Excitation Spectrum of the Néel Ensemble of Antiferromagnetic Nanoparticles as Revealed in Mössbauer Spectroscopy

Abstract

The excitation spectrum of the Néel ensemble of antiferromagnetic nanoparticles with uncompensated magnetic moment is deduced in the two-sublattice approximation following the exact solution of equations of motion for magnetizations of sublattices. This excitation spectrum represents four excitation branches corresponding to the normal modes of self-consistent regular precession of magnetizations of sublattices and the continuous spectrum of nutations of magnetizations accompanying these normal modes. Nontrivial shape of the excitation spectrum as a function of the value of uncompensated magnetic moment corresponds completely to the quantum-mechanical calculations earlier performed. This approach allows one to describe also Mössbauer absorption spectra of slowly relaxing antiferromagnetic and ferrimagnetic nanoparticles and, in particular, to give a phenomenological interpretation of macroscopic quantum effects observed earlier in experimental absorption spectra and described within the quantum-mechanical representation.

Permeability of the Composite Magnetic Microcapsules Triggered by a Non-Heating Low-Frequency Magnetic Field

“…Note that the line in the spectrum is strongly skewed toward the inner part of the spectra. This shape of Mössbauer lines is determined by the spectrum of thermal excitations of the magnetic moments of nanoparticles and indicates a slow relaxation of the moments in comparison with the lifetime of the nucleus in the excited state [38]. The analysis of the spectra was carried out within the model of the magnetic dynamics of ferromagnetic nanoparticles [38].…”

“…This shape of Mössbauer lines is determined by the spectrum of thermal excitations of the magnetic moments of nanoparticles and indicates a slow relaxation of the moments in comparison with the lifetime of the nucleus in the excited state [38]. The analysis of the spectra was carried out within the model of the magnetic dynamics of ferromagnetic nanoparticles [38]. An example of the use and detail description of such a model is presented elsewhere [39].…”

“…This approach allows one to describe not only qualitatively but also quantitatively the shape of the spectra over the entire temperature range. In addition to the standard parameters of hyperfine interaction, such as isomer shift δ, hyperfine magnetic field at the iron nucleus Hhf, and quadrupole coupling constant q, The analysis of the spectra was carried out within the model of the magnetic dynamics of ferromagnetic nanoparticles [38]. An example of the use and detail description of such a model is presented elsewhere [39].…”

Effects of Macromolecular Crowding on Nanoparticle Diffusion: New Insights from Mössbauer Spectroscopy

“…Figure (top) shows that the hyperfine structure of the absorption spectrum of dry CFNs looks like a superposition of a well-resolved Zeeman asymmetric line sextet, which is a characteristic of ferrimagnetic NPs, and a minor quadrupolar doublet, which can be attributed to the very small NPs . Due to the ferrimagnetic nature of cobalt ferrite, the absorption spectrum was treated within the model of the magnetic dynamics of an ensemble of ferrimagnetic NPs in the two-sublattice approximation. , In this model, each ferrimagnetic particle of an ensemble is characterized by the simplest expression for its energy density: where J is the positive exchange coupling constant, M 1 and M 2 are the sublattice magnetizations, K is the axial magnetic anisotropy constant, and θ 1 and θ 2 are the angles between vectors M 1 and M 2 and the easiest magnetization axis, respectively.…”

“…Then, the phenomenological consideration can be performed with the assumption that the magnetic moment of each i th sublattice precesses in the internal effective field: whereas the equations of motion for the sublattice magnetizations can be expressed in the form where γ i is the magneto-mechanical ratio for the i th sublattice. Solving these equations, one can deduce the excitation spectrum of the ensemble of ferrimagnetic particles, which represents four excitation branches corresponding to the normal modes of self-consistent regular precession of sublattice magnetizations and the continuous spectrum of nutations of magnetizations accompanying these normal modes. , The equilibrium state of the ensemble of particles at a given temperature T is described by the Gibbs distribution over the “quasi-stationary” states, i.e., precession and nutation trajectories of vectors M 1 and M 2 with given values of the integral of motions, the energy E , and the reduced total magnetic moment m : where V is the volume of particles and C is the normalization constant. Each of the “quasi-stationary” states is characterized by the average values of the longitudinal components of reduced sublattice magnetizations m ̅ 1 z ( E , m ) and m ̅ 2 z ( E , m ).…”