Langevin Function Research Articles

Investigation on electronic and magnetic properties of Cr doped V2O5 thin films prepared by chemical solution deposition method

The present study examines the role of Cr doping on the electronic and magnetic behaviour of V2O5i.e. V2-xCrxO5 (x = 0, 0.05, and 0.10) thin films, prepared by chemical-solution deposition technique on Si (111) substrate. X-Ray diffraction technique shows the purity of the films and confirms no secondary phase formation. The atomic force microscopy was used to confirm the roughness of the films. A morphological investigation is done using High-resolution scanning electron microscopy associated with Energy dispersive X-Ray mapping of each element of the film. Fourier transform Infrared spectroscopy is utilised to identify functional groups that are present in obtained samples. The band-gap of these obtained samples is in the range of 0.8–0.6 eV, as examined by UV–Vis i.e., its value is decreasing with Cr doping. Using vibrating sample magnetometer, it is clear that samples shows ferromagnetic (FM) behaviour with saturation magnetization 0.3–0.6 μB/cc consistent with Langevin function fitting. It concludes the presence of FM behaviour of films and magnetization increases with carrier density, consistent with the carrier-induced origin of the ferromagnetism. X-ray photoemission spectroscopy (XPS) is utilised to understand its electronic properties. Core level spectra measurements suggest that V is in mixed state of 5+ and 4+. However Cr is in 3+ states. XPS and UV–Vis measurements imply that oxygen vacancies significantly contribute to the declination of the band gap and the promotion of FM-like behaviour. This discovery offers a promising pathway for engineering novel devices.

Features of itinerant magnetism in Fe0.6Al0.4 film with B2-like short-range order

The complex relationship between spontaneous magnetization (M s) and structural parameters in Fe–Al systems should be attributed to the B2-like short-range order (SRO) and itinerancy-induced sensitivity of magnetism in B2 FeAl. We focused on the role of SRO in the magnetism of Fe0.6Al0.4 film with the B2-like SRO. The high-field susceptibility (χHF) was observed through magnetometry, X-ray magnetic circular dichroism, and magneto-optical Kerr effect measurement, through which different χHF values were obtained. The M s–T curves deviated from the Brillouin function, and it can be interpreted following the spin-wave theory with a low spin-wave stiffness of 0.75 meV nm2. Based on the observed χHF and M s trends, the magnetic moment in the B2-like SRO was found to be induced by the exchange field from the surrounding ferromagnetic region. The coexistence of weak and strong ferromagnetic regions can be a possible reason for the complex magnetism in the Fe–Al system.

Research on Spatial Localization Method of Magnetic Nanoparticle Samples Based on Second Harmonic Waves

Existing magnetic tracer detection systems primarily rely on fundamental wave signal acquisition using non-differential sensor configurations. These sensors are highly susceptible to external interference and lack tomographic localization capabilities, hindering their clinical application. To address these limitations, this paper presents a novel method for achieving the deep spatial localization of tracers. The method exploits second harmonic signal detection at non-zero field points. By considering the combined nonlinear characteristics of the coil’s axial spatial magnetic field distribution and the Langevin function, a correlation model linking the signal peak and bias field is established. This model enables the determination of the tracer’s precise spatial location. Building on this framework, a handheld device for localizing magnetic nanoparticle tracers was developed. The device harnesses the second harmonic response generated by coupling an AC excitation field with a DC bias field. Our findings demonstrate that under conditions of reduced coil turns and weak excitation fields, the DC bias field exhibits exclusive dependence on the axial distance of the detection point, independent of particle concentration. This implies that the saturated DC bias field corresponding to the second harmonic signal can be used to determine the magnetic nanoparticle sample detection depth. The experimental results validated the method’s high accuracy, with axial detection distance and concentration reduction errors of only 4.8% and 4.1%, respectively. This research paves the way for handheld probes capable of tomographic tracer detection, offering a novel approach for advancing magnetically sensitive biomedical detection technologies.

A Novel Brillouin and Langevin Functions Dynamic Model for Two Conflicting Social Groups: Study of R&D Processes

We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented.

Magnetic Properties of Gd-Doped Bi7Fe3Ti3O21 Aurivillius-Type Ceramics.

