Analytical model for shape anisotropy in thin-film nanostructured arrays: Interaction effects

When reducing the size of array elements and interelement separations to the nanoscale, long-range magnetostatic interactions become important. A methodology that extends the study of conventional single-element magnetostatics is presented, adding the effect of stacking nanoelements into close proximity in arrays and the consequent interaction effects. This would be very time consuming to model by micromagnetic simulations that are also very vulnerable to artifacts due to cell or boundary condition selection. The proposed method considers an analytical expression valid for short interelement separations and not very costly to evaluate by computational means. This approach allows the quantitative study of shape anisotropy in non-square-shaped arrays. It is also shown how it can be used to find anisotropy compensation conditions, where an anisotropy due to a magnetic element shape can be compensated by the shape anisotropy due to the array. The obtained results can be used to establish a criterion for the minimum number of elements to be considered for a micromagnetic simulation of an array to be realistic depending on the element size and separation.     

Size effect on the magnetism of nanocrystalline Ni films at ambient temperature

Size effect on the magnetization and the coercivity of nanocrystalline Ni films has been examined at room temperature. Agreement between modeling predictions and measurements reveals that the size-suppressed magnetization results from the drop of spin-spin exchange energy due to the coordination number (CN) imperfection of atoms near the surface edges, and that the size-enhanced coercivity arises from intergrain interaction that is proportional to the inverse of particle size. Findings herewith and reported previously on the size-induced lattice contraction and Curie temperature suppression evidence the significance of atomic CN imperfection on the unusual behavior of a ferromagnetic nanosolid.     

Tailoring the exchange bias of Ni/NiO nanogranular samples by the structure control

The exchange bias (EB) effect has been studied in Ni/NiO nanogranular samples obtained by annealing in H₂, at selected temperatures (200≤T_ann≤300 °C), NiO powder previously milled for 5, 10, 20 and 30 h. Both the as-milled NiO powders and the Ni/NiO samples have been analyzed by X-ray diffraction and the exchange bias properties have been investigated in the 5-200 K temperature range. The structure and the composition of the Ni/NiO samples can be satisfactorily controlled during the synthesis procedure by varying both T_ann and the milling time of the precursor NiO powders. In particular, by increasing this last parameter, the mean grain size of the NiO phase reduces down to the final value of 16 nm and the microstrain increases, which is consistent with an enhancement of the structural disorder. The structure of the milled NiO matrix strongly affects the process of nucleation and growth of the Ni nanocrystallites induced by the H₂ treatments, so that, T_ann being equal, the amount and the mean grain size D_Ni of the Ni phase vary substantially in samples having different milling times. Such features of the Ni phase determine the extent of the Ni/NiO interface and consequently the magnitude of the exchange field H_ex: the highest value (∼940 Oe) has been measured at T=5 K in a sample containing ∼7 wt% Ni and with D_Ni=19 nm. However, in Ni/NiO samples with very different structural characteristics and different values of H_ex at T=5 K, the EB effect vanishes at the same temperature (∼200 K) and the same thermal dependence of H_ex is observed. We consider that the evolution of the EB effect with temperature is ultimately determined by the microstructure of the Ni/NiO interface, which cannot be substantially modified by changing the synthesis parameters, milling time and T_ann.     

Dramatic suppression of antiferromagnetic coupling in nanoparticle CuO

Magnetic susceptibility and muon spectroscopy measurements are carried out on antiferromagnetic nanoparticles (AFN) of CuO that are directly prepared by ball-milling a single crystal. The recently reported ferromagnetic features in AFN CuO of sol-gel growth are confirmed. New and significant result of the present work is a direct observation of an unusual dramatic reduction of the antiferromagnetic transition temperature, T_N, from the bulk T_N=230 to 50 K in AFN CuO by the μSR measurement.     

Influence of relaxation phenomena in dynamic magnetization processes on magnetic power losses of non-oriented electrical steel sheets

We have reported that the magnetic power losses per magnetizing cycle change with the magnetization pausing time in a constant rate of magnetization change and some relaxation phenomena exist in the magnetization pausing period. We discuss the influence of the relaxation phenomena on the dynamic magnetic power losses and suggest that the relaxation phenomena seems to be causes of the frequency dependence of the magnetic losses and of the variation of losses that cannot be expressed only by magnetization speed dependence of losses.     

