Molecular Field Approximation Research Articles

Effect of Ho3+ Substitution on Magnetic Properties of ZnCr2Se4.

A series of ZnCr2-xHoxSe4 microcrystalline spinels (where x = 0.05, 0.075, and 0.10) containing holmium ions in octahedral coordination were obtained by sintering of adequate reactants at high temperatures. The obtained doped materials were characterized by X-ray diffraction, Scanning Electron Microscopy, UV-Vis-NIR, molecular field approximation, and XPS spectroscopies. Their thermal properties were also investigated. The doping of the ZnCr2S4 matrix with paramagnetic Ho3+ ions with a content of not more than 0.1 and a screened 4f shell revealed a significant effect of orbital and Landau diamagnetism, a strong reduction in short-range ferromagnetic interactions, and a broadening and shift of the peak of the first critical field by simultaneous stabilization of the sharp peak in the second critical field. These results correlate well with FPLO calculations, which show that Cr sites have magnetic moments of 3.19 µB and Ho sites have significantly larger ones with a value of 3.95 µB. Zn has a negligible magnetic polarization of 0.02 µB, and Se induces a polarization of approximately -0.12 µB.

Analysis of metamagnetic transitions in antiferromagnetic arrangements in the RRhIn5 (R[dbnd]Nd, Tb, Dy, and Ho) series using a four sublattice model

The RRhIn5 (RNd, Tb, Dy, and Ho) series of compounds crystallizes in the Ho2CoGa8 tetragonal type-structure, with P4/mmm space group. A Hamiltonian model of four magnetic sublattices is used to reproduce the metamagnetic transitions of these series, considering the crystalline electric field interaction and the exchange interaction in the molecular field approximation. The crystalline electric field parameters were extracted from literature sources, while the exchange parameters were adjusted to optimize the agreement between the proposed model and the experimental data. The four sublattice model presented here successfully describes the metamagnetic transitions that appeared, at the low magnetic fields, in the RRhIn5 (RNd, Tb, Dy, and Ho) series, in contrast to other molecular field model found in the literature that inadequately reproduces these transitions.

On the Theory of Magnetoelectric Coupling in Fe2Mo3O8.

In the last decade, Fe2Mo3O8 was recognized for a giant magnetoelectric effect, the origin of which is still not clear. In the present paper, we contribute to the microscopic theory of the magnetoelectric coupling in this compound. Using crystal field theory and the molecular field approximation, we calculated the low-lying energy spectrum for iron ions and their interaction with electric and magnetic fields. Classical ionic contribution to the electric polarization related to the ionic shifts is also estimated. It is found that the electronic and ionic contributions to the electric polarization are comparable and these mechanisms support each other at T<TN. The suggested electronic mechanism provides insight into the nature of huge jumps in polarization upon phase transitions from paramagnetic (PM) to antiferromagnetic (AFM) and then to ferrimagnetic (FRM) states under an applied external magnetic field as well as the large differential magnetoelectric coefficient.

119Sn Mössbauer and magnetization studies of the Heusler alloy Ni2Mn1.48Sn0.52

The results of experimental investigations of the crystal structure, magnetization and Mössbauer spectroscopy of the Heusler alloy Ni2Mn1.48Sn0.52 are reported. The alloy undergoes the martensitic transition from the L21-type cubic structure into 4O-type orthorhombic structure with a thermal hysteresis of ∼23 K. The martensitic transition temperature TM is 309 K. The Curie temperature in the austenitic phase TCA of Ni2Mn1.48Sn0.52 is found to be 316 K. The Mössbauer spectra from the high temperature paramagnetic state at 330 K and the martensitic state at 283 K were both singlets, showing a typical paramagnetic feature in the narrow temperature range just below TM. With further decrease of temperature, the ferromagnetic ordered state also appears in the martensitic phase. The Curie temperature in the martensitic phase TCM is found to be 256 K. Furthermore, the exchange bias effect is observed in the temperature range 1.8 K ≤ T ≤ TB (∼130 K), where TB is an exchange bias blocking temperature. The values of a hyperfine magnetic field at Sn nuclei of Ni2Mn1.48Sn0.52 fall significantly below the molecular magnetic field approximation for S = 1. On the basis of the experimental results, the electronic and magnetic properties of Ni2Mn1.48Sn0.52 are discussed.

