Random Anisotropy Model Research Articles

Law of Approach to Magnetic Saturation in Nanocrystalline Pr2Co7Cx(x≤1): Effects of Carbonation

We report on the effect of Carbon insertion on the microstructure and magnetic properties of nanocrystalline Pr2Co7Cx([Formula: see text]). The Pr2Co7Cx were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM) and physical property measurement system (PPMS9) Quantum Design. Mean field theory was utilized to depict the temperature dependence of magnetization and deduce the exchange interactions. The approach to saturation magnetization was as well used. The results were interpreted in the framework of random magnetic anisotropy model. From such analysis, some fundamental parameters were extracted.

Study of the low-field irreversibility line in the transverse component spin-glass phase of the amorphous Fe90Zr10 alloy

Amorphous FexZr100−x alloys display a complex magnetic phase diagram, particularly in the range 89% ≲ x ≲ 93% in which the phase transition from the paramagnetic to a soft ferromagnetic (FM) state at a critical temperature Tc precedes a second transition at Txy < Tc to a transverse spin-glass (SG) phase, with frozen spin components transverse to the magnetization. The softness of the FM phase and the coexistence of FM and SG orderings complicate exploring the low-temperature and low-field critical properties of the glassy transition. Here we study the irreversibility Almeida-Thouless (AT) line that marks the onset of the transverse SG phase in the Fe90Zr10 alloy in the low-field regime up to H = 60 Oe. While ZFC measurements give rise to an AT exponent ϕ = 4.6, similar to that of another amorphous FM compound with random local anisotropy, the induction of magnetic shiftings upon cooling the sample in a large field, − 85 kOe, displaces down the AT line and separates it into two distinct regimes: one also with ϕ = 4.6 for H above 20 Oe, nearly corresponding to the typical field to flip the remanent magnetization, and a new second regime at lower H, with field-induced remanent clusters and exponent ϕ = 3.6 that approaches the mean-field value ϕ = 3. Our findings are discussed on the light of the results from a random nonuniform anisotropy model with FM exchange interactions, which also reported the existence of a two-regimes scenario in the AT line with similar exponents.

Coercivity and Magnetic Anisotropy of (Fe0.76Si0.09B0.10P0.05)97.5Nb2.0Cu0.5 Amorphous and Nanocrystalline Alloy Produced by Gas Atomization Process.

We present the evolution of magnetic anisotropy obtained from the magnetization curve of (Fe0.76Si0.09B0.10P0.05)97.5Nb2.0Cu0.5 amorphous and nanocrystalline alloy produced by a gas atomization process. The material obtained by this process is a powder exhibiting amorphous character in the as-atomized state. Heat treatment at 480 °C provokes structural relaxation, while annealing the powder at 530 °C for 30 and 60 min develops a fine nanocrystalline structure. Magnetic anisotropy distribution is explained by considering dipolar effects and the modified random anisotropy model.

Processing of Soft Magnetic Fine Powders Directly From As-Spun Partial Crystalline Fe77Ni5.5Co5.5Zr7B4Cu Ribbon via Ball Mill Without Devitrification

A key property for high-frequency inductive applications is the magnetic softness, ideally characterized by complete reversibility of the hysteresis curve. Magnetic softness of alloys depends on the dimensional ratio of grain size to the correlation length. The random anisotropy model predicts the optimum magnetic softness if the crystallite size is well below the correlation length. Based on this theory, a common strategy in processing is to obtain extremely fine nanoscale grains via rapidly solidified alloys, followed by a controlled vacuum anneal. As is well known, this conventional approach requires two demanding experimental conditions: 1) an extremely high quench rate, >105 K/s, and 2) a high vacuum anneal near 600 °C to avoid oxidation. Furthermore, the completely amorphous ribbon is extremely elastic and mechanically strong and is not easily made into the fine powder form for net-shaping and 3-D printing of the soft magnets. Therefore, annealing to induce crystallization is a necessary step before using any conventional powdering techniques, such as ball milling. In this article, we report a new processing strategy of making Fe77Ni5.5Co5.5Zr7B4Cu powders directly from the as-spun ribbons without any crystallization annealing step. This is achieved by melt spinning of the alloy at a relatively low quenching rate, resulting in partially crystallized ribbons that deform plastically, a behavior that is in sharp contrast to its amorphous counterpart. The ribbon samples are ball milled into fine powders by tungsten carbide (WC) at various time intervals. Magnetization measurements show extremely low coercive field (Hc) of 0.51 Oe for the powder that is ball milled for 60 min. However, Hc consistently increases with ball milling time, as the samples are strain-hardened, introducing more magneto anisotropy. The coercive fields of these samples are easily recovered during the high-temperature magnetization measurement at 900 K, and an Hc of 3.78 Oe is obtained upon recovery. This strategy paves a new way for straightforwardly making soft magnetic powders while avoiding high quenching rate requirement and the possibility of oxidation during annealing.

