High-temperature Series Research Articles

Padé approximant for hard sphere ＋ square well and hard sphere ＋ square well ＋ square shoulder model fluids

The coupling parameter series expansion (CPSE) is used to calculate coefficientsai (i=1,2,3,…7) of the high temperature series expansion (HTSE) for two hard sphere ＋ square well models and two hard sphere ＋ square well ＋ square shoulder models, the four sets of coefficients are used to construct 28 Padé approximant variants Pn∕d for the four models. Based on the 28 Padé variants, six common thermodynamic functions for the four models are calculated and compared with corresponding results based on MC simulations reported in the literature and the HTSE truncated to seventh order in the present work, respectively. Several conclusions are generalized from the comparisons: (i) the commonly used rule of the minimum value for n−d to choose the best Padé approximation may not select the best one, which depends on the model and relevant parameters values and has to be determined in advance by reference to simulations. (ii) From the whole table of 28 Padé approximants, reliable (throughout the text, by “reliable” we mean the results are at least qualitatively correct) variants always can be singled out, which not only provides an improvement over the raw HTSE truncated at the optimal order but also is free of pole(s) and consequently applicable over reasonably wide phase space of interest; particularly, the improvement can be immense for most but not all of the models considered when the excess heat capacity is being considered. (iii) Among the reliable Pn∕dapproximations picked, some have high values of n+d indicating that the higher-order HTSE coefficients calculated by the CPSE provide important and reliable information for the unknown excess Helmholtz free energy, and the conventional Padé summation indeed provides an effective method to utilize the information. (iv) The Padé summation can be a resort in statistical mechanics perturbation theories of simple potential fluids because of its simplicity in the actual application and possibility in improving the raw HTSE; however, to ensure the use reliably, one comprehensive pre-research should be carried out.

Magnetic and Electronic Properties of LiVOPO4 and VOPO4 Cathodes

Magnetic and electronic properties of LiVOPO4 and VOPO4 cathodes have been studied using ab initio calculations, high temperature series expansions (HTSEs) calculations and Monte Carlo simulations (MCSs). Self-consistent ab initio calculations, based on Density Functional Theory approach (DFT) and using Full Potential Linear Augmented Plane Wave (FLAPW) method, were performed to investigate both electronic and magnetic properties of the LiVOPO4. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent V plans. Magnetic moments considered to lie along (010) axes are computed. Average equilibrium voltage over a full cycle ([Formula: see text]) of the LiVOPO4, battery have been estimated. Computed magnetic moments are used as input for HTSEs to compute other magnetic parameters using the mean field theory, MCSs and HTSEs. The obtained results by HTSEs and MCSs are comparable with experiments results.

Magnetic properties of spinels GeNi2−xCoxO4 systems: Green's function and high-temperature series expansions

ABSTRACTThe Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2−xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 − xCoxO4 systems. The critical exponents and associated with the magnetic susceptibility and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.

Diamond lattice Heisenberg antiferromagnet

We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.

Effect of Copper Substitution on Magnetic Properties of NiFe2O4 Ferrite

The many-body Green’s function theory has been used to study the magnetic properties of CuxNi1−xFe2O4 spinels. We present a new method to calculate the expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green’s functions. Magnetization and magnetic susceptibility are given when external magnetic field is applied in (x–z) plane. The mean field theory has been used to calculate nearest-neighbor exchange and next-nearest-neighbor superexchange interactions. The intraplanar and the interplanar interactions are deduced. The magnetic phase diagram is deduced using high-temperature series expansions. The ferrimagnetic and paramagnetic phases are determined. The critical exponents associated with the magnetic susceptibility \(\left( \gamma \right)\) and the correlation lengths \(\left( \nu \right)\) have been deduced. These results are comparable with those obtained by magnetic measurements and are comparable with those of 3D Heisenberg model.

Magnetic properties of NiAlxFe2−xO4spinels: A mean field approach and high-temperature series expansions study

The magnetic properties of NiAl[Formula: see text]Fe[Formula: see text]O4(NAFO) spinels were studied. Influence of Al doping on magnetic properties of NiFe2O4spinel were examined. The exchange interactions in NAFO were obtained. The general expression of saturation magnetization and the critical temperature were obtained using mean field theory. The high-temperature series expansions combined with the Padé approximant are given to determine the critical temperature of NAFO. The critical exponent associated with the magnetic susceptibility [Formula: see text] was also deduced. The obtained results were in good agreement with magnetic measurement.

