Random Anisotropy Axes Research Articles

Magnetic interaction and anisotropy axes arrangement in nanoparticle aggregates can enhance or reduce the effective magnetic anisotropy

The magnetic response of nanostructures plays an important role on biomedical applications being strongly influenced by the magnetic anisotropy. In this work, we investigate the role of the temperature, particle concentration and nanoparticles arrangement forming aggregates in the effective magnetic anisotropy of Mn-Zn ferrite-based nanoparticles. Electron magnetic resonance and coercivity temperature dependence analyses, were critically compared for the estimation of the anisotropy. We found that the temperature dependence of the anisotropy follows the Zener-Callen model, while the symmetry depends on the particle concentration. At low concentration one observes only an uniaxial term, while increasing a cubic contribution has to be added. The effective anisotropy was found to increase the higher the particle concentration on magnetic colloids, as long as the easy axis was at the same direction of the nanoparticle chain. Increasing even further the concentration up to a highly packed condition (powder sample) one observes a decrease of the anisotropy, that was attributed to the random anisotropy axes. Further, room temperature anisotropy decreased on the order of 50% in comparison to the low temperature values, thus impacting the theoretical estimations of the magnetic response of nanoparticles.

Role of the Fraction of Blocked Nanoparticles on the Hyperthermia Efficiency of Mn-Based Ferrites at Clinically Relevant Conditions

To investigate the role of magnetic anisotropy on magnetic hyperthermia heating efficiency at low field conditions, Mn, MnZn, and MnCo-ferrite nanoparticles were synthesized using the hydrothermal method. The coercive field temperature dependence method was used to determine the blocking temperature distribution of the particles by considering the temperature dependence of anisotropy and magnetization and the random anisotropy axis configuration. The data allowed one to estimate the room-temperature quasi-static superparamagnetic diameter, which was found to be lower than the theoretical value. Magnetic hyperthermia experiments of the magnetic nanocolloids at 522 kHz indicated that soft nanomagnets heat more efficiently at clinically relevant conditions. The heating performance was found to decrease at the higher fraction of blocked nanoparticles. For instance, samples with similar size distribution and mean diameter of 10 nm, at a field amplitude of only 120 Oe (9.6 kA m–1), showed a decrease of specific...

Magnetic states of nanostructures containing Ni2+ ions at the surface of SiO2 nanospheres

Ultra-small magnetic particles containing Ni2+ ions were grown at the surface of SiO2 spheroidal nanoparticles (typical diameter: 50 nm) starting from NiCl2 solutions. Depending on preparation details, two samples characterized by magnetic sub-nanostructures or lamellar sub-nanoparticles at the SiO2 nanosphere surface were obtained. The decorated SiO2 nanospheres were submitted to physico-chemical and magnetic characterization. In both samples, a magnetically blocked phase is observed at low temperature. Below 5 K, discontinuities in isothermal magnetization loops and magnetic relaxation effects suggest the onset of coherent quantum tunneling of nanoparticle magnetization (QTM). Relaxation effects give are described by a field- and temperature-dependent magnetic viscosity SV(H,T); the total spin number of magnetic units is estimated by fitting the isothermal SV(H) curve to a model for an assembly of particles with random anisotropy axes. The mean number of aligned spins involved in the low-temperature relaxation is 32 and 15 in the two considered samples. Phonon-assisted QTM plays an increasingly important role with raising temperature and the quantum regime gradually merges with the classical behavior. Above the blocking temperature the magnetic units behave as classical superparamagnetic particles. When the intra-particle ferromagnetic order disappears the Ni2+ ions respond individually to the magnetic field.

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

Using tempered Monte Carlo simulations, we study the the spin-glass phase of dense packings of Ising dipoles pointing along random axes. We consider systems of dipoles (i) placed on the sites of a simple cubic lattice with lattice constant d, and (ii) placed at the center of random close packed spheres of diameter d that occupy 64% of the volume. For both cases, we find a spin-glass phase below a certain temperature Tsg. By analysing the data obtained for the overlap parameter, the associated correlation length, as well as the statistics of the overlap distributions of individual samples, we find a behavior consistent with quasi-long-range order in the spin-glass phase, similar to the one previously found in strongly diluted dipolar systems.

Structural and magnetic properties of amorphous Co-W alloyed nanoparticles

W-capped Co nanoparticles dispersed in an alumina matrix are studied by means of high-resolution transmission electron microscopy, extended x-ray absorption fine structure, SQUID-based magnetic measurements, dc magnetization, ac magnetic susceptibility, and x-ray magnetic circular dichroism. Results show the formation of amorphous Co-W alloy nanoparticles, the magnetic properties of which are modified by the amount of W or Co present in the samples. The average Co magnetic moment depends on the number of W atoms surrounding it. Co-W particles show superparamagnetic behavior and are described as an array of noninteracting particles with random anisotropy axes and an average moment per particle proportional to the particle volume and to the average Co moment for each alloy composition. Values of the magnetic anisotropy constant of the particles are on the order of 10${}^{6}$ erg/cm${}^{3}$, higher than that of bulk Co. Evidence of short-range ordering within each amorphous particle is found that provides insight of the origin of their magnetic anisotropy.