The magnetic properties of Aurivillius-phase Bi7Fe3Ti3O21 (BFT) and Bi7-xGdxFe3Ti3O21, where x = 0.2, 0.4, and 0.6 (BGFT), were investigated. Ceramic material undoped (BGF) and doped with Gd3+ ions were prepared by conventional solid-state reaction. In order to confirm that the obtained materials belong to Aurivillius structures, XRD tests were performed. The XRD results confirmed that both the undoped and the gadolinium-doped materials belong to the Aurivillius phases. The qualitative chemical composition of the obtained materials was confirmed based on EDS tests. The temperature dependences of magnetization and magnetic susceptibility were examined for the ceramic material both undoped and doped with Gd3+ ions. The measurements were taken in the temperature range from T = 10 K to T = 300 K. Using Curie's law, the value of the Curie constant was determined, and on its basis, the number of iron ions that take part in magnetic processes was calculated. The value of Curie constant C = 0.266 K, while the concentration of iron ions Fe3+, which influence the magnetic properties of the material, is equal 3.7 mol% (for BFT). Hysteresis loop measurements were also performed at temperatures of T = 10 K, T = 77 K, and T = 300 K. The dependence of magnetization on the magnetic field was described by the Brillouin function, and on its basis, the concentration of Fe3+ ions, which are involved in magnetic properties, was also calculated (3.4 mol% for BFT). Tests showed that the material is characterized by magnetic properties at low temperatures. At room temperature (RT), it has paramagnetic properties. It was also found that Gd3+ ions improve the magnetic properties of tested material.

Magnetic anisotropy and GGG substrate stray field in YIG films down to millikelvin temperatures

Quantum magnonics investigates the quantum-mechanical properties of magnons, such as quantum coherence or entanglement for solid-state quantum information technologies at the nanoscale. The most promising material for quantum magnonics is the ferrimagnetic yttrium iron garnet (YIG), which hosts magnons with the longest lifetimes. YIG films of the highest quality are grown on a paramagnetic gadolinium gallium garnet (GGG) substrate. The literature has reported that ferromagnetic resonance (FMR) frequencies of YIG/GGG decrease at temperatures below 50 K despite the increase in YIG magnetization. We investigated a 97 nm-thick YIG film grown on 500 μm-thick GGG substrate through a series of experiments conducted at temperatures as low as 30 mK, and using both analytical and numerical methods. Our findings suggest that the primary factor contributing to the FMR frequency shift is the stray magnetic field created by the partially magnetized GGG substrate. This stray field is antiparallel to the applied external field and is highly inhomogeneous, reaching up to 40 mT in the center of the sample. At temperatures below 500 mK, the GGG field exhibits a saturation that cannot be described by the standard Brillouin function for a paramagnet. Including the calculated GGG field in the analysis of the FMR frequency versus temperature dependence allowed the determination of the cubic and uniaxial anisotropies. We find that the total crystallographic anisotropy increases more than three times with the decrease in temperature down to 2 K. Our findings enable accurate predictions of the YIG/GGG magnetic systems behavior at low and ultralow millikelvin temperatures, crucial for developing quantum magnonic devices.

Relationship between Inverse Langevin Function and r0-r1-Lambert W Function

The relationship between the inverse Langevin function and the proposed r0-r1-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable published approximations. High accuracy approximations, based on Schröder’s root approximations of the first kind, are detailed. Several applications are detailed.

Solving non-linearities of hyperelastic rubbery behaviour by the asymptotic numerical method: Highlighting with the case of a Hybrid Integral Approach (HIA) model

This paper presents mathematical modelling and simulation founded on an Asymptotic Numerical Method (ANM) for the rubber-like material hyperelastic behaviour. The basic models such as Mooney-Rivlin, and the Gent partial models and the Hybrid Integral Approach (HIA) model are considered. The HIA is a strong nonlinear model developed from the inverse Langevin function approximation is considered here for its efficiency. Explicit formulations of each model are presented as well as the associated asymptotic developments in the frame of the ANM. Various types of boundary conditions effects are analysed for each considered hyperelastic model. The effectiveness of the ANM compared to the Newton-Raphson method is demonstrated and particularly for the HIA model. We present as results stress-strain curves for the implementation of these different models where we specify the influence of the Imposed Displacement for tensile and compressive stresses when the structure is clamped and simply supported. In term of this study, we observe that the complete HIA model present the curves with the difference hardly perceptible when we vary results in term of stress-strain curves with different imposed Displacement. But when strain is high than 5%, the Mooney-Rivlin and the Gent partial models, presents the high disparities with different imposed Displacement. This observation justifying the limitations of partial models in term of characterisation of the behaviour law of hyperplastic materials.