Noncentrosymmetric Cu(II) Layered Hydroxide: Synthesis, Crystal Structure, Nonlinear Optical, and Magnetic Properties of Cu2(OH)3(C12H25SO4)

Single crystals of the layered copper hydroxide dodecylsulfate Cu2(OH)3(C12H25SO4) have been obtained for the first time, by controlled hydrolysis of an aqueous copper acetate solution. Interestingly, this compound crystallizes in a noncentrosymmetric space group (P21, a = 5.591(10) A, b = 6.108(11) A, c = 26.96(5) A, α = γ = 90°, β = 92.76°), which is further confirmed by nonlinear optical measurements. Within the course of the synthesis, a probable intermediate between Cu(OAc)2·H2O and the layered Cu2(OH)3(C12H25SO4) was isolated and characterized. X-ray structure analysis showed that this intermediate presents a ribbon-like structure of formula Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2. The magnetic properties of the layered Cu2(OH)3(C12H25SO4) have been analyzed in the high-temperature region (T > 20 K) by considering a high-temperature series expansion for a S = 1/2 Heisenberg two-dimensional triangular lattice. At lower temperature, the compound shows a three-dimensional antiferromagnetic ordering (TN = 1...

Effect of Zn Substitution on Magnetic Properties of CuFe2O4: a High-Temperature Series Expansions Study

The magnetic properties of spinel ferrites Cu1−xZnxFe2O4 are studied using high-temperature series expansions combined with the Padé approximates. The exchange interactions, inter and intra-sublattices , and are obtained using a probability distribution law. The critical exponent γ associated with the magnetic susceptibility is obtained.

Efficient generation of series expansions for ±J Ising spin glasses in a classical or a quantum field

We discuss generation of series expansions for Ising spin-glasses with a symmetric $\pm J$ (i.e. bimodal) distribution on d-dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problem, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field, $h$, for which we obtain high temperature series expansions in variables $\tanh(J/T)$ and $\tanh(h/T)$. The quantum problem is a $T=0$ study of the Ising spin glass in a transverse magnetic field $h_T$ for which we obtain a perturbation theory in powers of $J/h_T$. These methods require (i) enumeration and counting of \textit{all} connected clusters that can be embedded in the lattice up to some order $n$, and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order $n$, and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the $\pm J$ bonds, and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the $T=0$ quantum system. Details of the calculational methods are presented.

High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study

We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for different values of the Kitaev coupling $K$ and Heisenberg exachange coupling $J$ (with $|J|\le |K|$) are presented. These expansions show good convergence down to a temperature of a fraction of $K$ and in some cases down to $T=K/10$. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures $10$-times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat capacity maximum at the short-range order peak, is substantially smaller for small $J/K$ than for $J$ of order or larger than $K$. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat capacity and susceptibility data on Na$_2$IrO$_3$ are consistent with a dominant {\it antiferromagnetic} Kitaev exchange constant of about $300-400$ $K$.

Magnetic properties of undoped and Al doped layered [formula omitted]-Co(OH)2

Undoped, 10% and 20% Al doped samples of layered hexagonal α-Co(OH)2 are synthesized. X-ray diffraction patterns show that the samples are nanocrystalline with average crystallite size 15nm. Fourier transform infrared spectroscopy and thermogravimetric analysis are performed to establish molecular formula of samples. Analysis of susceptibility χ as a function of temperature T (5–300K) data indicates for ferromagnetic transitions in the system at lower temperatures. Curie transition temperature TC for undoped, 10% and 20% Al doped α-Co(OH)2 are found to be 9, 7.5 and 6.0K respectively. Fitting of χ vs. T data for T>TC to the high temperature series yields strength of intralayer and interlayer exchange interactions among Co2+ ions. For undoped sample values of these interactions are estimated to be 1.070 and 0.240K respectively. Strength of these interactions decrease with increasing concentration of Al3+ ions in the lattice. Magnetization as a function of applied magnetic field (up to ± 50kG) data confirm ferromagnetic nature of the samples at 5K.

De Almeida-Thouless instability in short-range Ising spin glasses.

We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d-dimensional hypercubic lattices for d=5-8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w=tanh^{2}J/T for arbitrary values of u=tanh^{2}h/T complete to order w^{10}. We find that the scaling dimension Δ associated with the ordering-field h^{2} equals 2 in the SK model and for d≥6. However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)PRLTAO0031-900710.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h-T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978)JPHAC50305-447010.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d→6. Within the convergence of our series analysis, we present evidence supporting an AT line in d≥6. In d=5, the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d=5.