Equilibrium spin-glass transition of magnetic dipoles with random anisotropy axes on a site-diluted lattice

We study partially occupied lattice systems of classical magnetic dipoles which point along randomly oriented axes. Only dipolar interactions are taken into account. The aim of the model is to mimic collective effects in disordered assemblies of magnetic nanoparticles. From tempered Monte Carlo simulations, we obtain the following equilibrium results. The zero temperature entropy approximately vanishes. Below a temperature T_c, given by k_B T_c= (0.95 +- 0.1)x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy and x is the site occupancy rate, we find a spin glass phase. In it, (1) the mean value <|q|>, where q is the spin overlap, decreases algebraically with system size N as N increases, and (2) D|q| = 0.5 <|q|> (T/x)^1/2, independently of N, where D|q| is the root mean square deviation of |q|.

Magnetic phase transition for three-dimensional Heisenberg weak random anisotropy model: Monte Carlo study

Magnetic phase transition (MPT) to magnetic quasi-long-range order (QLRO) phase in a three-dimensional Heisenberg weak (D/J=4) random anisotropy (RA) model is investigated by Monte Carlo simulation. The isotropic and cubic distributions of RA axes are considered for simple-cubic-lattice systems. Finite-size scaling analysis shows that the critical couplings for the former and latter are Kc=0.704 35(2) and Kc=0.709 98(4), respectively. While the critical exponent 1/ν=1.408 24(0) is the same for both cases. A second-order MPT to the QLRO phase is therefore evidenced to be possible in favor with the existence of the QLRO predicted by recent functional renormalization group theories.

Monte Carlo study of the equilibrium spin-glass transition of magnetic dipoles with random anisotropy axes

We study fully occupied lattice systems of classical magnetic dipoles which point along random axes. Only dipolar interactions are considered. From tempered Monte Carlo simulations, we obtain numerical evidence that supports the following conclusions: In three dimensions, (a) there is an equilibrium spin-glass phase at temperatures below ${T}_{c}$, where ${k}_{B}{T}_{c}=(0.86\ifmmode\pm\else\textpm\fi{}0.07){\ensuremath{\epsilon}}_{d}$ and ${\ensuremath{\epsilon}}_{d}$ is a nearest-neighbor dipole-dipole interaction energy, (b) in the spin-glass phase the overlap parameter is approximately given by $\sqrt{1\ensuremath{-}T/{T}_{c}}$, and (c) the correlation length $\ensuremath{\xi}$ diverges at ${T}_{c}$ with a critical exponent $\ensuremath{\nu}=1.5\ifmmode\pm\else\textpm\fi{}0.5$; in two dimensions $\ensuremath{\xi}$ diverges at or near $T=0$ and $\ensuremath{\nu}=3\ifmmode\pm\else\textpm\fi{}1$.

The micromagnetic simulations of CoNbCuSiB nanocrystalline material

The micromagnetic formalism was used to study the magnetic behaviour of an assembly of single-domain ferromagnetic particles with random anisotropy axes directions, embedded in a diamagnetic or weakly magnetic matrix. The calculated hysteresis loops present strong similarities with the experimental magnetisation curves of multiphase Co-based alloy.

Arrhenius–Néel thermal decay in polycrystalline thin film media

A simple expression for the remanent coercivity versus field time duration has been developed for polycrystalline thin film media with two-dimensional random anisotropy axis orientation. Explicit averaging of the thermally induced reversal for random grains is shown to be well approximated by the thermal decay of one particle with anisotropy axis at an angle of ≈21° to the applied field. The expression has no adjustable parameters and two slightly different forms apply to noninteracting and weakly interacting grains. Applicability is shown to be for times greater than approximately 100 ns. Good agreement is shown with measurements on two series of thin films with varying coating thickness.

Critical phenomena of an iron-nitride nanoparticle system

Critical phenomena are studied for the magnetic phase transition of a ferromagnetic nanoparticle system with dipolar interactions and random anisotropy axes. The divergences of the nonlinear susceptibility and the longest relaxation time are observed for a frozen magnetic fluid including uniform iron-nitride particles. These results indicate that the phase transition is similar to the spin glass transition.