Magnetoelastic effects and random magnetic anisotropy in highly strained ultrathin Ni nanowires epitaxied in a SrTiO3 matrix

We analyze the magnetic anisotropy of Ni nanowires with diameters smaller than 5 nm. The nanowires are vertically epitaxied in a SrTiO3(001) matrix which generates huge tensile strains up to 3.6% along the nanowire axis. This leads to an unusual anisotropy, characterized by an easy magnetization plane perpendicular to the nanowire axis. Hysteresis cycles M(H) unveil an overall in-plane isotropy, while an opening of the M(H) cycles and thermal activation measurements indicate the presence of local energy barriers inside the nanowires. Surprisingly, the coercive field Hc(T) decays exponentially with increasing temperature, for both the easy plane and the hard axis. Based on these findings, we provide an analysis of magnetoelastic effects in the nanowires. By considering global averaging over the anisotropy distribution and local averaging according to the Random Magnetic Anisotropy model, we find that the global anisotropy, with its hard axis and isotropic easy plane, is related to the mean strain, while coercivity arises from local strain variations. We evidence that a thermally activated anisotropy softening occurs in the nanowires, in addition to Sharrock’s law of thermal reduction of coercivity. Possible mechanisms responsible for this thermal softening of anisotropy are proposed and discussed. Our study eventually allows to identify two major competing effects at play in the present system: an increasing magnetic anisotropy with increasing strain and a reduction of the anisotropy with increasing local strain fluctuations.

Magnetic dilution by severe plastic deformation

Mixtures of Fe and Cu powders are cold-compacted and subsequently deformed with severe plastic deformation by high-pressure torsion, leading to bulk samples. The dilution of Fe in the Cu matrix is investigated with SQUID-magnetometry, whereas the magnetic properties change as a function of Fe-content from a frustrated regime to a thermal activated behaviour. The magnetic properties are correlated with the microstructure, investigated by synchrotron X-ray diffraction and atom probe tomography. Annealing of the as-deformed states leads to demixing and grain growth, with the coercivity as a function of annealing temperature obeying the random anisotropy model. The presented results show that high-pressure torsion is a technique capable to affect the microstructure even on atomic length scales.

Influence of dipolar interactions on the magnetic properties of superparamagnetic particle systems

Magnetic effects caused by dipolar interactions in single-domain magnetic ensembles at finite temperatures are described. A modified superparamagnetic approach based on the mean field theory and random anisotropy model has been developed to describe the magnetization curves of nanoparticle assemblies. The model was used to fit experimental zero-field-cooled and field-cooled magnetization curves in Fe3O4 nanoparticles embedded in paraffin. The fitting parameters were based on structural properties of the materials and the strength of the interactions between nanoparticles. The model provides a quantitative description of the effects of the nanoparticle interaction with good agreement with the experiment. In addition, the model was adapted to describe magnetic properties of a NiFe thin film patterned into a nanodot array, showing potential to be used as a framework to predict magnetic interaction effects in high-density 2D arrays such as bit patterned media.

