High-temperature Series Research Articles

Antiferromagnetism, spin-glass state, H–T phase diagram, and inverse magnetocaloric effect in Co2RuO4

Static and dynamic magnetic properties of normal spinel Co2RuO4 = (Co2+) are reported based on our investigations of the temperature (T), magnetic field (H) and frequency (f) dependence of the ac-magnetic susceptibilities and dc-magnetization (M) covering the temperature range T = 2 K–400 K and H up to 90 kOe. These investigations show that Co2RuO4 exhibits an antiferromagnetic (AFM) transition at TN ∼ 15.2 K, along with a spin-glass state at slightly lower temperature (TSG) near 14.2 K. It is argued that TN is mainly governed by the ordering of the spins of Co2+ ions occupying the A-site, whereas the exchange interaction between the Co2+ ions on the A-site and randomly distributed Ru3+ on the B-site triggers the spin-glass phase, Co3+ ions on the B-site being in the low-spin non-magnetic state. Analysis of measurements of M (H, T) for T < TN are used to construct the H–T phase diagram showing that TSG shifts to lower T varying as H2/3.2 expected for spin-glass state whereas TN is nearly H-independent. For T > TN, analysis of the paramagnetic susceptibility (χ) vs. T data are fit to the modified Curie–Weiss law, χ = χ0 + C/(T + θ), with χ0 = 0.0015 emu mol−1Oe−1 yielding θ = 53 K and C = 2.16 emu-K mol−1Oe−1, the later yielding an effective magnetic moment μeff = 4.16 μB comparable to the expected value of μeff = 4.24 μB per Co2RuO4. Using TN, θ and high temperature series for χ, dominant exchange constant J1/kB ∼ 6 K between the Co2+ on the A-sites is estimated. Analysis of the ac magnetic susceptibilities near TSG yields the dynamical critical exponent zν = 5.2 and microscopic spin relaxation time τ0 ∼ 1.16 × 10−10 sec characteristic of cluster spin-glasses and the observed time-dependence of M(t) is supportive of the spin-glass state. Large M–H loop asymmetry at low temperatures with giant exchange bias effect (HEB ∼ 1.8 kOe) and coercivity (HC ∼ 7 kOe) for a field cooled sample further support the mixed magnetic phase nature of this interesting spinel. The negative magnetocaloric effect observed below TN is interpreted to be due to the AFM and SG ordering. It is argued that the observed change from positive MCE (magnetocaloric effect) for T > TN to inverse MCE for T < TN observed in Co2RuO4 (and reported previously in other systems also) is related to the change in sign of (∂M/∂T) vs. T data.

Honeycomb rare-earth magnets with anisotropic exchange interactions

We study the rare-earth magnets on a honeycomb lattice, and are particularly interested in the experimental consequences of the highly anisotropic spin interaction due to the spin-orbit entanglement. We perform a high-temperature series expansion using a generic nearest-neighbor Hamiltonian with anisotropic interactions, and obtain the heat capacity, the parallel and perpendicular spin susceptibilities, and the magnetic torque coefficients. We further examine the electron spin resonance linewidth as an important signature of the anisotropic spin interactions. Due to the small interaction energy scale of the rare-earth moments, it is experimentally feasible to realize the strong-field regime. Therefore, we perform the spin-wave analysis and study the possibility of topological magnons when a strong field is applied to the system. The application and relevance to the rare-earth Kitaev materials are discussed.

Structural and magnetic properties of Cd-Ni spinel ferrites: density functional theory calculations and high-temperature series expansions

ABSTRACT First-principles calculations of density functional theory (DFT) using the generalized gradient approximation (GGA) and generalized gradient approximation with the Hubbard U (GGA + U) for the exchange-correlation energy functional are used to investigate the structural, electronic, and magnetic properties of the spinel system in the range . High-temperature series expansions (HTSE) combined with the Padé approximants (PA) method and mean field theory (MFT) are applied to the systems. The lattice parameter and magnetic moment of Fe and Ni ions increase when Cd content x increases. Density of States (DOS) calculations show that the has a semiconductor behaviour. The obtained theoretical results show that the Curie temperature decreases with x. These obtained results are in agreement with experimental ones.

Ferromagnetism of the semi-simple cubic lattice

Heisenberg ferromagnet on a lattice with a low coordination number, $$Z=3$$ , has been studied by means of high-temperature series and harmonic spin-wave expansion. The lattice is constructed by removing every second bond from the simple cubic lattice and therefore called ’semi-simple cubic’; it is topologically similar to the Laves graph, alias $$K_4$$ crystal. The openness of the lattice does not prevent ferromagnetic ordering and the thermal dependence of spontaneous magnetization differs little from that of other common lattices with higher Z. The study extends naturally toward a more general model where the bonds previously removed are now reinstated but endowed with a distinct exchange integral, $$J_2$$ . We concentrate on the more interesting frustrated case, $$J_2<0<J_1$$ , and a first prediction in this direction is that ferromagnetism disappears at $$J_2/J_1=2\surd 2-3=-0.172$$ , giving way to a long-wavelength spiral structure propagating along [111].

