Effective Molecular Field Research Articles

Self-organization of tip-functionalized elongated colloidal particles.

Weakly attractive interactions between the tips of rodlike colloidal particles affect their liquid-crystal phase behavior due to a subtle interplay between enthalpy and entropy. Here we employ molecular dynamics simulations on semiflexible, repulsive bead-spring chains where one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic-A, smectic-B, and crystalline states. For tip attraction energies lower than the thermal energy, our results are qualitatively consistent with experimental findings: We find that an increase of the attraction strength shifts the nematic to smectic-A phase transition to lower volume fractions, with only minor effect on the stability of the other phases. For sufficiently strong tip attraction, the nematic phase disappears completely, in addition leading to the destabilization of the isotropic phase. In order to better understand the underlying physics of these phenomena, we also investigate the clustering of the particles at their attractive tips and the effective molecular field experienced by the particles in the smectic-A phase. Based on these results, we argue that the clustering of the tips only affects the phase stability if lamellar structures ("micelles") are formed. We find that an increase of the attraction strength increases the degree of order in the layered phases. Interestingly, we also find evidence for the existence of an antiferroelectric smectic-A phase transition induced by the interaction between the tips. A simple Maier-Saupe-McMillan model confirms our findings.

Thermodynamic properties of multiferroic Mg doped YbMnO3

Calorimetric studies of polycrystalline samples Yb1−xMgxMnO3 with x=0.0 and 0.05 are reported. It is revealed that the Mg doping raises the antiferromagnetic ordering temperature, TN, from 83K for x=0.0 to 86K for x=0.05. A ferromagnetic ordering is also observed around 3K. The broad feature in the specific heat data just above ferromagnetic ordering, is attributed to the Schottky anomaly. The estimated effective molecular fields from the Schottky analysis are Hmf=3.0 and 3.5T for YbMnO3 and Yb0.95Mg0.05MnO3, respectively. High temperature shift of Schottky anomaly with Mg doping indicates increase in effective molecular field of Mn at the Yb 4b site. The data supports that the idea that although molecular field is mainly responsible for the Schottky anomaly in Yb1−xMgxMnO3 and Mn3+ spin ordering also affects it. Magnetic part of the specific heat is obtained by subtracting the lattice contribution estimated using two Debye temperatures. The magnetic entropy change (ΔSmag) for pure and doped samples are 2.0Jmol−1K−1 and 2.1Jmol−1K−1 respectively, while the relative cooling power (RCP) calculate 26.1J/mol, 27.2J/mol for a field change of 10T.

Magnetic structure and interaction in (Sb, Co) co-doped ZnO thin films

The magnetic behaviour of (Co, Sb) co-doped ZnO thin films grown by pulsed laser deposition is investigated. The irreversibility (ZFC–FC bifurcation) in low field (H = 100 Oe) magnetization and small hysteresis below 300 K are similar in samples with or without Sb co-doping. Both the phenomena originate from the presence of blocked supermoments in the samples. Incorporation of Sb only increases the saturation magnetization and coercivity. The quantitative increase in moment due to Sb co-doping suggests a transfer of electrons from Co ions to Sb-related acceptor complexes. This is supported by a decrease in the number of electronic transitions from Co d electrons to the conduction band seen in optical transmission spectroscopy when Sb is added. The high field susceptibility data show the existence of supermoments with antiferromagnetic interaction between them. We find that the value of the effective antiferromagnetic molecular field constant decreases with increasing Co concentration, revealing that the supermoments are bound magnetic polarons around intrinsic donors, rather than coming from Co precipitates. True ferromagnetism (overlapping polarons) can emerge either with larger intrinsic donors, or with acceptors with shallower levels, than those created by Sb co-doping. Our results suggest that Sb-related acceptor states may be unstable towards accepting electrons from deep d levels of Co ions.

Integrable multi-phase thermodynamic systems and Tsallis' composition rule

We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems such as the van der Waals gas and the effective molecular field model. The case of N–phase systems is also discussed in detail in connection with entropies depending on the order parameter according to Tsallis' composition rule.

Estimation of single-ion anisotropies, crystal-field and exchange interactions in Gd-based frustrated pyrochlore anti-ferromagnets Gd2M2O7 (M=Ti, Sn, Hf, Zr)

The temperature dependence of the experimental results of dc (macroscopic) magnetic susceptibility and nuclear hyperfine properties of frustrated magnetic Gd-based pyrochlore compounds, Gd2Ti2O7, Gd2Sn2O7, Gd2Hf2O7 and Gd2Zr2O7, are analyzed within the frame work of appropriate crystal-field theory and a mean field approximation by introducing effective anisotropic molecular field tensors, and formulating an exact relation between single-ion susceptibility tensors and site susceptibility tensors. Components of the calculated susceptibility along and perpendicular to the local 〈111〉 axis of the tetrahedral sublattice of pyrochlore structure show that these pyrochlores are easy-planar anisotropic magnetic systems. The crystal-field parameters and anisotropic exchange coupling have been determined and their systematic variations over the Gd-based pyrochlores studied here are discussed.

