Intergrain Exchange Interaction Research Articles

Magnetization Processes of Exchange Coupled Nd2(Fe,Co)14B Alloys in Various Demagnetized States

Processes of magnetization in exchange-coupled rapidly quenched nanocrystalline alloys Nd2(Fe1-xCox)14B, where x = 0, 0.07, 0.2, 0.5, have been studied. Initial magnetization curves and interaction plots δM(H) for various demagnetized states were obtained. Based on comparison of measurement results, influence of the pinning type mechanism on magnetization process in the Nd2(Fe1-xCox)14B melt-spun ribbons is shown. Using δM(H) plots, change in intergrain exchange interaction depending on cobalt concentration in rapidly quenched Nd2(Fe1-xCox)14B nanocrystalline alloys was investigated.

Structural and magnetic properties of CoTi thin films deposited by magnetron sputtering method

ABSTRACT Co1–xTix (x = 0.3, 0.5 and 0.7) thin films were prepared on Si (100) substrate using DC-magnetron sputtering deposition technique. A structural phase transition occurs from hexagonal to cubic crystal structure when the Ti composition is above 30 percentage. The thickness of the films obtained from X-ray Reflectivity data is about 30 nm. The average particle size of the CoTi thin films was calculated using the Atomic Force Microscopy image. The Magneto-Optic Kerr Effect measurements suggest that only Co0.7Ti0.3 thin film exhibits soft magnetic behaviour whereas the other thin films have no magnetic properties because of small grain size and reduction of inter-grain exchange interaction. Co0.7Ti0.3 thin film has twofold magnetic anisotropy. The angle-dependent coercivity (H c) is numerically fitted with a two-phase model of magnetization reversal, which confirms the presence of magnetic anisotropy. The magnetization reversal occurs via coherent rotation of spins along the hard axis.

δM plots of nanocrystalline hard magnetic alloys

Magnetic properties of nanocrystalline hard magnetic alloys such as coercivity and maximum energy product are strongly depended on microstructure and interactions between grains. There are a lot of advanced experimental techniques for microstructure characterization but the analysis of intergrain interactions is still challenging. One of the wide-spread methods for doing that is plotting δM(H). This work is aimed to elucidate how different factors effect δM(H) plots for high-anisotropy nanocrystalline alloys. Specifically, changes of δM(H) plots caused by both intergrain exchange and magnetostatic interactions, grain size dispersion, and demagnetization factor are analyzed systematically using macrospin-based simulations. It is demonstrated that all these factors should be considered for a reliable evaluation of exchange coupling in alloys. A concept of such analysis is presented and applied to rapidly quenched Nd-FeCo-B alloy.

Additive manufacturing of heavy rare earth free high-coercivity permanent magnets

Laser based powder bed fusion is a promising manufacturing method that can be used for the fabrication of hard magnets such as NdFeB with nearly any given geometrical shape. However, the weak performance, e.g., low coercivity, of the 3D-printed magnets currently hinder their application. In this work, we demonstrated a proof-of-concept of powder bed additive manufacturing of heavy rare earth free NdFeB magnets with technologically attractive coercivity values. The 3D-printed NdFeB magnets exhibit the highest (up-to-date for the additively manufactured magnets without heavy rare earth metals) coercivity values reaching μ0Hc = 1.6 T. The magnets were synthesized using a mixture of the NdFeB-based and the low-melting eutectic alloy powders. The essential function of the eutectic alloy, along with binding of the NdFeB-based magnetic particles, is the significant improvement of their coercivity by the in-situ grain boundary (GB) infiltration. The fundamental understanding of the magnetization reversal processes in these 3D-printed magnets leads to the conclusion that the excellent performance of the additively manufactured hard magnets can be achieved through the delicate control of the intergrain exchange interaction between the grains of the Nd2Fe14B phase.

Effect of intergrain exchange interaction on magnetic viscosity of nanocrystalline isotropic NdFeB magnets

The coefficient of magnetic viscosity, S, of NdFeB alloys with varied intergrain exchange interaction constant, KIEI, was measured. The observed dependences of fluctuation field, Hf, on the applied field, H, are strongly correlated with KIEI value. Cooperative magnetization reversal of single domain interacting particles leads to improve the temperature stability of permanent magnets and magnetic systems based on them.