The Ag2Te-SnTe-Bi2Te3 system and thermodynamic properties of the (2SnTe)1-x(AgBiTe2)x solid solutions series

Phase relations and ternary solubility of the binary and ternary compounds in the Ag2Te-SnTe-Bi2Te3 system were experimentally investigated by means of differential thermal analysis (DTA) and powder X-ray diffraction (PXRD) techniques, as well as microhardness and electromotive force measurements (EMF) of concentration chains with Ag4RbI5 solid electrolyte. Five isopleth sections SnTe-AgBiTe2, Ag2Te-0.5SnBi2Te4, [AgSn0.5Te]-AgBiTe2, 0.5SnBi2Te4-AgBiTe2 and [AgSn0.5Te]-Bi2Te3 and two isothermal sections at 300 and 800 K as well as liquidus surface projection of the system were constructed. The primary crystallization fields of phases and homogeneity range of binary and ternary phases were also determined. The character and temperature of the various non- and monovariant equilibria were identified based on solidifications behavior of several key alloys. The system includes high-temperature cubic structured solid solutions series (γ-phase) along the SnTe-AgBiTe2 section. The partial molar thermodynamic functions for silver in the (2SnTe)1-x(AgBiTe2)x (where x = 0.1; 0.2; 0.4; 0.6 and 0.8) solid solutions were calculated based on the EMF measurements results.

A comprehensive comparison between thermodynamic perturbation theory and first-order mean spherical approximation: Based on discrete potentials with hard core

Using the TL (Tang and Lu, 1993) method, Ornstein-Zernike integral equation is solved perturbatively under the mean spherical approximation (MSA) for fluid with potential consisting of a hard sphere plus square-well plus square-shoulder (HS+SW+SS) to obtain first-order analytic expressions of radial distribution function (RDF), second-order direct correlation function, and semi-analytic expressions for common thermodynamic properties. A comprehensive comparison between the first-order MSA and high temperature series expansion (HTSE) to third-, fifth- and seventh-order is performed over a wide parameter range for both a HS+SW and the HS+SW+SS model fluids by using corresponding “exact” Monte Carlo results as a reference; although the HTSE is carried out up to seventh-order, and not to the first order as the first-order MSA the comparison is considered fair from a calculation complexity perspective. It is found that the performance of the first-order MSA is dramatically model-dependent: as target potentials go from the HS+SW to the HS+SW+SS, (i) there is a dramatic dropping of performance of the first-order MSA expressions in calculating the thermodynamic properties, especially both the excess internal energy and constant volume excess heat capacity of the HS+SW+SS model cannot be predicted even qualitatively correctly. (ii) One tendency is noticed that the first-order MSA gets more reliable with increasing temperatures in dealing with the pressure, excess Helmholtz free energy, excess enthalpy and excess chemical potential. (iii) Concerning the RDF, the first-order MSA is not as disappointing as it displays in the cases of thermodynamics. (iv) In the case of the HS+SW model, the first-order MSA solution is shown to be quantitatively correct in calculating the pressure and excess chemical potential even if the reduced temperatures are as low as 0.8. On the other hand, the seventh-order HTSE is less model-dependent; in most cases of the HS+SW and the HS+SW+SS models, the seventh-order HTSE improves the fifth- and third-order HTSE in both thermodynamic properties and RDF, and the improvements are very demonstrable in both the excess internal energy and constant volume excess heat capacity; for very limited cases, the seventh-order HTSE improves the fifth-order HTSE only within lower density domain and even shows a bit of inadaptation over higher density domain.

Magnetic investigations of phase transitions, exchange interactions, and magnetic ground state in nanosheets of β-Co(OH)2

