a particle and on the formalism of Liouville operators for describing the hyperfine interaction for a hyperfine field changing in both the magnitude and direction for various stationary states. The general scheme of calculating relaxation Mössbauer spectra in terms of a standard stochastic approach is substantially optimized using operations with block matrices and a unique tridiagonalization of high-rank non-Hermitian matrices with a simple nonorthogonal transformation in the calculation procedure. The resulting model can easily be implemented on a personal computer. It considers the physical mechanisms of formation of a hyperfine structure in a spectrum of nanoparticles in a real situation and self-consistently describes the qualitative features of the nontrivial evolution of spectra with the temperature and the magnetic-field direction and strength, which has been detected in ⁵⁷Fe nucleus experiments performed on magnetic nanoparticles for half a century.

[en] A three-level stochastic model taking into account the magnetic anisotropy, precession and diffusion of uniform magnetization of single-domain particles is developed in order to describe the Moessbauer absorption spectra of an ensemble of magnetic nanoparticles in a weak magnetic field. In contrast to conventional approaches searching for a distribution of the hyperfine field at nuclei, this model allows one to take into consideration physical mechanisms of formation of the magnetic hyperfine structure within the magnetic dynamics inherent to such materials. A number of qualitative effects observed in experimental Moessbauer spectra taken on small magnetic particles even in zero magnetic field can be self-consistently explained within the model in terms of the mean-field interparticle interaction. In particular, this model predicts the appearance of ⁵⁷Fe magnetic sextets with a small hyperfine splitting slightly dependent on the particle size and temperature in a weak magnetic field and at high temperature, which look like effective 'doublets' of lines often observed in experimental spectra.

[en] A standard multi-level relaxation model of magnetic dynamics of single-domain particles together with recently developed quantum-mechanical and continual models of specific thermo- and magnetic dynamics of antiferromagnetic particles were applied to analyse temperature series of Mössbauer spectra of Fe_2O_3 based nanoparticles. Advantages of these models, their comparison and further generalizations are discussed on the example of the particular experimental data.

[en] The influence of the rotation of a particle's magnetic moment in the magnetic anisotropy field on the shape of the Moessbauer spectra of hyperfine structure is analysed theoretically. It is found that, due to rotation, a renormalization of the nuclear g-factors occurs, which results in a qualitative transformation of Moessbauer absorption spectra. In particular, along with the magnetic sextet which is well known in the Moessbauer spectroscopy of the ⁵⁷Fe isotope, partial spectra can be formed that consist of 'magnetic' quintuplet, quartet, triplet and even doublet lines. This peculiarity in forming the spectra of magnetic hyperfine structure should be taken into account in analysing the Moessbauer spectra of materials with nano-sized magnetic particles

[en] Magnetic relaxation effects revealed in Moessbauer spectra and magnetization measurements of nanoparticles are discussed in the framework of specific models for magnetic dynamics of an ensemble of single-domain particles, which allow one to treat both the temperature and magnetic field-dependent magnetization curves and Moessbauer spectra in a self-consistent way within the same set of physical parameters inherent to the system studied. Based on the stochastic approaches, a simplified three-level stochastic model taking into account the magnetic anisotropy, precession and diffusion of uniform magnetization of single-domain particles is developed in order to describe the Moessbauer absorption spectra of nanoparticles in a weak magnetic field.

[en] It is experimentally demonstrated that the shape of Moessbauer spectra of polymer composites based on single-domain magnetic particles depends more on an inter-particle interaction than on superparamagnetic properties of a separate particle. The characteristic features of the spectra of such systems with strong inter-particle interactions are separated, such as an asymmetric shape of lines with sharp outer and smeared inward sides and presence of central anomalously splitted doublet. It is shown that the three-level relaxation model, which takes into account the precession and diffusion of magnetization of single-domain particles between two local energy minima and one absolute energy maximum, allows to describe all characteristic features of the spectra of such systems.

[en] This paper deals with the extension of the well known Stoner-Wohlfarth (SW) model widely used to compare magnetic properties of real single-domain particle systems with its ideal predictions. The model is often discussed in connection with nanomagnetism. The extension of this successful SW model is gained by combining it with Neel's ideas concerning the dynamical behavior and relaxation of the magnetization in such systems. We present the derivation of a universal relaxation equation which holds for the populations of the SW energy levels defined by the SW model. By solving this differential equation with properly chosen initial conditions, a number of magnetization phenomena observed experimentally versus temperature, time, and external magnetic fields can be understood and described quantitatively. So, hysteresis loops, including those in high-frequency external magnetic fields, can be calculated within this model as a function of temperature, and demagnetization curves for arbitrary heating rates in different external magnetic fields can be simulated. In contrast to the difficulties encountered when treating the experimental data within more general stochastic models based on the Landau-Lifshitz-Gilbert equation, one can easily fit to a first approximation a wide set of data taken from the same sample within the extended SW model. The well known Henkel and Thamm-Hesse plots are reviewed and it is shown that by using these for plotting experimental data deviations from the ideal SW behavior and influences caused by relaxation can be detected. The plot recently proposed by Michele-Hesse-Bremers is shown not to be sensitive to relaxation influences and therefore reveals only the particle-particle interaction