The effect of structure on magnetic properties of Co nanowire arrays

Co nanowire arrays with three typical diameters of 20, 50 and 120 nm have been fabricated into anodic alumina oxide templates using an ac electrodeposition method. It is found that the crystal texture of the Co nanowires depends on the pH value of the deposition electrolyte. X-ray diffraction results show that the (1 0 0) texture appears at pH 6.2, while the diffraction peaks of (1 0 0) and (1 0 1) appear at pH 6.4 with the diameter of 20 nm. In addition, the (0 0 2), (1 0 0) and (1 0 1) peaks appear with an increase of pH value for the nanowire arrays with diameters of 50 and 120 nm, respectively. Magnetic measurements indicate the effect of structure on the magnetic properties of the nanowire arrays, which depend strongly on the different diffraction peaks, as adjusted by the pH value.     

The influence of thermal annealing on the structural and magnetic properties of gold nanoparticles

In the past few years ferromagnetic-like behavior has been reported in metal gold nanoparticles coated with diverse organic surfactants. In this work we report on the effect of thermal annealing on the ferromagnetic-like behavior of oleic acid and oleylamine coated gold nanoparticles of about 7 nm size. The magnetic moment of the “as prepared” sample is about 3×10⁻² emu/g and the coercive field is 200 Oe at 10 kOe and 5 K, after the annealing the behavior changes from ferromagnetic-like to paramagnetic and the magnetization at 10 kOe decreases at a factor of 10. These results are compared with those obtained for oleylamine coated gold nanoparticles, which are diamagnetic at room temperature.     

Optically induced magnetization in diluted magnetic quantum dots

We report the effect of intense laser field on donor impurities in a semimagnetic Cd_1-xinMn_xinTe/Cd_1-xoutMn_xoutTe quantum dot. The spin polaronic energy of different Mn²⁺ is evaluated for different dot radii using a mean field theory in the presence of laser field. Magnetization is calculated for various concentrations of Mn²⁺ ions with different dot sizes. Significant magnetization of Mn spins can be obtained through the formation of polarized exciton magnetic polarons (EMPs). A rapid decrease of the laser dressed donor ionization energy for different values of dot sizes with increasing field intensity is predicted. Also, it is found that the polarization of EMPs increases rapidly at higher excitation energies.     

Effect of the addition of Ge to the FINEMET alloy

The results obtained by partially substituting Ge for B and Si in the FINEMET alloy for the purpose of improving its magnetic properties at high temperatures are presented in this work. Nanocrystalline ribbons were obtained from controlled crystallization of amorphous material made employing the melt spinning technique. The studied compositions were: Fe_73.5Si_13.5Ge₂Nb₃B₇Cu₁ and Fe_73.5Si_13.5Ge₄Nb₃B₅Cu₁. The structural evolution of these alloys was studied using X-ray diffraction (XRD) and differential scanning calorimetry (DSC) and these results were correlated with their magnetic properties at different annealing temperatures. The coercivity obtained for both alloys was below 1 A/m at anneling temperatures between 773 and 823 K. The amorphous saturation magnetization was satisfactory, almost 137 emu/g, comparable with that obtained for FINEMET alloys. The nanocrystallization and the Curie temperatures are dependent on Ge concentration.     

Effect of the surface anisotropy and the shape on the magnetization behavior in an egg-shaped nanoparticle

Using the classical Heisenberg model and Monte Carlo simulation, we compute the magnetization behavior of a ferromagnetic nanoparticle with an egg-shape in an external magnetic field along the symmetry axis. The particle is in a single-domain state with a surface anisotropy axis perpendicular to the surface of the particle. At low temperature, it is found that exchange bias appears in the hysteresis loop, which does not exist in the spherical and ellipsoidal nanoparticles. The bias field produced by the frozen spins on the surface of the egg-shaped nanoparticle may be the reason to produce the phenomenon of the exchange bias.     