Detailed investigations of the magnetic properties of the layered system β-Co(OH)2 are presented. X-ray diffraction and scanning electron microscopy of the sample show it to consist of hexagonal nanosheets with thickness ≈30 nm and width ~100 nm–200 nm. Analysis of its measured magnetization (M) as a function of temperature (T = 2 K to 300 K) and magnetic field (H up to 90 kOe) yields a Neel temperature TN = 9.2 K. This lower TN = 9.2 K, compared to TN = 11.6 K reported for bulk β-Co(OH)2, is due to finite-size effects. Analysis of the data for T > TN shows that the M versus T data does not quite fit the Curie–Weiss law since both the Curie constant C and Weiss temperature θ have noticeable temperature dependence. This temperature dependence is interpreted to be due to the effect of spin–orbit coupling, yielding a low-temperature effective spin S = 1/2 ground state with magnetic moment µ = 4.745 µB and g = 5.479. For T < TN, M versus H data show two transitions, first at HC1 ≃ 15 kOe and second at HC2 ≃ 32 kOe. The transition at HC1 is a spin-flop transition and HC2 is due to forced alignment of the spins yielding saturation magnetization MS = 160 emu g−1 at 2 K, in agreement with the calculated MS = 163 emu g−1 for the complete alignment of the spins at T = 0 K for the spin S = 1/2 ground state with g = 5.479. The fitting of the M versus T data for T > TN to the high temperature series for S = 1/2 XY model yields the in-plane ferromagnetic exchange constant J1/kB = (1.8 ± 0.2) K for Co2+ ions, with the interplane exchange constant J2/kB ≃ −0.2 K determined from the magnitude of TN. The temperature dependence of HC1 and HC2 is presented and discussed.

Thermometry for Laughlin States of Ultracold Atoms.

Cooling atomic gases into strongly correlated quantum phases requires estimates of the entropy to perform thermometry and establish viability. We construct an ansatz partition function for models of Laughlin states of atomic gases by combining high temperature series expansions with exact diagonalization. Using the ansatz we find that entropies required to observe Laughlin correlations with bosonic gases are within reach of current cooling capabilities.

Application of the high temperature series expansions method Green’s function theory to the spinel systems: AxA’1-xB2X4

The magnetic properties of Mn-Cu ferrites MnxCu1-xFe2O4, have been studied using the many-body Green’s function theory (GFT) and high temperature series expansion theory (HTSE). The thermal magnetization and the magnetic susceptibility are given for different values of magnetic field and dilution x. The transition temperature TC is calculated as a function of Mn concentration. The obtained results are in good agreement with experimental results. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.

Effect of magnesium substitution on the magnetic properties of diluted magnetic spinels Ni1-xMgxFe2O4

The magnetic properties of Ni-Mg ferrites with compositions Ni1-xMgxFe2O4, have been studied using the mean field theory and high temperature series expansion theory (HTSE), extrapolated with the Padé approximants method. The nearest neighbour super-exchange interactions for intra-sites and inter-sites of the Ni-Mg ferrites in the range 0 ≤ x ≤ 1 have been computed using the distribution method of magnetic cations. The transition temperature TC is calculated as a function of Mg concentration. The critical exponent associated with the magnetic susceptibility was then deduced. The obtained results are in good agreement with experimental results and critical exponent values are consistent with those suggested by the universality hypothesis.

Exchange-coupled terbium-radical complex Tb-phNO showing slow reversal of magnetization

A novel terbium(III)-nitroxide complex [TbIII(hfac)3(phNO)(H2O)] (phNO=tert-butyl phenyl nitroxide, hfac=1,1,1,5,5,5-hexafluoropentane-2,4-dionate) was synthesized towards development of 4f-2p compounds with strong ferromagnetic exchange coupling. There are two crystallographically independent molecules in a unit cell. The ac magnetic susceptibility at Hdc=2000Oe showed double χm″ peaks accompanied by frequency dependence and afforded Ueff(1)/kB=46.3(7)K with τ0(1)=1.9(3)×10−9s for the high-temperature peak series and Ueff(2)/kB=21(2)K with τ0(2)=1.3(9)×10−8s for the low-temperature peak series. Every molecule is proven to behave as a potential single-molecule magnet (SMM). In contrast, the corresponding dysprosium(III) analogue did not exhibit meaningful out-of-phase ac magnetic susceptibility. In the strongly exchange-coupled regime owing to the direct radical coordination bond, the whole molecular electron counting may provide a useful criterion to predict Kramers molecules as potential SMM candidates.

Ba8CoNb6O24: A spin-12triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit

The perovskite ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ comprises equilateral effective spin-$\frac{1}{2} {\mathrm{Co}}^{2+}$ triangular layers separated by six nonmagnetic layers. Susceptibility, specific heat, and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ is basically a two-dimensional magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ is very close to be a realization of the paradigmatic spin-$\frac{1}{2}$ triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperatures according to the Mermin and Wagner theorem.