Spin force analysis using the Brillouin function for spin half particles in magnetised non-relativistic quantum plasma

Spin force analysis using the Brillouin function for spin half particles in magnetised non-relativistic quantum plasma

Strong signature of uncompensated magnetization in frustrated cobalt manganites using x-ray magnetic circular dichroism study

The present study is focused on the investigation of the distorted tetragonal phase of mixed spinel oxides, due to their technological relevance in the field of electronics, spintronics, magnetism, catalysis, and electrochemical energy storage. Herein, we report on solgel synthesized multivalent cobalt manganites, CoMn2O4 (CMO), and subjected them to a comprehensive analysis to elucidate their physicochemical characteristics at room temperature. Analysis employing powder x-ray diffraction patterns and electron microscopy (including field-emission scanning electron microscopy and high-resolution transmission electron microscopy) results confirmed the formation of a pure and exceptionally crystalline, distorted tetragonal phase of mixed CMO. Synchrotron-based x-ray absorption spectroscopic (XAS) measurements in the total electron yield mode examined local electronic structures affirming the formation of CMO with uncompensated electronic states involving Co2+, Co3+, Mn2+, Mn3+, and Mn4+ cations. Concurrently, XAS and x-ray magnetic circular dichroism analyses revealed antiferromagnetic coupling within Co and Mn sublattices in CMO, indicating the presence of uncompensated electronic states. Vibrating sample magnetometry results demonstrated clear hysteresis behavior, explicitly indicating the coexistence of super-paramagnetic and canted antiferromagnetic characteristics in CMO, as validated through the Langevin function fitting and x-ray magnetic circular dichroism results. The noticeable absence of saturated magnetization confirmed the high degree of spin canting, primarily stemming from the presence of the Yafet–Kittel spin arrangement.

New heteroleptic l-argininato copper(II) complex with bromide and N, N’– heterocyclic ligands – synthesis, supramolecular, spectroscopic, magnetic and theoretical investigations

A new heteroleptic [CuBr(l−Arg)(bpy)]Br·2H2O (1) (l−Arg=l−Arginine, bpy=2,2’−bipyridine) complex has been synthesized and its molecular and supramolecular structure aspects have been discussed based on the X−ray single crystal structure and Hirshfeld analyses. In addition, the properties of complex 1 have been elucidated using different spectroscopic methods (FT−IR / FIR, Raman, NIR−Vis−UV, Q− / X− band EPR) and magnetic measurements. In this complex, the bromide anion occupies the apex of a slightly distorted square pyramid (τ = 0.12). The [CuBr(l−Arg)(bpy)]+ complex units exhibit a ribbon−like organization, with Cu(II) metal centers located at the corners of triangles where the shortest Cu∙∙∙Cu distance is 5.579 Å. The aromatic moieties of bpy are aligned nearly parallel leading to π···π interactions. Both, non−bonded and coordinated, Br− ions act as hydrogen−bond acceptors for guanidinium groups. Hirshfeld analysis indicated the importance of the Br∙∙∙H (17.9 − 18.4 %), O∙∙∙H (14.9−15.2 %), and H∙∙∙H (42.3−43.1 %) interactions in the molecular packing of the studied complex. Atoms in molecules (AIM) calculations indicated mainly the closed shell character for the Cu−N, Cu−O and Cu−Br coordination interactions. The G value calculated using the Q−band EPR spectra parameters g|| = 2.235 and g⊥= 2.05 is 4.7, what indicating negligible coupling and that local tetragonal axes are aligned parallel. A negative value of Weiss temperature θCW = -0.32 K indicates the presence of weak antiferromagnetic coupling between the neighboring Cu(II) ions mediated through hydrogen bonds and π-π stacking of aromatic moieties of bpy. The value of gav= 2.113 obtained from Q−band EPR spectra is consistent with that corresponding to the Curie constant (C = 0.4138 emu K mol−1), i.e.g = 2.101, and that obtained from the best fitting to the Brillouin function: g = 2.139.

Photo-strain induced magnetoresistance modulation in magnetoelectric heterostructure-based devices

The electric-field control of magnetic dynamics and magnetization in magnetoelectric (ME) heterostructures holds promise for energy-efficient beyond-CMOS devices. However, such techniques entail a high-saturation operational electric field near the device breakdown voltage and introduce complexity due to the requirement for electrical contacts. This study circumvents this issue by light-induced magnetoresistance (MR) modulation in a Ni/PMN-PT ME heterostructure driven by photo-strain-induced internal electric field. Reduced MR, especially in the perpendicular mode, is observed, signifying a localized reduction in the external magnetic field required for magnetization alignment, as elucidated by Langevin function analysis. The proposed method could facilitate better integration and scalability of ME-based spintronic devices, paving the way for low-power beyond-CMOS technologies.