Characterisation of high-anisotropy nanocrystalline alloys based on magnetic susceptibilities in the remanent state

The macroscopic magnetic properties of nanocrystalline alloys are strongly dependent on microstructural and micromagnetic inhomogeneities along with intergranular interactions. In particular, magnetic susceptibility is sensitive to these factors and frequently used for alloy characterisation. In this work reversible magnetic susceptibility in the remanent state of the nanocrystalline alloy with randomly oriented easy magnetisation axes is considered. Due to intergranular interactions the susceptibilities measured parallel and perpendicular to the remanence can be distinctly different from each other. When the intergrain exchange is the dominant interaction this susceptibility feature has potential for its quantitative evaluation. Here this opportunity is studied by means of two approaches: analytical solutions based on the mean-field approximation and simulations using the kinetic Monte Carlo model. The dependence of the magnetic susceptibility on the exchange coupling strength are investigated taking into account the effects of grain size distribution and magnetostatic interactions. These results lead us to propose an experimental susceptibility-based method for the estimation of both intergrain exchange interaction strength and effective magnetic anisotropy constant. This method can be used for the characterisation of high-anisotropy nanocrystalline alloys with randomly oriented easy magnetisation axes that is a widespread case. The method is applied to rapidly quenched Nd2(Fe0.8Co0.2)14B nanocrystalline alloy giving strong exchange coupling and a reasonable value for the anisotropy constant.

High-coercivity Nd7.5Y2.7Fe62B22.3Nb3.1Cu2.4 nanocomposite magnet produced by rapid solidification process

Nanocomposite hard magnets in the form of cones have been synthesized by rapid solidification process with Nd7.5Y2.7Fe62B22.3Nb3.1Cu2.4 alloy. X-ray diffraction studies deduced that as-cast alloys have a mixture of α-Fe, Fe3B, Nd2Fe14B and amorphous phase which, upon annealing, transformed into α-Fe, Fe3B and Nd2Fe14B magnetic phases. Transmission electron microscopy and three dimensional atom probe analysis elucidated a nanocrystalline microstructure consists of magnetically soft α-Fe, Fe3B and hard Nd2Fe14B nanograins. The good hard magnetic properties such as remanence (Br) of 0.45 T, coercivity (iHc) of 1315 kA/m and maximum energy product (BH)max of 56.7 kJ/m3 were obtained after annealing the Nd7.5Y2.7Fe62B22.3Nb3.1Cu2.4 alloy at 1013 K for 15 min. Henkel plot yielded the existence of strong inter-grain exchange interactions between magnetically soft and hard grains. High coercivity of 1315 kA/m for the optimally annealed Nd7.5Y2.7Fe62B22.3Nb3.1Cu2.4 alloy is ascribed to the large volume fraction of hard magnetic phase, high magnetocrystalline anisotropy and interface effects.

Micromagnetic simulation for the magnetization reversal process of Nd-Fe-B hot-deformed nanocrystalline permanent magnets

We numerically demonstrated the magnetization reversal process inside a hot-deformed nanocrystalline permanent magnet. We performed large-scale micromagnetics simulation based on the Landau–Lifshitz–Gilbert equation with 0.1 billion calculation cells. The simulation model for the hot-deformed nanocrystalline permanent magnet consists of 2622 tabular grains that interact with each other by inter-grain exchange and dipole interactions. When the strength of the external field approached a coercive force, nucleation cores were created at the grain surface. The magnetization reversal was propagated by the inter-grain and dipole interactions. When the grains had overlapping regions parallel to the external field, the magnetization reversal propagated quickly between the grains due to the dipole interaction. In contrast, the motion of the magnetic domain wall was inhibited at interfaces between the grains perpendicular to the external field. Reversal magnetic domains had a pillar-shaped structure that is parallel to the external field. In the perpendicular direction, the reversal magnetic domain expanded gradually because of the inhibition of the domain wall motion.

Influence of the Coulomb interaction on the exchange coupling in granular magnets

We develop a theory of the exchange interaction between ferromagnetic (FM) metallic grains embedded into insulating matrix by taking into account the Coulomb blockade effects. For bulk ferromagnets separated by the insulating layer the exchange interaction strongly depends on the height and thickness of the tunneling barrier created by the insulator. We show that for FM grains embedded into insulating matrix the exchange coupling additionally depends on the dielectric properties of this matrix due to the Coulomb blockade effects. In particular, the FM coupling decreases with decreasing the dielectric permittivity of insulating matrix. We find that the change in the exchange interaction due to the Coulomb blockade effects can be a few tens of percent. Also, we study dependence of the intergrain exchange interaction on the grain size and other parameters of the system.