Structural and Magnetic Properties of CrN: Investigated by First-Principles Calculations, Monte Carlo Simulation, and High-Temperature Series Expansions

We have employed first-principles calculations of density functional theory (DFT) with GGA and GGA+U exchange correlation to study structural, magnetic, and electronic properties of chromium nitride (CrN) in the rock salt (NaCl) structures. The obtained data from DFT calculations is used as an input in high-temperature series expansions (HTSEs) combined with the Pade approximants (PA) method and Monte Carlo simulation (MC) for the Ising model to investigate the magnetic properties of CrN. The obtained results show that CrN is more stable in the antiferromagnetic order, and undergoes structural and magnetic transitions from an antiferromagnetic NaCl structure to a nonmagnetic Pnma phase at 201 GPa. The density of states (DOS) with GGA approach shows that CrN has a metallic behavior in both FM and AFM configurations whereas with GGA+U CrN is semiconductor in AFM and half-metallic in FM order. The Neel temperature (TN) obtained by HTSE and MC is in agreement with available experimental data.

One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses.

The de Almeida-Thouless (AT) line is the phase boundary in the temperature-magnetic field plane of an Ising spin glass at which a continuous (i.e., second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension d, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: (a) For d-6 small and positive, with increasing field on the AT line, first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as d→6^{+}. (b) For d≤6, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in some simulations and in high-temperature series expansions. We also draw attention to the similarity of the "dynamically frozen" state, which occurs at temperatures just above the quasi-first-order transition, and the "metastate-average state" of the one-step RSB phase, and discuss the issue of the number of pure states in either.

Effect of perturbations on the kagome S=12 antiferromagnet at all temperatures

The ground state of the $S=\frac{1}{2}$ kagome Heisenberg antiferromagnet is now recognized as a spin liquid, but its precise nature remains unsettled, even if more and more clues point towards a gapless spin liquid. We use high-temperature series expansions (HTSEs) to extrapolate the specific heat ${c}_{V}(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ over the full temperature range, using an improved entropy method with a self-determination of the ground-state energy per site ${e}_{0}$. Optimized algorithms give HTSE coefficients up to unprecedented orders (20 in $1/T$) and as exact functions of the magnetic field. Three extrapolations are presented for different low-$T$ behaviors of ${c}_{V}$: exponential (for a gapped system), and linear or quadratic (for two different types of gapless spin liquids). We study the effects of various perturbations to the Heisenberg Hamiltonian: Ising anisotropy, Dzyaloshinskii-Moriya interactions, second- and third-neighbor interactions, and randomly distributed magnetic vacancies. We propose an experimental determination of $\ensuremath{\chi}(T=0)$, which could be nonzero, from ${c}_{V}$ measurements under different magnetic fields.

Critical properties of the Ising model in hyperbolic space.

The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume in hyperbolic space. As a result, boundary conditions play an important role even when taking the thermodynamic limit. We investigate the bulk thermodynamic properties of the Ising model in two- and three-dimensional hyperbolic spaces using Monte Carlo and high- and low-temperature series expansion techniques. To extract the true bulk properties of the model in the Monte Carlo computations, we consider the Ising model in hyperbolic space with periodic boundary conditions. We compute the critical exponents and critical temperatures for different tilings of the hyperbolic plane and show that the results are of mean-field nature. We compare our results to the "asymptotic" limit of tilings of the hyperbolic plane: the Bethe lattice, explaining the relationship between the critical properties of the Ising model on Bethe and hyperbolic lattices. Finally, we analyze the Ising model on three-dimensional hyperbolic space using Monte Carlo and high-temperature series expansion. In contrast to recent field theory calculations, which predict a non-mean-field fixed point for the ferromagnetic-paramagnetic phase-transition of the Ising model on three-dimensional hyperbolic space, our computations reveal a mean-field behavior.

Structural and Magnetic Properties of Cd–Co Ferrites: Density Functional Theory Calculations and High-Temperature Series Expansions

First-principles calculations of density functional theory (DFT) are used to investigate the structural, electronic, and magnetic properties of the spinel system CdxCo1−xFe2O4 (x = 0, 0.5, and 1). High-temperature series expansions (HTSE) combined with the Pade approximants (PA) method and mean field theory (MFT) have been used to calculate the critical temperature (TC). The lattice parameter and the local magnetic moments of Co and Fe increased when Cd content x increases. The obtained theoretical results show that the Curie temperature decrease with x. Density of states (DOS) calculations show a half-metallic behavior for x = 0.5 and semiconducting behavior for x = 0 and 1. This work, provide useful information for the substitution effect of a nonmagnetic ion on the properties of spinel ferrites, based on first-principles calculations and HTSE.