Magnetic microstructure of the Finemet-type thin films

Fe73.9Cu1Nb3Si13.2B8.9 thin films were deposited on the glass substrates by means of ion-plasma radio frequency sputtering. Heat treatment at temperatures of 350, 400 and 450 °C was performed for 30 minutes in order to control thin film structural state. The X-ray powder diffraction showed that the crystallization of α-Fe(Si) nanograins took place at the temperature of 420 °C whilst the other samples stayed in the amorphous state. The magnetic microstructure of the Fe73.9Cu1Nb3Si13.2B8.9 films was discussed in the framework of random anisotropy model and law of approach of magnetization to saturation. The parameters of magnetic microstructure were determined, and relations between structure and macroscopic magnetic properties were interpreted by means of magnetic microstructure analysis.

Scattering theory of transport through disordered magnets

We present a scattering theory of transport through noncollinear disordered magnetic insulators. For concreteness, we study and compare the random field model (RFM) and the random anisotropy model (RAM). The RFM and RAM are used to model random spin disorder systems and amorphous materials, respectively. We utilize the Landauer-Buttiker formalism to compute the transmission probability and spin conductance of one-dimensional disordered spin chains. The RFM and the RAM both exhibit Anderson localization, which means that the transmission probability and spin conductance decay exponentially with the system length. We define two localization lengths based on the transmission probability and the spin conductance, respectively. Next, we numerically determine the relationship between the localization lengths and the strength of the disorder. In the limit of weak disorder, we find that the localization lengths obey power laws and determine the critical exponents. Our results are expressed via the universal exchange length and are therefore expected to be general.

Study of exchange interaction, magnetization correlations and random magnetic anisotropy in nanocrystalline Pr2Co7 films deposited on Si substrate

In this work, we studied the exchange interaction as a function of X thickness for nanocrystalline Pr2Co7 thin films prepared by electron beam evaporation on Si(100) substrate. A quantitative analysis of static ferromagnetic correlations was realized by two methods: the correlation magnetometry technique (CMT) and magnetic force microscopy (MFM). Using random magnetic anisotropy model, the thickness dependence of magnetic macroscopic properties (exchange interaction energy A, the magnetic correlation length Rc, the anisotropy constant Ka) and magnetic microscopic properties (saturation magnetization Ms, coercivity Hc) were investigated. In addition, many fundamental magnetic parameters were extracted. The exchange interaction energy A decreases from 6.151 × 10-7 for X = 10 nm to 6.132 × 10-7 erg/cm for X = 400 nm. This causes a decrease in the coercivity Hc from 81.2 × 104 to 10.4 × 104 A/m. The soft magnetic properties of these films are due to interaction of magnetization correlations and random magnetic anisotropy. The nanocrystalline Pr2Co7 films can be considered as suitable candidates for basic surveys of magnetization correlations.

Structural and magnetic properties of amorphous and nanocrystalline Fe–Si–B–P–Nb–Cu alloys produced by gas atomization

Fe–Si–B–Nb–Cu alloy powders, with and without P additions, were produced by gas atomization. The particles smaller than 20 μm are fully amorphous, exhibiting good soft magnetic properties. The crystallization process was studied by differential scanning calorimetry, demonstrating that its kinetics changes dramatically with small variations in the composition. The (Fe0.76Si0.09B0.10P0.05)97.5Nb2.0Cu0.5 (at. %) alloy was annealed in the supercooled liquid region (480 °C) and at the first crystallization peak (530 °C). The structural characterization by means of differential scanning calorimetry, X-ray diffraction, and transmission electron microscopy provided information that explained the excellent soft magnetic properties. Annealing at 480 °C produced an amorphous relaxed structure with improved soft magnetic properties. At 530 °C, a two-phase material formed by nanocrystals with an average grain size of 16–17 nm embedded in an amorphous matrix was developed. Partial nanocrystallization increased the saturation magnetization from 139 to 144 emu/g and reduced the coercivity from 2.24 to 0.69 Oe. These results can be understood in terms of the algebraic contribution of both phases to the magnetization and the application of the random anisotropy model to nanocrystalline soft magnetic materials.