High concentration of hematite nanoparticles in a silica matrix: Structural and magnetic properties

The α-Fe₂O₃/SiO₂ nanocomposite containing 45 wt% of hematite was prepared by the sol-gel method followed by heating in air at 200 °C. The so-obtained composite of iron(III) nanoparticles dissolved in glassy silica matrix was investigated by X-ray powder diffraction (XRPD), transmission electron microscopy (TEM), and superconducting quantum interference device (SQUID) magnetometry. XRPD confirms the formation of a single-phase hematite sample, whereas TEM reveals spherical particles in a silica matrix with an average diameter of 10 nm. DC magnetization shows bifurcation of the zero-field-cooled (ZFC) and field-cooled (FC) branches up to the room temperature with a blocking temperature T_B=65 K. Isothermal M(H) dependence displays significant hysteretic behaviour below T_B, whereas the room temperature data were successfully fitted to a weighted Langevin function. The average particle size obtained from this fit is in agreement with the TEM findings. The small shift of the T_B value with the magnetic field strength, narrowing of the hysteresis loop at low applied field, and the frequency dependence of the AC susceptibility data point to the presence of inter-particle interactions. The analysis of the results suggests that the system consists of single-domain nanoparticles with intermediate strength interactions.     

The grain size effect on the magnetic properties in NiZn ferrite and the quality factor of the inductor

Polycrystalline ferrite materials with the chemical composition of Ni_0.49Zn_0.49Co_0.02Fe_1.90O_x have been fabricated using the conventional ceramic sintering method. Grain sizes have been adjusted from ∼2.2 to ∼13.5 μm with changing sintering conditions. From the measurements of the complex permeability, it is suggested that the permeability is dominated only by the spin rotation at mono-domain state and both domain wall and spin rotation contribute at multi-domain state. At mono-domain state, the core loss has been drastically decreased similar to the other work. The measurement result for the loss angle indicates that the low loss state can be maintained up to the higher magnetic field with smaller grain size in spite of the mono-domain state. The simplified wire-wounded type inductors have been also fabricated and characterized. The results have shown that the inductor fabricated with the smaller grain size has a better performance in the quality value under relatively higher current.     

Synthesis and anomalous magnetic properties of CoCr2O4 nanocrystallites with lattice distortion

Nanocrystalline Cobalt chromite (CoCr₂O₄) ceramic has been synthesized under a mild condition, rather than by a high-temperature sintering (e.g. >1673 K, in general). A shifted hysteresis loop with an exchange-bias field of 35.7 kA/m and a high coercivity of 627.9 kA/m at 4.2 K was achieved under the cooling field of 2.39×10⁶ A/m. X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) results reveal that a strong lattice distortion and a large amount of surface defects exist in CoCr₂O₄ nanocrystallites (NCs). The anomalous magnetic properties, such as bias field and large coercivity, are attributed not only to the nanosize effect but also to the lattice distortion and crystal defects.     

FINEMET type alloy without Si: Structural and magnetic properties

Magnetic and structural properties of a Finemet type alloy (Fe_73.5Ge_15.5Nb₃B₇Cu₁) without Si and high Ge content were studied. Amorphous material was obtained by the melt spinning technique and was heat treated at different temperatures for 1 h under high vacuum to induce the nanocrystallization of the sample. The softest magnetic properties were obtained between 673 and 873 K. The role of Ge on the ferromagnetic paramagnetic transition of the as-quenched alloys and its influence on the crystallization process were studied using a calorimetric technique. Mössbauer spectroscopy was employed in the nanocrystallized alloy annealed at 823 K to obtain the composition of the nanocrystals and the amorphous phase fraction. Using this data and magnetic measurements of the as-quenched alloy, the magnetic contribution of nanocrystals to the alloy annealed at 823 K was estimated via a linear model.     

Low-temperature magnetization in nanofilms

The low-temperature magnetization of a film was analyzed by the use of exact Bose representation of spin operators that does not suffer from the presence of unphysical states. The magnetization of thin films has exponentially small temperature correctness, so that Dyson’s proof about exponentially small correction coming from two bosons at ideal lattice point cannot be used in film analyses. The main conclusions of this work are that magnetic lattice of a thin film is more rigid than the macroscopic lattice and that the autoreduction process (the three layer film divides into two layer subfilms) takes place in the film.     