Magnetization reversal processes of isotropic permanent magnets with various inter-grain exchange interactions

We performed a large-scale micromagnetics simulation on a supercomputing system to investigate the properties of isotropic nanocrystalline permanent magnets consisting of cubic grains. In the simulation, we solved the Landau–Lifshitz–Gilbert equation under a periodic boundary condition for accurate calculation of the magnetization dynamics inside the nanocrystalline isotropic magnet. We reduced the inter-grain exchange interaction perpendicular and parallel to the external field independently. Propagation of the magnetization reversal process is inhibited by reducing the inter-grain exchange interaction perpendicular to the external field, and the coercivity is enhanced by this restraint. In contrast, when we reduce the inter-grain exchange interaction parallel to the external field, the coercivity decreases because the magnetization reversal process propagates owing to dipole interaction. These behaviors show that the coercivity of an isotropic permanent magnet depends on the direction of the inter-grain exchange interaction.

Competition of the Coulomb and hopping-based exchange interactions in granular magnets

We study exchange coupling due to the interelectron Coulomb interaction between two ferromagnetic grains embedded into an insulating matrix. This contribution to the exchange interaction complements the contribution due to virtual electron hopping between the grains. We show that the Coulomb and the hopping-based exchange interactions are comparable. However, for most system parameters these contributions have opposite signs and compete with each other. In contrast to the hopping-based exchange interaction the Coulomb-based exchange is inversely proportional to the dielectric constant of the insulating matrix $\ensuremath{\varepsilon}$. The total intergrain exchange interaction has a complicated dependence on the dielectric permittivity of the insulating matrix. Increasing $\ensuremath{\varepsilon}$ one can observe the ferromagnet-antiferromagnet (FM-AFM) and AFM-FM transitions. For certain parameters no transition is possible, however even in this case the exchange interaction has large variations, changing its value three times by increasing the matrix dielectric constant.

A New Method of Intergrain Exchange Interaction Energy Determination in Nanostructured Alloys with Spontaneous Spin-Reorientation Transition

A new method of intergrain exchange interaction energy determination in nanostructured magnetically hard alloys with spontaneous spin-reorientation transition has been developed and verified. It is based on the knowing of the material magnetic anisotropy constants values at its “easy cone” state and the external negative magnetic field strength H, which reversibly “tears” the exchange coupling between nanograins. It should be more than exchange field and smaller than coercivity value. Using this method the exchange interaction energy parameter for MQP-B+ alloy was estimated. Its value is in agreement with estimated one by FMR technique for film system Fe-Nd2Fe14B and close to that obtained from the remanent magnetization temperature dependences measurements in negative magnetic fields.

Inter-grain interaction in random magnetic anisotropy simulation in magnetic nanocrystals

Effect of inter-grain exchange interaction on the coercive forces was analyzed with a numerical simulation in magnetic materials with random magnetic anisotropy. The magnetization of an assembly of magnetically interacting grains with randomly oriented uniaxial anisotropy was calculated using the Landau-Lifshitz-Gilbert equation. We supposed a single spin model where the magnetizations in a grain were aligned in the same direction, for simplicity. Calculations were carried out for an N×N×N system, where the number of grains on a side, N ranged from 16 to 128. The relation between the coercive forces HC and the grain size D is represented by HC∝Dk. With the increase of N, k decreased gradually and tended to reach a saturated value around k = 4.5–5, which dose not correspond to the primitive theory of the random anisotropy model where k = 6. The deviation was discussed in terms of the inter-grain interaction, essentially proportional to the inverse of D.

Intergrain exchange interaction estimation from the remanence magnetization analysis

Abstract Analysis of δ m ( H ) = [ M d ( H ) − M r ( ∞ ) + 2 M r ( H ) ] / M r ( ∞ ) curves constructed from dc demagnetization and isothermal remanent magnetization ( M d ( H ) and M r ( H ) respectively) is important for characterization of the interactions in ferromagnets. Up to now, it has been mainly used for qualitative deductions about them. In this work, the novel functional relation between the maximum of the δ m ( H ) plot and the microscopic parameters of the weakly coupled Stoner–Wohlfarth ensemble with the isotropic distribution of easy magnetization axes was established using computer modeling. It allows quantitative analysis in the frame of the model to be performed. Finally, a new method of estimating the intergrain exchange interaction constant for nanostructured high anisotropy magnets could be formulated taking into account the results of the modeling.

Effects of W substitution on the magnetic properties, phase evolution and microstructure of rapidly quenched Co80Zr18B2 alloy

The effects of a partial substitution of W for Zr on the magnetic properties, phase evolution, and microstructure of Co80Zr18−xWxB2 (x=0, 1, 2 and 3) melt-spun ribbons are investigated in this paper. For the as-spun samples, the optimal magnetic properties of iHc=6.6kOe and (BH)max=4.5MGOe are achieved in the Co80Zr16W2B2. Thermomagnetic analysis (TMA) and x-ray diffraction (XRD) results suggest that the as-spun Co80Zr16W2B2 mainly comprises of hard magnetic phase. Scanning electron microscope (SEM) results indicate that W addition refines the microstructure, which results in an increase in the intergrain exchange interaction. The effects of heat treatment on the magnetic properties of as-spun Co80Zr18−xWxB2 (x=0, 1, 2 and 3) are also studied. The maximum iHc of 7.3kOe with a (BH)max of 3.8MGOe is obtained in the Co80Zr16W2B2 after a heat treatment at 550°C. The origin of coercivity enhancement in Co80Zr16W2B2 is ascribed to the increase in magnetocrystalline anisotropy field (Ha) of hard magnetic phase.