Magnetism and structure in nanocomposite Fe nanoparticle/Al matrix films

We describe magnetometry measurements performed on nanocomposite films formed of Fe nanoparticles embedded in Al matrix. The samples were prepared using a flexible co-deposition technique under Ultra-High Vacuum (UHV) environments. Fe nanoparticles, made by using a gas aggregation source, were co-deposited with an atomic Al beam, made by an MBE source. The Volume Filling Fraction (VFF) of nanoparticles was varied controllably between 4% and 45%, while the mean diameter of Fe nanoparticles produced by the source was ∼ 2 nm. Fe K edge extended x-ray absorption fine structure (EXAFS) experiments show that there is a high degree of alloying between Fe nanoparticles and Al atoms. Magnetism in the embedded Fe nanoparticle samples was investigated using a SQUID magnetometer. Atomic moment of Fe in the Fe/Al nanocomposite films increases slightly when the proportion of Fe nanoparticles is increased, but is still significantly lower than the bulk Fe value. In a more detailed analysis, the magnetisation curves were fitted using the Random Anisotropy Model (RAM) which allowed the exchange field and random anisotropy field to be evaluated. The findings and issues raised by this approach are discussed.

Coherent Magnetization Rotation of a Layered System Observed by Polarized Neutron Scattering under Grazing Incidence Geometry

The in-plane magnetic structure of a layered system composed of polycrystalline grains smaller than the ferromagnetic exchange length was studied to elucidate the mechanism controlling the magnetic properties considerably different from the bulk using polarized neutron scattering under grazing incidence geometry. The measured result, together with quantitative analysis based on the distorted wave Born approximation, showed that the in-plane length of the area with a uniform orientation of moments ranging from 0.5–1.1 μ m was not significantly varied during the process of demagnetization followed by remagnetization. The obtained behavior of moments is in good agreement with the two-dimensional random anisotropy model where coherent magnetization rotation is dominant.

Zn-doped cobalt ferrite: Tuning the interactions by chemical composition

Magnetic nanoparticles represent complex but very interesting objects. They combine the bulk properties with novel phenomena emerging at the nanoscale due to finite-size effects. The recent development of the synthetic procedures allows having a strong control on the size and shape of individual particles and on their physical-chemical structure. Among different magnetic materials, spinel ferrite nanoparticles offer strong chemical and physical stability as well as tunable magnetic properties. In the present article, we investigate the effect of Zn substitution in cobalt ferrite nanoparticles. The technological development of nanoparticle-based magnetic materials aims to find a balance between a well-defined magnetic behavior of individual elements and their strong interactions, which arise from the need of miniaturization that leads to dense ensembles of the system's constituents. Within this complex context, we provide one route to optimize the properties of small spinel ferrite particles by tuning their chemical composition without compromise their structural properties, and with full control of their size and shape. Furthermore, we propose an advanced analysis of their magnetic properties in the framework of the random anisotropy model. We will show that the chemical composition not only determines the intrinsic anisotropy energy of each nanoparticle but also owns a profound effect on the interparticle interactions.

Two‐Mode Stochastic Magnetic Structure in Nanocrystalline Soft Magnetic Fe–Zr Films

The magnetic structure of Fe100–xZrx films (x = 0, 0.6, 1.8, 2.9, and 4.1 ± 0.1 at%), which is characterized by the existence of stochastic domains determined by correlation magnetometry method, is discussed in terms of the random anisotropy model. It is found that two modes of the magnetic anisotropy field of stochastic domains are formed, which differ in the exchange stiffness magnitude and determine the existence of two modes of the coercive field found in the magnetic hysteresis loops.

Microstructure and magnetic properties of dilute nanocrystalline Fe-Si prepared by high energy ball milling

The microstructure and magnetic properties of nanocrystalline Fe-Si soft magnetic material fabricated by high energy vibratory milling are investigated. Fe-Si × wt% (x = 1.78, 3.51, 3.80, 5.08, 6.06, 6.98, 8.04) compositions are studied, with the 3.5 wt% case being used as a model system to investigate effects of processing time. X-ray diffraction (XRD) measurements indicate that the Si is fully in solution in the Fe lattice and no ordered phases are present. It is shown that microstructural evolution is accelerated compared with previously observed lower energy milling processes of iron-based alloys. It is also shown that magnetic properties are in disagreement with the formulas derived from the random anisotropy model, and explanations are provided for potential sources of this discrepancy in this and other reported work.