Enhancement of surface magnetization in antiferromagnetic nanoparticles

We report enhancement of magnetization below the antiferromagnetic ordering temperature T_N in nanoparticles of two antiferromagnets, viz CoRh₂O₄ and Cr₂O₃. The enhancement of magnetization below T_N is systematic, being larger for sample with smaller particle size. Scaling analysis showed that such enhancement of magnetization in CoRh₂O₄ nanoparticles is due to the superparamagnetic type contribution of surface (shell) spins. The present work shows that similar analysis can also be applied in Cr₂O₃ nanoparticles.     

Magnetic properties of p-doped GaMnN diluted magnetic semiconductors containing clusters

Magnetic properties of p-doped GaMnN diluted magnetic semiconductors, having both randomly distributed Mn ions and Mn_xN_y clusters, are presented under the theory based on the hole-mediated ferromagnetism. The critical temperature of the second order phase transition between ferromagnetic and paramagnetic phases and the magnetization as a function of temperature are obtained from the free energy calculation. The Curie temperature of the p-doped GaMnN containing clusters depends not on the type of clusters but on the composition rate of clusters. The behavior of the spontaneous magnetization as a function of temperature is strongly affected by carrier concentration. The p-doped GaMnN diluted magnetic semiconductors containing clusters have room temperature ferromagnetism regardless of the magnetic type of clusters, as long as hole-mediated spin-spin interactions occur in them.     

Elastic Modulus of Fe72.5Ga27.5 Magnetostrictive Alloy

The elastic modulus of Fe72.5Ga27.5 magnetostrictive alloy is determined by testing ac impedance resonance frequency and first-principle calculations. The observed elastic modulus is 90.2 GPa for a directionally solidified sample and 103.4 GPa for a water-quenched sample tested in a dc magnetic field of 32. 7mT without compressive pre-stress. The bulk modulus by first-principles calculation is 179.3GPa which is basically consistent with the experimental result. The elastic modulus first increases and then decreases with increasing dc magnetic field, attributed to magnetostriction occurrence in the Fe72.5Ga27.5 alloy. The elastic modulus increases with increasing compressive pre-stress, resulting from the initial magnetic states change under the applied compressive pre-stress. The elastic modulus increases match well with the improved magnetostriction after quenching.     

Thermal treatment effects in the self-assembly of FePt nanoparticle arrays

This work concentrates on the influence of synthetic mechanisms of FePt nanoparticles on their self-arrangement and some structural and magnetic properties as studied by means of different electron microscopy techniques and SQUID magnetometry. High-reflux points associated with long boiling durations seem adequate to increase the iron precursor's decomposition yield and facilitate the simultaneous cubic to tetragonal FePt transformation, in single-phase FePt nanoparticles. Nevertheless, such conditions also result in the loss of long-range arrangement and in the appearance of coalescence effects. A core–shell structure comprising of FePt and Fe₃O₄ is favored under mild thermal conditions during synthesis, which seems to confront the undesirable atomic diffusion. Additionally, particle isolation due to the surfactant coating leads in an hcp-symmetry self-assembly. Moreover, working at lower temperatures allows a homogeneous mixture between different phases producing binary composite arrays.     

Structural and magnetic correlation of Finemet alloys with Ge addition

The correlation between saturation magnetization and the magnetic moment per Fe atom in the nanocrystalline state is studied for Finemet-type alloys. These studies were performed on nanocrystalline ribbons whose compositions were Fe_73.5Si_13.5−xGe_xNb₃B₉Cu₁ (x=8, 10 and 13.5 at%). We used a simple lineal model, X-ray diffraction and Mössbauer spectroscopy data to calculate the magnetic contribution of the nanocrystals and the results were contrasted with the measured saturation magnetization of the different alloys. The technique presented here provides a very simple and powerful tool to compute the magnetic contribution of the nanocrystalline phase to the alloy. This calculus could be used to determine the volume fraction of nanocrystalline and amorphous phases in the nanocrystallized alloy, without using a very sophisticated microscopy method.