Structural and magnetic properties of Co–Zn ferrites: Density functional theory calculations and high-temperature series expansions

In this paper the electronic structures and magnetic properties of spinel ZnxCo1−xFe2O4 (x = 0, 0.5 and 1.0) have been studied systematically by the first-principles calculations. High-temperature series expansions (HTSE) combined with the Padé approximants (PA) method was applied to the ZnxCo1−xFe2O4 systems to estimate the Critical temperature (Tc). The optimized structures with the antiferromagnetic (AFM) orderings shows that the crystal lattice parameter increases with increasing Zn content. The results also indicate that the magnetic moment of Co/Fe ion increases, and show that the Curie temperature decreases when Zn content increases. These obtained results are in agreement with experimental ones.

On the Chemical Potential of Ideal Fermi and Bose Gases

Knowledge of the chemical potential is essential in application of the Fermi–Dirac and the Bose–Einstein distribution functions for the calculation of properties of quantum gases. We give expressions for the chemical potential of ideal Fermi and Bose gases in 1, 2 and 3 dimensions in terms of inverse polylogarithm functions. We provide Mathematica functions for these chemical potentials together with low- and high-temperature series expansions. In the 3d Bose case we give also expansions about T_{{{{mathrm {B}}}}}. The Mathematica routines for the series allow calculation to arbitrary order.

Extended high-temperature series for the Spin- Heisenberg ferromagnet

ABSTRACTHigh-temperature series for the magnetic susceptibility and hypersusceptibility of the Heisenberg ferromagnet have been extended to 14th order in for four common lattices. Hence improved estimates have been deduced for the critical points, (fcc), 0.3968(2) (bcc), 0.596(1) (sc), 1.124(2) (diamond), as well as for the critical exponents, and . The latter are distinct from the respective values for the classical Heisenberg model, and .

Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as various thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat, and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=\frac{1}{2}$ and 1. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound ${\mathrm{NaCaNi}}_{2}{\mathrm{F}}_{7}$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 ...8 meV for ${\mathrm{NaCaNi}}_{2}{\mathrm{F}}_{7}$. We analyze the static structure factor ${S}_{\mathbf{q}}$ to find regions of maximal ${S}_{\mathbf{q}}$. The high-temperature series of the ${S}_{\mathbf{q}}$ provide a fingerprint of weak order by disorder selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $\ensuremath{\pi}$.

Investigating the general condition of compensation temperature appearance in ferrimagnetic system

In this paper, we use the double-time Green’s function method to study the magnetic properties of the mixed spin-1/2 and spin-1 Heisenberg ferrimagnets with magnetic fields on a simple cubic lattice. We derive the equations of motion of the Green’s function by a standard procedure. In the course of this, the higher order Green’s functions have to be decoupled. A Tyablikov or random phase approximation decoupling is used to decouple the higher order Green’s functions. Based on the above procedures, the effects of the magnetic fields on the critical and compensation temperatures are investigated. The cause of compensation temperature appearance of a spin-1/2 and spin-1 ferrimagnetic system is discussed in detail. Our results show that the magnetizations of the two sublattices approach to zero at the phase transition point when h a= h b=0. When h a=0, the dropping speed of the sublattice magnetization | m b| with the increase of temperature is slower than that of sublattice magnetization | m a| of small spin when the value of h b increases. Under general condition, S b is larger than S a so that | m a| is always smaller than | m b|. It means that the relation of m a=– m b≠0 cannot be satisfied. It indicates that when h a=0, no matter what value of other parameters in the Hamiltonian is, the compensation temperature cannot appear. On the contrary, in the case of h b=0, as the value of h a increases, the dropping speed of | m b| with the increase of temperature is faster than that of | m a|. It indicates that the difference between | m a| and | m b| decreases with the increasing of h a below the critical temperature. As h a increases to a certain value h amin, we obtain m a=– m b≠0 below the critical temperature. It means that the compensation point appears. The compensation temperature increases with increasing h a. And the value of h amin depends on h b=0. Therefore the condition for T com to appear is that h a/ h b should be beyond some value that depends on h b. By comparing and analyzing the previous research, we obtain the general condition for the appearance of compensation temperature of the ferrimagnetic system, that is, there is at least one additional force. This additional force causes that the decreasing speed of the sublattice magnetization of the large spin with increasing temperature is greater than that of the sublattice magnetization of the small spin. Only in this way, the relation m a=– m b≠0 can be satisfied, i.e., the compensation temperature appears. Otherwise the compensation point will not occur. Meanwhile, it should be noted that our Hamiltonian will recover an ordinary three-dimensional Heisenberg antiferromagnetic model with the nearest-neighbor interactions at S a= S b. Our results agree with the high temperature series, the linked-cluster series approach and ratio method results.