Inversion of magnetic diameter distribution of magnetic fluids under high and low temperatures

The magnetic diameter is a crucial factor affecting the magnetic properties of magnetic fluids. The magnetic diameter distribution can be estimated based on the magnetic properties. However, the magnetic dipole interaction of magnetic nanoparticles (MNPs) and the variation of the magnetic diameter with temperature have received relatively little attention in previous research. Hence, this research proposes the AP-MMF1-L method to inverse the magnetic diameter which considers the magnetic dipole interaction and derives the magnetic diameter at different temperatures. Firstly, the AP-MMF1-L uses the least square method between the first-order modified mean-field Langevin function (MMF1-L) and the measured magnetization curve as the objective function. Meanwhile, the hybrid Artificial bee colony-particle swarm (AP) optimization algorithm is introduced to inverse the optimal magnetic diameter distribution. Secondly, the hydrodynamic diameter distribution experimental values are compared with the theoretical values, demonstrating the AP-MMF1-L method obtains accurate inversion results of the magnetic diameter distribution when compared to other models. Finally, the arithmetic mean of the magnetic diameter at different temperatures is investigated, revealing a decreasing trend as the temperature rises, approximately following a linear distribution. The AP-MMF1-L provides a novel and effective tool for accurately determining the magnetic diameter of the MNPs across various temperatures.

The influence of Nd3+ doping on the structural, optical, magnetic, and dielectric characteristics of nanoscale hexagonal wurtzite type ZnO

Nd3+ doped ZnO nanoparticles (NPs) Zn1−xNdxO (x = 0, 0.01, 0.03, and 0.05) were successfully synthesized via simple co-precipitation method. To extract precise crystallite size and lattice strain from the X-Ray Diffraction (XRD) pattern, Halder-Wagner method was employed. High Resolution Transmission Electron Microscopy (HRTEM) analysis clearly substantiates the NPs formation.The band gap variation in the doped samples in comparison with the pristine sample is extracted from UV–Vis diffuse reflection spectroscopy. The decrease in Photo-luminance (PL) intensity is observed to be significant for enhanced photocatalytic applications. At room temperature (RT), all Nd3+doped ZnO samples exhibit a distinct hysteretic loop. The initial magnetization graph and M-T curve fitted by the modified Brillouin function and combination of spin wave and Curie-Weiss law respectively. The well-fittings indicate the co-existence of paramagnetic (PM) and ferromagnetic (FM) phases in the doped sample, and the quantitative contribution to each phase is also extracted. Significantly high dielectric constant and low ac conductivity at a low frequency region support the presence of large dipolar effect-induced frequency-dependent short-range conductivity in these pristine and Nd3+ doped ZnO samples.

Modeling the Effect of Material Viscoelasticity on the Dielectric Permittivity of Deformed Elastomers.

Elastomers, as a typical category of soft dielectrics, have shown great potential for developing stretchable electronics and soft transducers. However, the performance of dielectric elastomers (DEs) is susceptible to the dielectric permittivity of the material, whether as insulators or actuators. On the other hand, experiments suggest that the material viscoelasticity significantly influences the dielectric permittivity of DEs. Based on the theory of finite-deformation viscoelasticity, this work adopts the Brillouin function to develop a modeling framework to examine the effect of material viscoelasticity on the dielectric permittivity for the first time. A comparison of the data fitting results between the models with and without consideration of the material viscoelasticity is presented. Simulation results also reveal that the viscous network of the elastomer exerts a mitigation effect on the decrease in the dielectric permittivity when the material is deformed. Furthermore, it is found that the loading rate is a key parameter that strongly affects the dielectric permittivity, mainly through the inelastic deformation.

An Effectively Uncoupled Gd8 Cluster Formed through Fixation of Atmospheric CO2 Showing Excellent Magnetocaloric Properties.

The [Gd8(opch)8(CO3)4(H2O)8]·4H2O·10MeCN coordination cluster (1) crystallises in P1¯. The Gd8 core is held together by four bridging carbonates derived from atmospheric CO2 as well as the carboxyhydrazonyl oxygens of the 2-hydroxy-3-methoxybenzylidenepyrazine-2-carbohydrazide (H2opch) Schiff base ligands. The magnetic measurements show that the GdIII ions are effectively uncoupled as seen from the low Weiss constant of 0.05 K needed to fit the inverse susceptibility to the Curie-Weiss law. Furthermore, the magnetisation data are consistent with the Brillouin function for eight independent GdIII ions. These features lead to a magnetocaloric effect with a high efficiency which is 89% of the theoretical maximum value.