Effects of dipolar interactions on the magnetic properties of granular solids

We use the Monte Carlo simulation technique to study the coercive behaviour of an assembly of single-domain ferromagnetic particles with random anisotropy axes directions, embedded in an insulating matrix and interacting via dipolar forces. We present results for the dependence of the coercivity on the volume packing fraction and temperature. We find a peak of the coercive field at the percolation threshold. We compare our theoretical results with experimental findings.

Weak disorder in the two-dimensionalXYdipole ferromagnet

The effects of random field and random anisotropy axis disorder on the two-dimensional $\mathrm{XY}$ dipole ferromagnet are studied. It is shown that the disorder leads to an instability of the ferromagnetic phase. The correlation function of the magnetization is calculated at low temperatures using the self-consistent harmonic approximation. In the random-field case, the correlation function obeys a power law as a function of the distance. For random axis disorder, a logarithmically slow decrease of the correlation function is found.

Magnetization correlations in thin film media in the presence of a recorded transition

Magnetization correlations in thin film media in the presence of a written transition have been studied utilizing numerical micromagnetic simulation. Polycrystalline films are modeled by a hexagonal array of identical grains each with random anisotropy axis orientation. A transition is written in the medium and the positional variance, the stationary cross track correlation, and the nonstationary down track correlation functions are determined by suitable averaging over statistical ensembles.

Field-induced crossover behavior in quantum Heisenberg spin glasses with random-anisotropy axes.

The infinite-range quantum Heisenberg spin-glass model with random-anisotropy axes and external magnetic field (h) is studied by means of the thermofield dynamics for the spin value S=1/2. The stability of the mean-field-type solution against the action of fluctuations has been evaluated in the presence of h leading to the upper and lower critical lines in the field-temperature (h-T) plane. For small values of the anisotropy variance we find a crossover of the upper critical line from the de Almeida--Thouless-type behavior for small fields to the Gabay-Toulouse-like behavior for large fields and a reversed type of behavior at the lower critical line for corresponding values of the random anisotropy---in close analogy to the recently analyzed quantum vector spin glass with random Dzyaloshinsky-Moriya interactions.

Long range order in random anisotropy magnets

High temperature series for the magnetic susceptibility, χ, of random anisotropy axis models in the limit of infinite anisotropy are presented, for two choices of the number of spin components, m. For m=2, we find Tc=1.78 J on the simple cubic lattice, and on the face-centered cubic lattice we find Tc=4.29 J. There is no divergence of χ at finite temperature for m=3 on either lattice. For the four-dimensional hypercubic lattice, we find finite temperature divergences of χ for both m=2 and m=3.

Test of the coherent-anisotropy-field approximation for a lattice model of a random-axis ferromagnet in a high magnetic field.

We report the results of a numerical test of the coherent-anisotropy-field approximation (CAFA) for characterizing the high-field limit of the magnon spectrum for a lattice model of a ferromagnet with random anisotropy axes. The CAFA reproduces the downward shift in the ferromagnetic resonance frequency and accounts for the modification of the density of states induced by the disorder. The agreement confirms the analogy between the random-axis model in the high-field limit and the potential fluctuation model for the random-alloy problem.

Microscopic theory of magnetic excitations in ferromagnets with random anisotropy axes

We present a microscopic theory of the harmonic magnetic excitations in ferromagnets with random anisotropy axes. The theory is analogous to the theory of excitations in spin glasses developed by Walker and Walstedt, with the difference that the disorder arises from the anisotropy rather than the exchange interaction. We report the results of numerical calculations of magnon density of states and the ferromagnetic resonance frequency for a model system where the spins occupy sites on a fcc lattice. The exchange interaction is between nearest neighbors, and the anisotropy axis varies randomly from site to site with no correlation between different sites. Data are obtained with a range of values of the ratio of the anisotropy to the exchange interaction in both the zero-field and high-field limits.

Spin-glass transition in the random anisotropy axis model

The critical behavior of the Random Anisotropy Axis model (RAM) is studied by the Monte Carlo simulation method in the limit of infinite anisotropy. Finite size scaling analysis of the data for equilibrium averages strongly suggests a zero temperature critical point in two dimensions and a finite temperature phase transition in three dimensions. The values of the critical exponents in both two and three dimensions indicate that RAM belongs to the same universality class as that of short-range Ising spin-glass models.

High-field magnons in ferromagnets with random anisotropy axes.

We investigate magnons in ferromagnets with random anisotropy axes. It is assumed the applied field is large in comparison with the exchange and anisotropy fields. A coherent-anisotropy-field approximation is introduced, where the effect of the disorder is represented by a complex, energy-dependent anisotropy field, analogous to the coherent potential in the random-alloy problem. The real part of the anisotropy field represents the shift in the magnon energy, whereas the imaginary part gives the damping. The shift and damping of the uniform mode and the damping rate across the magnon band are calculated for both a uniform and a nonuniform distribution in the cosine of the angle between the anisotropy axis and the applied field.