Magnetic Properties of Diluted Spinels Mg&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ni&lt;sub&gt;1−&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; Systems: Are Studied by Green’s Functions and Mean Field Theories

Many-body Green's function, and mean field theories have been developed for magnetic systems MgxNi1−xFe2O4. We apply this theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, by considering all components of the magnetisation when an external magnetic field is applied in (x-z)-plane. The critical temperatures of MgxNi1−xFe2O4 systems in the range 0 ≤ x ≤ 1 have been deduced. The Green's function results are compared with the results of high temperature series expansion technique, and experimental magnetic measurements.

Three-Dimensional Magnetic Exchange Networks in Trigonal Bisdithiazolyl Radicals.

The N-methyl-4-phenyl-pyridine-bridged bisdithiazolyl radical PhBPMe is polymorphic, crystallizing from cold acetonitrile in a trigonal α-phase, space group P3121, and from hot dichloroethane in an orthorhombic β-phase, space group Pca21. The crystal structures of both phases consist of slipped π-stacks of undimerized radicals aligned laterally into herringbone arrays. In the β-phase, there are two independent radicals in the asymmetric unit, and the resulting π-stacks form corrugated layers interspersed by methyl and phenyl groups which block the approach of neighboring radicals. In the α-phase, the methyl/phenyl groups and the radical π-stacks separately form spirals about 31 axes, the latter giving rise to a 3D network of close radical/radical contacts. Variable temperature magnetic susceptibility measurements on the β-phase indicate strong antiferromagnetic coupling. Weaker but predominantly antiferromagnetic interactions (θ = -20.7 K) are observed in the α-phase. A high temperature series expansion analysis of the magnetic data for the α-phase affords antiferromagnetic exchange energies for the one- and two-step radical/radical interactions about the 31 spirals ( J1 = -1.2 K, J2 = -10.9 K, respectively), with weak ferromagnetic interactions along the π-stacks ( Jπ = +1.8 K). Despite the presence of a 3D network based on the dominant J2 interactions, which affords two independent bipartite sublattices, no evidence of bulk antiferromagnetic order has been observed above T = 2 K. The magnetic results are discussed in light of exchange energies calculated using density functional theory broken symmetry methods.

Incipient and well-developed entropy plateaus in spin- S Kitaev models

We present results on entropy and heat-capacity of the spin-S honeycomb-lattice Kitaev models using high-temperature series expansions and thermal pure quantum (TPQ) state methods. We study models with anisotropic couplings $J_z=1\ge J_x=J_y$ for spin values 1/2, 1, 3/2, and 2. We show that for $S>1/2$, any anisotropy leads to well developed plateaus in the entropy function at an entropy value of $\frac{1}{2}\ln{2}$, independent of $S$. However, in the absence of anisotropy, there is an incipient entropy plateau at $S_{max}/2$, where $S_{max}$ is the infinite temperature entropy of the system. We discuss possible underlying microscopic reasons for the origin and implications of these entropy plateaus.

Monte Carlo Methods for the Ferromagnetic Potts Model Using Factor Graph Duality

Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models. Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo methods, which are known to work well at high temperatures but to fail at low temperatures. We propose Monte Carlo methods (uniform sampling and importance sampling) in the dual normal factor graph and demonstrate that they behave differently: they work particularly well at low temperatures. By comparing the relative error in estimating the partition function, we show that the proposed importance sampling algorithm significantly outperforms the state-of-the-art deterministic and Monte Carlo methods. For the ferromagnetic Ising model in an external field, we show the equivalence between the valid configurations in the dual normal factor graph and the terms that appear in the high-temperature series expansion of the partition function. Following this result, we discuss connections with Jerrum–Sinclair’s polynomial randomized approximation scheme (the subgraphs-world process) for evaluating the partition function of ferromagnetic Ising models.

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S=1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter- and intradimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions.

Magnetic and electronic properties of Mn2Sn thin films: First-principles calculations and high temperature series expansions

In this paper, first-principles calculations have been performed in order to study the electronic and magnetic properties of the bulk and the (0 0 1) surface of Mn2Sn thin films using self-consistent ab initio calculations, based on the density functional theory approach and using the product of the muffin-tin radius and the maximum reciprocal space vector, RMT. Kmax, we full potential linear augmented plane wave methods. Spin-polarized calculations within the framework of density-functional theory are a powerful tool for describing the magnetism of itinerant electrons in solid state materials. The total and partial density of states of Mn2Sn thin films were calculated. The magnetic moments considered to lie along the c axes are computed. The data obtained from the ab initio calculations are used as an input for the high temperature series expansions calculations used to compute other magnetic parameters. The critical temperature and exchange interactions between the magnetic atoms in the Mn2Sn thin films are obtained using high temperature series expansions and mean field theory, respectively.