The Nd–Mn exchange interaction, low temperature specific heat and magnetism of Nd2/3Ca1/3MnO3

The low temperature specific heat and magnetic characteristics of Nd2/3Ca1/3MnO3 perovskite are studied in a wide range of magnetic fields (up to 9T). Temperature dependent specific heat data show a broadened Schottky-like anomaly below 20K caused by splitting of the Nd3+ ions ground-state doublet in the effective molecular field Hex, determined by exchange interaction between Nd and Mn spin systems supplemented by an applied external magnetic field. Existence of the splitting at zero magnetic field and expressed field dependence is the evidence of a strong exchange coupling between Nd and Mn magnetic subsystems. The Nd-ions magnetic ordering leads to an additional contribution to the magnetic moment of the system below 30K, producing anomalies of the magnetic loss and field-cooled and zero-field-cooled magnetizations. The observed broadened Schottky-like anomalies are fitted for each applied magnetic field by the sum of three Schottky functions. Applied magnetic field extends the anomaly region and shifts it to higher temperatures. Splitting of the higher crystal field Kramers doublets gives an additional contribution to the heat capacity in magnetic fields. The ground state doublet g-factors g|| and g⊥ were estimated to be 3.4 and 2.2, respectively, and Hex was estimated to be 9T. The Nd3+ ions magnetic moment estimated from the magnetization data agrees with the value obtained from the specific heat data.

Crystal-field and Nd-Mn exchange interaction in Nd2/3Ca1/3MnO3

A study of the low field magnetization and specific heat in magnetic fields up to 9 T of Nd2/3Ca1/3MnO3 perovskite in the 2-30 K temperature range has been done. All the specific heat data show broadened Schottky-like anomaly below 20 K. We suppose that such a behavior originates from the Nd magnetic ordering caused by the splitting of the Nd3+ ions ground-state doublet (GSD) in the effective molecular field Hex of Mn spin system supplemented by an applied external magnetic field. The zero field GSD splitting is an evidence of a strong exchange coupling between Nd and Mn magnetic subsystems. The Nd-ions magnetic ordering introduces an additional contribution to the ferromagnetic moment producing anomalies of the field-cooled and zero-field-cooled magnetizations of the system below 28 K. The broadened Schottky-like anomalies found are fitted for every field by a set of three Schottky functions. Applied magnetic field extends the anomaly region and shifts it to the higher temperatures. Splitting of the higher crystal field Kramers doublets gives an additional contribution to the heat capacity under magnetic fields. The GSD g-factors g|| and g⊥ was estimated as 3.4 and 2.2, respectively, and Hex as 9 T.

Cotunneling through a magnetic quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

By means of the second-order perturbation theory, we analyze theoretically spin-dependent electronic transport through a singly occupied quantum dot in the cotunneling regime. The system is described by the impurity Anderson Hamiltonian with arbitrary Coulomb correlation parameter U. The dot is coupled to two ferromagnetic leads whose magnetic moments are noncollinear. It is also assumed that the dot level is intrinsically spin-split due to an effective molecular field. It is shown that the tunnel magnetoresistance strongly depends on the angle between the leads’ magnetizations.

Spin-polarized transport through a single-level quantum dot in the Kondo regime

Nonequilibrium electronic transport through a quantum dot coupled to ferromagnetic leads(electrodes) is studied theoretically by the nonequilibrium Green function technique. Thesystem is described by the Anderson model with arbitrary correlation parameterU. Exchange interaction between the dot and ferromagnetic electrodes is taken into account via an effective molecular field. The following situations are analysed numerically:(i) the dot is symmetrically coupled to two ferromagnetic leads, (ii) one of thetwo ferromagnetic leads is half-metallic with almost total spin polarization ofelectron states at the Fermi level, and (iii) one of the two electrodes is nonmagneticwhereas the other one is ferromagnetic. Generally, the Kondo peak in the density ofstates (DOS) becomes spin-split when the total exchange field acting on the dot isnonzero. The spin-splitting of the Kondo peak in DOS leads to splitting andsuppression of the corresponding zero-bias anomaly in the differential conductance.

Cotunneling through a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

Spin-dependent electronic transport through a quantum dot has been analyzed theoretically in the cotunneling regime by means of the second-order perturbation theory. The system is described by the impurity Anderson Hamiltonian with arbitrary Coulomb correlation parameter $U$. It is assumed that the dot level is intrinsically spin-split due to an effective molecular field exerted by a magnetic substrate. The dot is coupled to two ferromagnetic leads whose magnetic moments are noncollinear. The angular dependence of electric current, tunnel magnetoresistance, and differential conductance are presented and discussed. The evolution of a cotunneling gap with the angle between magnetic moments and with the splitting of the dot level is also demonstrated.

