Surface anisotropy broadening of the energy barrier distribution in magnetic nanoparticles (original) (raw)
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Surface anisotropy and orbital moment in Fe $ _ {3} $ O $ _ {4} $ nanoparticles
2008
The effect of surface anisotropy on the distribution of energy barriers in magnetic fine particles of nanometer size is discussed within the framework of the T ln(t/τ 0) scaling approach. The comparison between the distributions of the anisotropy energy of the particle cores, calculated by multiplying the volume distribution by the core anisotropy, and of the total anisotropy energy, deduced by deriving the master curve of the magnetic relaxation with respect to the scaling variable T ln(t/τ 0), enables the determination of the surface anisotropy as a function of the particle size. We show that the contribution of the particle surface to the total anisotropy energy can be well described by a size-independent value of the surface energy per unit area which permits the superimposition of the distributions corresponding to the particle core and effective anisotropy energies. The method is applied to a ferrofluid composed of non-interacting Fe 3−x O 4 particles of 4.9 nm average size and x about 0.07. Even though the size distribution is quite narrow in this system, a relatively small value of the effective surface anisotropy constant K s = 2.9 × 10 −2 erg cm −2 gives rise to a dramatic broadening of the total energy distribution. The reliability of the average value of the effective anisotropy constant, deduced from magnetic relaxation data, is verified by comparing it to that obtained from the analysis of the shift of the ac susceptibility peaks as a function of the frequency.
Surface Contribution to the Anisotropy of Magnetic Nanoparticles
Physical Review Letters, 2003
We calculate the contribution of the Néel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Néel surface anisotropy, scales with the particle's volume and has cubic symmetry with preferred directions [±1, ±1, ±1].
Acta Physica Polonica A, 2016
We use the Monte Carlo simulation method to investigate the influence of the signs of magnetocrystalline anisotropy constants and the magnetic dipole-dipole interactions on the zero field cooled-field cooled magnetization experiments and hysteresis curves of a system of magnetic nanoparticles. Positive first cubic anisotropy constant K1 results in larger blocking temperatures and larger coercive fields of a system, while the second anisotropy constant K2 is practically of negligible importance for the phenomena investigated. Magnetic dipole-dipole interactions are important only in the most dense systems of particles and their effects practically disappear for systems where the distance between the closest particles exceeds three particle diameters.
Effective anisotropies and energy barriers of magnetic nanoparticles with Neel surface anisotropy
Physical Review B, 2007
Magnetic nanoparticles with Néel surface anisotropy, different internal structures, surface arrangements and elongation are modelled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure and elongation. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects: (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) The competition between the core and surface anisotropies leads to a new energy that contributes to both the 2 nd − and 4 th −order effective anisotropies. We also evaluate energy barriers ∆E as functions of the strength of the surface anisotropy and the particle size. The results are analyzed with the help of the effective one-spin potential, which allows us to assess the consistency of the widely used formula ∆E/V = K∞ + 6Ks/D, where K∞ is the core anisotropy constant, Ks is a phenomenological constant related to surface anisotropy, and D is the particle's diameter. We show that the energy barriers are consistent with this formula only for elongated particles for which the surface contribution to the effective uniaxial anisotropy scales with the surface and is linear in the constant of the Néel surface anisotropy.
Journal of Magnetism and Magnetic Materials, 2003
We present results for the FMR line shape modelling of non-interacting magnetic nanoparticle systems. We compare the results of the Smit and Beljers formalism and the usual linear-model, where the effective anisotropy field, H eff A ; in the superparamagnetic regime is considered as a perturbation to the Zeeman interaction and added to the applied field, H: While the difference between these approaches is negligible for small H eff A (high temperature regime), it becomes more pronounced when H eff A EH: We show how these results influence the determination of the parameters characterizing an array of random particles. r
Effective anisotropy field variation of magnetite nanoparticles with size reduction
The European Physical Journal B, 2008
Size effect on the internal magnetic structure has been investigated on weakly interacting magnetite (Fe3O4) nanoparticles by ferromagnetic resonance experiments at 9.5 GHz as a function of temperature (4-300 K). A set of three samples with mean particle size of 2.5 nm, 5.0 nm and 13.0 nm, respectively, were prepared by chemical route with narrow size distribution (σ < 0.27). To minimize the dipolar interaction, the particles were dispersed in a liquid and a solid polymer matrix at ∼0.6% in mass. By freezing the liquid suspension with an applied external field, a textured was obtained. Thus, both random and textured suspensions were studied and compared. The ferromagnetic resonance experiments in zero-field-cooled and field-cooled conditions were carried out to study the size effect on the effective anisotropy field. The dc magnetization measurements clearly show that the internal magnetic structure was strongly affected by the particle size.
Journal of Physics D-applied Physics, 2001
From an initial ferrofluid with magnetite particles dispersed in kerosene and stabilized with oleic acid, having particle concentration n = 7.7×1016 cm-3 (determined from magnetic measurements), 11 samples were obtained by successive dilution with kerosene (with a dilution ratio 2:3). Using magnetic resonance measurements for each ferrofluid sample, we have studied the dependence on particle concentration of the effective anisotropy constant of magnetite colloidal particles. The obtained results show an increase of the effective anisotropy constant by increasing the particle concentration. This behaviour is assigned to interparticle magnetic interactions.
Magnetic anisotropy in fine magnetic particles
Journal of Magnetism and Magnetic Materials, 1993
In this work, the magnetization curves and the anisotropy energy constants K are calculated for three systems of Fe,O, fine particles using a simple model for the particle-size distribution function. The model gives a value for the mean particle diameter which is in good agreement with the value obtained from transmission electron micrographs. Also, the results for the anisotropy constant are in good agreement with those obtained from the temperature dependence of the remanent magnetization. Furthermore, Mijssbauer spectra are used, together with the calculated anisotropy constants, to determine the particle-size distribution.