Nanocrystalline soft magnetic materials from binary alloy precursors with high saturation magnetization

A brief survey of the recent advances in Fe-based nanocrystalline soft magnetic alloys has shown that the saturation magnetization (Js) of these alloys is governed by the mass fraction, rather than the atomic fraction, of the nonmagnetic additives. Thus, the ultimate limit of Js in the alloys prepared by nano-crystallization of amorphous precursors is expected in an Fe-B binary system where amorphization by rapid quenching takes place with the lowest mass fraction of glass forming elements in Fe-based systems. We will demonstrate that nano-crystallization is possible in this binary system when the precursor amorphous phase is annealed ultra-rapidly. While the grain size after conventional annealing for amorphous Fe-B alloys is too large for the exchange softening effect, a small grain size well below the exchange length is obtained after annealing with a heating rate of 103 – 104 K/s. This results in magnetically soft nanostructures with Fe content up to 97.2 wt. %, leading to a high Js ≥ 1.9 T with a small coercivity (Hc) between 3.8 and 6.4 A/m. An addition of Co to nc-Fe87B13 results in a higher Js of 2.0 T with a slight increase of Hc to 9.3 A/m. The soft magnetic properties of these ultra-rapidly annealed alloys (named HiB-Nanoperm) is well understood by the random anisotropy model. The formation of nano-meter scale microstructures in a simple binary system unlocks previously unavailable alloy design strategies in nanostructured systems which is not only relevant to magnetic materials but, also to structural materials.

Two modes of magnetic structure of nanocrystalline FeZrN films prepared by oblique-angle magnetron sputtering

Abstract The rf oblique-angle magnetron sputtering was used to prepare nanocrystalline Fe77Zr7N16 (at.%) films (with grain size of 2–7 nm); the phase composition of the films is the α-Fe-based solid solution supersaturated with nitrogen and zirconium. The magnetic structure of the films is represented by stochastic domains. Using the correlation magnetometry method, two modes of stochastic domains were found, which correlate with two modes of the coercive force found in the magnetic hysteresis loops. Both modes of the coercive force are considered in terms of the random anisotropy model.

Anisotropy of Assemblies of Densely Packed Co-Alloy Nanoparticles Embedded in Carbon Nanotubes

We report on the magnetic properties of an array of binary metal CoFe, CoNi, and CoPt nanoparticles (NPs) embedded inside vertically oriented carbon nanotubes (CNTs). Samples were synthesized by chemical vapor deposition activated by current discharge plasma and hot filaments. Assemblies of Co-based catalytic NPs were prepared on SiO2/Si substrates by sputtering ultrathin films followed by reduction in an H2/NH3 mixture. As a result of the CNT growth, each CNT contained only one ferromagnetic NP located at the top. For all samples, the easy axis of magnetization was along the CNT axis. The magnetic parameters, including effective anisotropy constant and the contributions of dipole interactions and shape, magnetocrystalline, and magnetoelastic anisotropies, were estimated based on the experimental data and a random-anisotropy model. The magnetoelastic contribution was decisive. From the magnetoelasticity, the stresses in the NPs embedded in the CNTs were determined. Finally, the magnetization distribution in CoFe, CoNi, and CoPt NPs was simulated considering the magnetoelastic contribution.

Rotatable anisotropy in Fe4N thin film with quasi-single magnetic domain

Unique rotatable anisotropy is designed and achieved in Fe4N thin film with quasi-single magnetic domain structure by the exchange coupling between magnetic crystalline grains. It is found that the rotatable anisotropy can be characterized with isotropic rectangular in-plane hysteresis loops with remanence ratio close to 0.9 and angle-independent permeability spectra with quasi-isotropic resonance frequency, line-width and amplitude. Strength of the rotatable anisotropy is estimated by the random anisotropy model theoretically and it is comparable with the experimental results. Its rotatable feature can be understood from the equivalent remanence state established along different directions and the nucleation magnetization reversal. Moreover, a static method is established to determine rotatable anisotropy of the Fe4N thin film. A 50 Oe rotatable anisotropy was determined by M-H curve measured by B-H loop analyzer, which is close to 58 Oe derived from the permeability spectra. Our work provides the new way to search and characterize the rotatable anisotropy in magnetic systems.