Rotatable magnetic anisotropy in Si/SiO2/(Co2Fe)xGe1−x Heusler alloy films

Polycrystalline (Co2Fe)xGe1−x Heusler alloy films are fabricated by sputtering on amorphous substrates and shown to possess three types of magnetic anisotropy. The nearly stoichiometric composition of x = 50 m.f.% shows a rectangular hysteresis loop and isotropic coercive and ferromagnetic resonance fields when the film is field-magnetized along any in-plane direction, thus predominantly possessing rotatable in-plane magnetic anisotropy. Higher-x compositions show evidence of two- and fourfold in-plane anisotropy superposed on the rotatable one. A qualitative model of the observed anisotropic magnetic properties is proposed. The model explains the rotatable anisotropy by taking into account dry friction for the in-plane rotation of the magnetization direction in a fine-grained polycrystalline film with the magnetic grain size smaller than the correlation length of the inter-grain exchange interaction. The observed two- and fourfold magnetic anisotropy contributions are attributed to partial texturing of the fine-grained films, even though the films are grown on amorphous SiO2 substrates. These results should be valuable for understanding and controlling the magnetic behaviour of highly spin-polarized Heusler alloy films used in various magnetic nanodevices.

High performance Co80Zr15Ti3B2 melt-spun ribbons

The small substitution of Ti for Zr in the Co80Zr18B2 melt-spun ribbons resulted in a significant improvement of magnetic properties. The optimal magnetic properties of coercivity Hc=4.5kOe, and maximum energy product (BH)max=5.0MGOe were obtained in the Co80Zr15Ti3B2 ribbons produced at a wheel speed of 30m/s. X-ray diffraction (XRD) and thermomagnetic analysis (TMA) revealed that the Co–Zr–Ti–B ribbons mainly consisted of Co11Zr2 phase and Ti substitution made the phase more unstable. The investigation of microstructure indicated that the grain size decreased significantly with the increase of Ti content. A suitable grain size of Co11Zr2 phase was believed to be the main reason for the drastic increase in coercivity. On the other hand, the appropriate refinement of grain led to a significant enhancement of intergrain exchange interaction in the Co80Zr15Ti3B2.

The Magnetocaloric Effect in Two-Phase Y-Fe Nanocrystalline Alloys

Synthesis of nanocomposite based on binary compound and determination of dependence between the values of magnetocaloric effect (MCE) and the grain size of such specimens are the purposes of this work. The results of the investigation in microcrystalline and nanocrystalline samples Y25Fe75 and Y35Fe65 alloys show, that reduction of the grain size down to 80-100 nanometers on nanocrystalline samples of Y25Fe75 and Y35Fe65 alloys leads to increasing of value of MCE by 20-25 % from comparison with values on microcrystalline samples. It can be explained by intergrain exchange interaction in nanocrystalline alloys.

Evidence of finite-size effect on the Néel temperature in ultrathin layers of CoO nanograins

A significant reduction in the N\'eel temperature of CoO ultrathin films is revealed by highly sensitive specific heat measurement. It is found that the films consist of weakly coupled antiferromagnetic (AF) grains. The ${T}_{N}$ reduction from large to small grain samples scales with the grain size reduction, according to the Binder theory of critical phenomena in systems of reduced dimensions. In these finite AF nanosystems, the intergrain exchange interaction is reduced by the presence of surface Co spins, weakly coupled to Co moments inside the grains.

“In-plane” and “out-of-plane” uniaxial anisotropy of amorphous precursors and nanocrystalline FeCuNbSiB alloys

The “in-plane” and “out-of-plane” angular dependence of ferromagnetic resonance data demonstrate that both cubic and uniaxial magnetocrystalline anisotropies are present in FeCuNbSiB nanocrystalline alloys. The intergrain exchange interactions, mediated by the spins of the amorphous ferromagnetic matrix, are unable (able) to average out the local uniaxial magnetocrystalline anisotropy of the Fe3B and Fe2Si nanocrystalline grains and, thereby, lead to the magnetic hardening (softening) in the early stages of nanocrystallization in most of the compositions (remaining ones).