Low-field magnetocaloric effect in Nd2Ni2ln intermetallic compound / Efeito magnetocalórico de baixo campo no composto intermetálico Nd2Ni2ln

In this work, we consider a model which describes the CEF and magnetic interaction applied to two sublattices, where the magnetic interaction is described by a Hamiltonian who considers the Zeeman and exchange interactions in the molecular field approximation. The isothermal magnetic entropy change ΔS as a function of temperature was computationally obtained in the [001] crystallographic direction, from the equation of state of magnetization M(H, T) and entropy S (H, T) by diagonalization of the total Hamiltonian (HTot). We obtained a good agreement between the theory and the experiment was using the estimated crystal-field parameters and the exchange integral for Nd2Ni2In.

Molecular-Field Approximation in the Theory of Ferromagnetic Phase Transition in Diluted Magnetic Semiconductors

In this pedagogical paper, the comparative analysis of two common approaches describing the ferromagnetic phase transition in diluted magnetic semiconductors (DMS) is expounded in terms of the Weiss field approximation. Assuming a finite spin polarization of the magnetic ions, the treatment of carrier-ion exchange interaction in the first order evokes a homogeneous Weiss molecular field that polarizes the spins of free carriers. In turn, this spin polarization of the free carriers exerts the effective field that may stabilize the DMS spin polarization belowa critical temperature TC. The treatment of such self-consistent spontaneous DMS magnetization can be done in terms of the spin-spin interaction independent of the inter-ion distance and the infinitesimal in thermodynamic limit. On the other hand, by additionally accounting for the second-order effects of the carrier-ion exchange interaction, we can treat a Weiss field in terms of the Ruderman–Kittel–Kasuya–Yosida indirect spin-spin interaction, which oscillates and does not disappear at finite inter-ion distances in the case of a finite concentration of carriers. These both approaches result in the same Curie temperature TC provided a non-correlated homogeneous random distribution of the localized spin moments over the sample volume. We discuss the origin of such coincidence and show when this is not a case in other more realistic models of the conducting DMSs.

Molecular-statistical theory of elasticity in nematic liquid crystals composed of polar and nonpolar molecules.

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant K_{11} which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.

Structures and magnetic properties of five lanthanide-radical complexes constructed by 8-methoxyquinoline substituted tridentate chelating nitronyl nitroxide radical

Five lanthanide complexes [Ln(hfac)3(8-MeOTQ-2-NIT)] constructed by a tridentate chelating 8-methoxyquinoline substituted nitronyl nitroxide radical (Ln ​= ​Gd (1), Tb (2), Dy (3), Ho (4), Er (5), hfac ​= ​hexafluoroacetylacetonate, 8-MeOTQ-2-NIT ​= ​2-(8-methoxyquinoline)-4,4,5,5- tetra-methylimidazoline-1-oxyl-3-oxide) have been successfully synthesized and characterized. The five complexes have similar mononuclear two-spin structures with one LnIII ion and one radical (Rad) in the molecules. And all LnⅢ ions are nine-coordinated in the geometry between mono-capped square antiprism (C4v) and a trigonal bipyramidal (D3h). Alternating current magnetic studies show that Tb and Dy complexes display frequency dependence of out of phase signals indicating the slow magnetic relaxation behavior of single molecular magnets. The ferromagnetic interactions in Gd/Tb-Rad complexes and the very weak antiferromagnetic interactions in Dy/Ho/Er-Rad complexes were estimated by the rough model combining lanthanide single ions approximation and molecular-field approximation.

ПЕРВОПРИНЦИПНЫЕ ИССЛЕДОВАНИЯ ФАЗОВЫХ ПРЕВРАЩЕНИЙ В СПЛАВАХ Fe-Si

In this paper, the structural and magnetic properties of Fe100-xSix alloys (10 ≤ x ≤ 25,0 at. %) were calculated. The structural phase transition temperatures for the crystal structures A2, B2, and D03 were estimated from the geometry optimization. The Curie temperatures were calculated in a molecular-field approximation using the constants of magnetic exchange interaction calculated ab initio. For all the considered concentrations, with the temperature increase, we observed the structural transitions from the ordered cubic phase to a disordered structure, with the intermediate stage of a partially disordered state. The ferromagnet–paramagnet transition was observed for all the compositions, though in various crystal phases.