Spin effects in electron tunneling through a quantum dot coupled to noncollinearly polarized ferromagnetic leads

Spin-dependent transport through an interacting single-level quantum dot coupled to ferromagnetic leads with noncollinear magnetizations is analyzed theoretically. The transport properties and average spin of the dot are investigated within the nonequilibrium Green function technique based on the equation of motion in the Hartree-Fock approximation. Numerical results show that Coulomb correlations on the dot and strong spin polarization of the leads significantly enhance precession of the average dot spin around the effective molecular field created by the external electrodes. Moreover, they also show that spin precession may lead to negative differential conductance in the voltage range between the two relevant threshold voltages. Nonmonotonous angular variation of electric current and change in sign of the tunnel magnetoresistance are also found. It is also shown that the diodelike behavior in asymmetrical junctions with one electrode being half-metallic is significantly reduced in noncollinear configurations.

Schottky-like anomaly in the low-temperature specific heat of single-crystal NdMnO 3

The specific heat of single-crystal NdMnO 3 was investigated from 2 to 20 K under different magnetic fields up to 8 T. All the specific heat data show a Schottky-like anomaly, which becomes more indistinctive as increasing magnetic field. The experiment data were successfully fitted by taking into account factors such as crystal-field splitting, the two-level Schottky anomaly, the lattice vibration, and type-A antiferromagnetic (A-AF) spin waves. It was found that the splitting of the ground state doublet of Nd 3+ ion increases linearly with magnetic field. The above phenomena can be interpreted in terms of the model of unchanged effective molecular field at Nd 3+ site caused by the ferromagnetic component of A-AF structure of Mn spins. This ferromagnetic component is likely caused by the GdFeO 3-type octahedron rotation. In addition, it was also found that the magnetic field increases the spin-wave stiffness coefficient, but reduces the Debye temperature.

Magnetic ordering of itinerant systems in modified CPA approximation

We will analyze the itinerant model for ferromagnetism with both single-site and two-site electron correlations. We will include band degeneration into the model. This will allow us to consider the on-site exchange interactions in the Hamiltonian. The modified Hartree–Fock approximation for the two-site interactions will be used. This approximation will give the relative one spin band broadening with respect to the other, in addition to the shift in position of majority and minority spin bands. Next, we will use the coherent potential approximation technique (CPA) with two self-energies. One will describe the on-site correlation and the second one the inter-site correlation. We will separate from these self-energies, the linear terms arising from Hartree–Fock approximation which will be applied to both; the on-site and inter-site interactions. These terms will contribute to the effective molecular field and the remaining ones (non-linear) will contribute to the correlation factors. The Green function technique and CPA decoupling will allow for the change in the shape of spin bands, which has been described by the correlation factors and which will decrease the kinetic energy of the system. The gain in kinetic energy due to the on-site and inter-site correlation factors will drive the ferromagnetism and significantly reduce the effective Hartree field necessary to create this ordering.

Spin fluctuation in RCo 2 compounds

Electrical resistivity and magnetization measurements have been used to study the character of the spin fluctuations in the paramagnetic phase of RCo 2 (R=Er, Ho, Tb) and Er(Co,Ni) 2 compounds. The localized 4f moments present some local effective molecular field above T c that polarizes the Co atoms leading to an additional increase in the scattering process.

Decoupling of the magnetic ordering of the rare-earth and the Co sublattice inEr1−xYxCo2compounds driven by substitution or pressure

The thermodynamic and transport properties of the ${\mathrm{Er}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{Co}}_{2}$ system were studied in the concentration range $0.0l~xl~1.0.$ In this system, the first-order magnetic phase transition observed in ${\mathrm{ErCo}}_{2}$ at ${T}_{\mathrm{C}}=32$ K is related to the itinerant electron metamagnetism of the d subsystem (Co sublattice) driven by the onset of magnetic ordering within the Er sublattice. By employing magnetic, specific heat, thermal expansion, and resistivity measurements we show that in a limited concentration range ${x}_{{\mathrm{cr}}^{\ensuremath{'}}}lxl{x}_{\mathrm{cr}}$ and pressure ${P}_{{\mathrm{cr}}^{\ensuremath{'}}}lPl{P}_{\mathrm{cr}}$ the itinerant Co sublattice orders magnetically at ${T}_{\mathrm{C}}^{\mathrm{Co}},$ which is lower than ${T}_{\mathrm{C}}^{R}$ of the Er sublattice. This is referred either to a weakening of the effective molecular field acting on the Co sites owing to the yttrium subsititution or to a pressure-driven increase of the critical field necessary to induce a magnetic moment on the Co sites. On further increasing the yttrium concentration or the pressure only the Er sublattice exhibits long-range order. The theoretical calculations within the molecular field approximation are in agreement with the experimental magnetic x-$T$ phase diagram of the ${\mathrm{Er}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{Co}}_{2}$ system and confirm the effect of a separate ordering of the magnetic sublattices with reasonable parameters used for the intrasublattice Er-Er and intersublattice Er-Co exchange interactions. A field-induced collapse of the Co moment, inverse itinerant electron metamagnetism, is well observable by magnetoresistance measurements at appropriate values of concentration and external pressure. The existence of itinerant electron metamagnetism in the Co sublattice is found to be limited in temperature by ${T}_{0},$ a characteristic temperature which is sensitive to substitution and pressure.