Giant excitonic magneto-optical Faraday rotation in single semimagnetic CdTe/Cd1-xMnxTe quantum ring

Magnetic tuning of the bound exciton states and corresponding giant Zeeman splitting (GZS) between σ+ and σ− excitonic transitions in CdTe/Cd1-xMnxTe quantum ring has been investigated in the Faraday configuration for various concentrations of Mn2+ ions, using the variational technique in the effective mass approximation. The sp-d exchange interaction between the localized magnetic impurity ions and the delocalized charge carriers has been accounted via mean-field theory with the inclusion of a modified Brillouin function. The enhancement of the GZS, and in turn, the effective g-factor with the application of an external magnetic field, is strikingly manifested in type-I – type-II transition in the band structure, which has been well explained by computing the overlap integral between the electron and hole, and the in-plane exciton radius. This highlights the extraordinary magneto-optical properties, including the giant Faraday rotation and associated Verdet constant, which have been calculated using single oscillator model. The oscillator strength has been estimated, and is found to be larger than in the bulk diluted magnetic semiconductors (DMS) and quantum wells, reflecting stronger confinement inside the quantum ring. More extensive Zeeman splitting and a higher oscillator strength in the DMS-based QR lead to an ultra-high Verdet constant of 2.6×109rad/Teslam, which are a few orders of magnitude larger than in the existing quantum systems and magneto-optical materials.

A comprehensive study on MnZn ferrite materials with high saturation magnetic induction intensity and high permeability for magnetic field energy harvesting

Manganese-zinc (MnZn) ferrites have important applications in energy conversion, transmission, and harvesting. MnZn ferrite for magnetic field energy harvesting is expected to enhance the saturation magnetic induction (Bs), initial permeability (μi), and Curie temperature (Tc) aspects simultaneously, which is beneficial to the energy harvesting efficiency and safety of the device. In this paper, various formulations of MnZn ferrite samples were prepared by the conventional oxide ceramic process. The cation distribution was determined through Rietveld refinement of XRD patterns Based on this, the M–T curves were fitted by combining Néel molecular field theory with Brillouin functions. The greatest influence on the Curie temperature was found to be the molecular field coefficient between the A and B sites. The magnetization mechanism of MnZn ferrite was comprehensively analyzed by fitting the complex permeability spectrum, magnetocrystalline anisotropy constant, and magnetostriction coefficient. The ratio of domain wall displacement magnetization to domain rotation magnetization shows an increasing and then decreasing trend with Fe content, while |K1| shows an opposite trend. Finally, MnZn ferrite materials with excellent overall performance (Bs = 505mT, μi = 9016, Tc = 447 K) were prepared by investigating the magnetization mechanism.

Magnetic phase transition in dimer-based metal-organic frameworks through structural modulation

The flexibility of a structure is an important factor that affects the magnetic interactions, anisotropy, phase transitions, and domain structure of materials. It is essential to consider this factor for a thorough analysis of magnetic properties, as it enables researchers to design materials with specific magnetic characteristics for different purposes. In this work, experimental measurements were conducted to investigate the magnetic properties of DUT-8(Ni), composed of a Ni(II) dimer paddle wheel as the metal cluster and an organic linker. DUT-8(Ni) exhibits two distinct structures, one porous (open structure) and the other nonporous (closed structure), which have a significant impact on its magnetic properties. Our study focuses on the changes in its magnetic behavior due to these structural variations. The Ni(II) dimer's basic unit displays antiferromagnetic properties, and we observed interactions between intra- and inter-units in the 3D structure with the magnetic data we measured. To gain a deeper understanding, the magnetization of the open and closed structures is analyzed using a modified Langevin function.

Comparative study of Kondo effect in Vanadium dichalcogenides VX2 (X=Se & Te)

We report on the electrical transport, magnetotransport, and magnetic properties studies on the transition metal dichalcogenides VSe2 and VTe2 and draw a comprehensive comparison between them. We observe Kondo effect in both systems induced by the exchange interaction between localized moments and conduction electrons at low temperature, resulting into resistance upturn at 6 K for VSe2 and 17 K for VTe2. From the field dependent resistance measurements we find that the data is fitted best with modified Hamann equation corrected by the quantum Brillouin function for VSe2, while the data is fitted best with modified Hamann equation corrected by the classical Langevin function for VTe2. Interestingly, we observe a contrasting magnetoresistance (MR) property between these systems across the Kondo temperature. That means, negative MR is found in both systems in the Kondo state. In the normal state MR is positive for VSe2, while it is negligible for VTe2. In addition, both systems show weak ferromagnetism at low temperature due to intercalated V atoms.