Магнитные и магнитокалорические эффекты в системах с реверсивными переходами первого рода

Within the framework of the model of interacting parameters of magnetic and structural orders, a theoretical analysis of magnetostructural reversible first-order phase transitions is carried out. Reversible phase transitions are characterized by a jump-like appearance of magnetic order with decreasing temperature (as in a first-order phase transition), and with a reverse increase in temperature, the magnetic order gradually disappears (as in a second-order phase transition). Such transitions are observed in some alloys of the Mn_{1-x}Cr_{x}NiGe magnetocaloric system under pressure (x = 0.11) and without (x = 0.18) and are accompanied by specific magnetic and magnetocaloric features. A phenomenological description of these features is carried out within the concept of a soft mode for the structural subsystem undergoing first-order structural phase transition (P6_{3}/mmc-P_{nma}) and the Heisenberg model for the spin subsystem. For systems with magnetostructural instability within the molecular field approximation for the spin subsystem and the shifted harmonic oscillator approximation for the lattice subsystem, it is shown that the reversible phase transitions arise when the temperature of magnetic disordering is in the temperature hysteresis region of the 1st order structural phase transition P6_{3}/mmc-P_{nma}. It is also shown that the two-peak form of the isothermal entropy, which is characteristic of reversible transitions, is due to the separation of the structural and magnetic entropy contributions.

Nature of the Pseudogap Phase of HTSC Cuprates

The pseudogap phase of HTSC cuprates is associated with the formation of a system of quantum electron–hole (EH) dimers similar to the Anderson RVB phase. A specific role of the electron–lattice relaxation in the formation of metastable EH dimers in cuprates with the T and T ' structures is considered. An effective spin–pseudospin Hamiltonian of the CuO2 plane of cuprate is introduced in the model of charge triplets and S = 1 the pseudospin formalism. In the molecular-field approximation (MFA), for the coordinate representation, the main MFA phases have been found: antiferromagnetic insulator, charge density wave, boson superconductor with the d-symmetry of the order parameter, and two metallic Fermi-phases that form the “strange”-metal phase. MFA is shown to enable, as a whole, a proper description of the features of the phase diagrams typical of cuprates. As in the case of typical s = 1/2 quantum antiferromagnet, the actually observed cuprate phases such as the charge ordering and the superconductivity reflect a “physical” ground state close to MFA phases but with strongly reduced values of local order parameters.

Ab Initio Studies of Phase Transformations in Fe100 – xSix

A concentration phase diagram for Fe100 – xSix (9.375 ≤ x ≤ 25.0 at %) alloys has been built on the base of the structural and magnetic phase transition temperatures estimated theoretically from the first principles. The structural phase transition temperatures for the experimentally observed crystal structures are obtained from the geometric optimization of the crystal structure. The Curie temperatures are estimated in a molecular field approximation using the constants of magnetic exchange interaction calculated ab initio. As temperature increases, the structural transitions from the ordered cubic phase to a completely disordered structure occur via a partially disordered structure over the entire concentration range. As for the magnetic transformations, the ferromagnet–paramagnet transition is observed for all the compositions, but in various crystal phases.

Global phase diagrams in a polymer-solvent system under the positive and negative pressure at and near the mathematical double points

Global phase diagrams are one of the crucial tools to investigate the phase behavior of simple and complex mixtures both theoretically and experimentally. The critical lines and global phase behavior of polymer-solvent systems under the negative pressure at and near the mathematical double points (MDPs) are studied. We present the critical lines of polymer mixtures in three different planes for various values of interaction energy parameters, and change the factor (r) and the deviation coefficient (Δ) from the MDPs. We use the full Tompa model to obtain the equation for the critical line within the molecular-field approximation. We find that r and Δ values influence the critical lines and global phase behavior of the system. Moreover, as the r increases, the MDPs shift to the low-pressure region and it will be located in a negative pressure region forr≥9.

Природа псевдощелевой фазы ВТСП купратов

The pseudogap phase of HTSC cuprates is associated with the formation of a system of quantum electron-hole (EH) dimers similar to the Anderson RVB-phase. We considered the specific role of electron-lattice relaxation in the formation of metastable EH dimers in cuprates with T- and T′-structures. In the model of charge triplets and S = 1 pseudospin formalism, the effective spin-pseudospin Hamiltonian of the cuprate CuO2 plane is introduced. In the framework of the molecular field approximation (MFA) for the coordinate representation, the main MFA phases were found: an antiferromagnetic insulator, a charge density wave, a bosonic superconductor with d-symmetry of the order parameter, and two metal Fermi-phases forming the phase of the "strange" metal. We argue that the MFA can correctly reproduce all the features of the typical cuprate phase diagrams. As for typical s = 1/2 quantum antiferromagnet the actually observed cuprate phases such as charge order and superconductivity reflect "physical" ground state, which is close to MFA-phases but with strongly reduced magnitudes of the local order parameters.