A MOLECULAR MODELLING STUDY OF DICARBOXYLATE ANIONS AND ZINC OXALATE COMPLEX EXTRACTION BY DIPHOSPHONIUM EXTRACTANTS

Abstract A molecular modelling method is used as an aid to predict and to account for the results of solvent extraction of dianions by an ion-exchange extractants such as diphosphonium compounds (polymethylenebis(trioctylphosphonium)s abbreviated as CnBP2+). The extraction ability of CnBP2+ extractants was surprisingly dependent on the dianionic species and on the length of bridging methylene chain connecting the two phosphonium cationic centers which offers an effective molecular recognition field. The dianions studied are phthalate, isophthalate, terephthalate, dibenzoyltartrate and zinc oxalate complex. All of them have their negative charges carried by oxygen atoms. The extracted species considered for a dianion A2− are 1:1 and 2:2 ion-pair species such as (CnBP2+, A2−), (2 CnBP2+, 2 A2−rpar; with n = 2, 4, 6, 8, 10, 12. These ion-pair species are modelled and minimized. The total energy values obtained are processed to calculate the association energies of ion-pair species which allow comparison of 1...

A MOLECULAR MODELLING STUDY OF ANIONIC METAL COMPLEXES EXTRACTION BY MONO- AND DICATIONIC EXTRACTANTS.

ABSTRACT Molecular modelling method is used as an aid to predict and to account for the results of solvent extraction of dianionic metal complexes by anion-exchange extractants such as mono- and diphosphonium compounds (butyltrioctyl-phosphonium and polymethylenebis(trioctylphosphonium)s abbreviated as BuMP and CnBPs respectively). The extraction ability of CnBPs extractants was surprisingly dependent on the length of bridging methylene chain connecting the two phosphonium cationic centers which offers an effective molecular recognition field. The studied dianionic species, noted A2−, are MCI42−, M(CN)42− and M(C2O42)2− with M = Zn2+. The software used is the one meant to produce special molecular geometries for organic molecules. So, to model complexes with a metal cation, it is necessary to introduce characteristic parameters of the metal and its bonds. The extracted complexes considered are ion-pair complexes such as (CnBP2+, 2A2−), (2 CnBP2+, 2 A2−) with n equals; 2,4,6, 8, 10, 12 and (2 BuMP+, A2−) T...

A MOLECULAR MODELLING STUDY OF DIBENZOYLTARTRATE EXTRACTION BY MONO- AND DICATIONIC EXTRACT ANTS

ABSTRACT Molecular modelling is used as a novel aid to account for the results of solvent extraction of dianionic species such as dibenzoyltartrate with monocationic extractant (butyltrioctylphosphonium) and dicationic extractants such as polymethylenebis(trioctylphosphonium)s abbreviated as CnBPs. The extraction ability of CnBPs was remarkably dependent on the length of bridging methylene chain connecting the two phosphonium cationic centers which offers an effective molecular recognition field. The anionic species and cationic extractants are modelled separately in their conformations corresponding to the absolute energy minimum. Then, 1:1 and 2:2 ion-pair complexes are built and minimized by taking into account their atomic charge distributions. The minimized energies quantify the steric and electrostatic effects of complexes. The results show that the 2:2 association takes the best account for experimental data and that the electrostatic energy is an important component of the total energy of complexe...

On the correlated molecular field theory of amorphous ferromagnets

The correlated molecular field theory of amorphous ferromagnets is extended by incorporating explicitly, within a phenomenological approach, the correlated spin fluctuations occuring at the transition. In the original version of the theory these spin fluctuations have been taken into account only implicitly when calculating the effective molecular field. The results are compared with experimental data for amorphous Fe 20Ni 56B 24.

Effective molecular field at some rare earth ions in ordered intermetallic compounds Re1−xGdxAl2

Hyperfine fields at rare earth nuclei 167Er and 159Tb have been measured by NMR in ordered RE1−xGdxAl2 compounds as a function of x (0 ⩽ x < 1). The results suggest a lower value of the effective molecular field than expected and a decrease of the conduction band polarization in Er Alloys.