Проблемы теории магнитной восприимчивости антиферромагнетиков выше температуры Нееля, связанные с приближением молекулярного поля

Проблемы теории магнитной восприимчивости антиферромагнетиков выше температуры Нееля, связанные с приближением молекулярного поля

Magnetic properties of Ho0.9Er0.1Fe3(BO3)4

The magnetic properties of Ho0.9Er0.1Fe3(BO3)4 ferroborate with the competing Ho–Fe and Er–Fe exchange couplings have been experimentally and theoretically investigated. The measured magnetic characteristics (Ma,c(B), χa,c(T)) and observed features are interpreted using a single theoretical approach based on the molecular-field approximation and calculations within the crystal-field model of the rare-earth ion. Interpretation of the experimental data includes determination of the crystal-field parameters for Ho3+ and Er3+ ions in Ho0.9Er0.1Fe3(BO3)4 and parameters of the Ho–Fe and Er–Fe exchange couplings.

Helical solutes orientationally ordered in anisotropic media composed of helical particles: Formulation of a mean torque potential sensitive to P and M chirality as a tool for the assignment of the absolute configuration of enantiomers

In this paper, a chirality-sensitive effective orientational potential is, for the first time, proposed. It describes, within the Molecular Field approximation, different solute-solvent ordering interactions, according to the P (clockwise) or M (counterclockwise) nature of helical particles dissolved in uniaxial anisotropic solvents composed, in their turn, of helical P or M particles. By making use of Monte Carlo-simulated order parameters, it is shown that the model is, in principle, able to lead to the absolute enantiorecognition of the unknown chirality of the helical solute particles. This makes it a possible interesting tool for exploiting NMR anisotropic observables in order to achieve the absolute enantiomer assignment of chiral helical solutes.

Quantum Stochastic Model for Spin Dynamics in Magnetic Systems

We develop a numerical model that reproduces the thermal equilibrium and the spin transfer mechanisms in magnetic nanomaterials. We analyze the coherent two-particle spin exchange interaction and the electron-electron collisions. Our study is based on a quantum atomistic approach and the particle dynamics is performed by using a Monte Carlo technique. The coherent quantum evolution of the atoms is interrupted by instantaneous collisions with itinerant electrons. The collision processes are associated to the quantum collapse of the local atomic wave function. We show that particle-particle interactions beyond the molecular field approximation can be included in this framework. Our model is able to reproduce the thermal equilibrium and strongly out-of-equilibrium phenomena such as the ultrafast dynamics of the magnetization in nanomatrials.

Magnetocaloric Effect in an Ising Ferromagnet in the Constant Coupling Approximation

The magnetocaloric effects in an Ising ferromagnet with short-range exchange interactions between nearest magnetic neighbors are calculated using the constant coupling cluster approximation. It is shown that, compared with the results given by the molecular field approximation, the constant coupling approximation gives greater effects both in the magnetic entropy under isothermal magnetization and in the sample temperature upon adiabatic switching of the magnetic field.

Single nanowire measurements of room temperature ferromagnetism in FeSi nanowires and the effects of Mn-doping

Semiconductors with magnetic response at room temperature are sought for spintronics in solid-state devices. Among possible materials for this applications, the magnetic response of FeSi and doped FeSi have produced contradictory results at the nanoscale and more precise measurements and deeper studies are needed to clarify its potential capabilities. For that reason, in this work, single nanowire measurements of ferromagnetic semiconducting FeSi and Mn-doped FeSi nanostructures have been performed using magnetic force microscopy and electron holography. Results obtained confirm the presence of magnetic domains at room temperature with a magnetic moment per Fe atom of Spin polarized density functional calculations confirm a net magnetic moment between in Fe surface atoms with an estimated Curie temperature of 417 K by means of the molecular field approximation. The nanowires present a crystalline B20 cubic structure as confirmed by x-ray diffraction and high-resolution electron microscopy. Their electrical transport measurements confirm p-type nature and thermal activation. A remanent magnetization of 1.5 × 10−5 emu and 0.5 × 10−5 emu was measured at room temperature for FeSi and Mn-doped FeSi respectively, with spin freezing behavior around 30 K for the Mn-doped nanowires.