Ground states of classical spin polygons: rigorous results and examples

Density functional theory (DFT) has been highly successful in supporting experimental materials science; however, a correct electronic ground state is required to realize the full theoretical capacity of DFT. The uranium oxides, $\ensuremath{\alpha}\ensuremath{-}{\mathrm{U}}_{3}{\mathrm{O}}_{8}$ in particular, are simultaneously technologically important materials and theoretically challenging for DFT because the uranium magnetic ground state is not obvious. This is true for both experiment and theory---magnetic susceptibility measurements indicate an antiferromagnetic (AFM) ground state with transitions near 4.2 and 8.0 K, but the ordering itself is not known. Theoretical literature reports are in contradiction, with independent studies finding paramagnetic, ferromagnetic (FM), and AFM states as the lowest energy configuration. However, recent inelastic neutron scattering experiments suggested an uninvestigated magnetic structure with ordering along the [0.5 1 1] plane, motivating a theoretical reinvestigation. Using this insight, we calculated the relative energy of FM and AFM orderings along [0.5 1 1], [0.5 0 0], [0 1 0], and [0 0 1] using noncollinear DFT calculations with spin-orbital coupling. We found that the [0.5 1 1] AFM structure is lower in energy than FM or AFM orderings along the low Miller index directions. We also investigated polarization of the magnetic moment along each lattice vector and found that polarization along the out-of-plane direction is the energetically preferred orientation for the AFM structures. Additionally, we found in all calculations that moments initially pointing along the in-plane lattice vectors significantly relax until they point along the coordinate between the two crystallographically distinct uranium sites with complex noncollinear magnetic configurations. The new [0.5 1 1] AFM magnetic structure provides an additional path forward toward understanding the electronic structure of \ensuremath{\alpha}-${\mathrm{U}}_{3}{\mathrm{O}}_{8}$ and lends theoretical credibility to recent neutron scattering results.

The lowest energy configurations of short odd open chains with classical spins are determined for antiferromagnetic bilinear and biquadratic nearest-neighbor exchange interactions. The zero field residual magnetization generates differences with the magnetic behavior of even chains, as the odd chain is like a small magnet for weak magnetic fields. The lowest energy configuration is calculated as a function of the total magnetization M, even for M less than the zero field residual magnetization. Analytic expressions and their proofs are provided for the threshold magnetic field needed to drive the system away from the antiferromagnetic configuration and the spin polar angles in its vicinity, when the biquadratic interaction is relatively weak. They are also given for the saturation magnetic field and the spin polar angles close to it. Finally, an analytic expression along with its proof is given for the maximum magnetization in zero magnetic field for stronger biquadratic interaction, where the lowest energy configuration is highly degenerate.

Manganese is one of the most intriguing elements showing multiple magnetic phases. In order to shed some light on the complex behavior, the manganese dimer has been the focus of extensive interest in theoretical research. Various quantum techniques have been utilized to comprehend the characteristics of the Mn dimer. Several approaches and functionals have been employed that suggest that the ferromagnetic (FM) state is its lowest energy configuration. Nevertheless, these findings are inconsistent with the experimental results showing that Mn2 has an antiferromagnetic (AFM) Σg+1 configuration at an interatomic Mn-Mn distance of dMn-Mn = 3.40Å. This work presents a comparative assessment of outcomes obtained through several levels of the exchange-correlation functional: generalized gradient approximation (GGA), meta-GGA, GGA+U, and the hybrid Heyd-Scuseria-Ernzerhof (HSE06), the Perdew-Burke-Ernzerhof 0, and the Becke, 3-parameter, Lee-Yang-Parr. The results of our investigation are discussed based on previous theoretical and experimental reports. We found that the best description is obtained with the hybrid HSE06 functional. The Mn2 has a FM coupling at short distances and the characteristic AFM Σg+1 state at dMn-Mn = 3.27Å. Furthermore, we obtained a magnetic moment (μ) per Mn atom of μ = 4.527 μB, a stretching frequency of ω = 80 cm-1, and a binding energy of Eb = -195meV, which is in good agreement with the experimental results.

The majority of recent works devoted to spin nematic phases deal with either frustrated magnets or with those described by Hamiltonians with large non-Heisenberg terms. We show in the present study that nonfrustrated antiferromagnets (AFs) containing ferromagnetic (FM) bonds can show nematic phases in a strong magnetic field. Among the particular spin systems discussed are a ladder with FM rungs, two AF layers coupled ferromagnetically, a chain containing alternating AF and FM bonds, and an AF anisotropic spin-1 chain.

In this paper we have considered an Ising model defined on tangled chain, in which inure bonds have been added to those of [jure [sing chain. To understand their competition, particularly between ferromagnetic and antiferromagnetic bonds, we have studied, using the transfer matrix method, some simple analytical calculations and an iterative algorithm, the behaviour of the free energy and entropy, particularly in the zeroheld and. zero temperature limit, for different configurations of the ferromagnetic tangled chain and different types of additional interaction (ferromagnetic or antiferromagnetic). We found that the condition J = J' between the ferromagnetic interaction ,7 along the chain and the antiferromagnetic interaction .7' across the chain is somewhat as a transition region condition for this behaviour. Our results indicate also the existence of non-zero entropy at zero temperature. MIR AM ARE TRIESTE April 1993 Classification numbers: 05.50.+q,05.5(1+111.70.10.Hk,75.10.Nr FVmifineut address; Department of Physics, University of Tirana, Tirana, Albania.

Some special types of low energy dislocation configurations in annealed α-Ti single crystals

Using first-principles density functional calculations, at both generalized gradient approximation (GGA) and $\text{GGA}+U$ levels we have investigated the electronic structure and magnetic properties of Fe/Co codoped ZnO nanowire. Here we have addressed some of the key issues such as, the preferable sites that Fe/Co can occupy, the coupling mechanism, and role of defects in coupling. We found that the spin alignment between the transition-metal atoms depends on their location. When Fe and Co atoms are nearest neighbors on the outer surface of the nanowire along [0001] direction is the lowest energy configuration with ferrimagnetic (FiM) ground state. At GGA level of description ferromagnetic ordering is observed when impurity atoms sit at surface and subsurface interface forming Fe-O-Co magnetic path, however at $\text{GGA}+U$ level of description antiferromagnetic superexchange interaction dominates and all configuration leads to FiM ground state. $\text{GGA}+U$ are found to give more realistic description of electronics structure of Fe/Co codoped ZnO nanowire. Interestingly ${\text{Fe-V}}_{\text{O}}\text{-Co}$ defect configurations formed by removing the O atom from Fe-O-Co magnetic path are ferromagnetic when Fe-Co separation is less than 2.596 at GGA and $2.801\text{ }\text{\AA{}}$ at $\text{GGA}+U$ irrespective of the location of transition ions. We have also found that Co atom has a tendency to form clusters around Fe atom leading to inhomogeneous doping concentrations. O vacancy is found to be crucial in case of promoting ferromagnetism in this system. Two competing factors are the Ruderman-Kittel-Kasuya-Yosida (RKKY) type of exchange interaction in bulk environment due to O vacancy and direct exchange interaction of carriers due to ${\text{Fe-V}}_{\text{O}}\text{-Co}$ defect configuration on the surface.

The n·replica method with positive integer n (Suzuki's real replica method) is applied to the Syozi model (the random bond model in the annealed system) for a mixture system with ferromagnetic and anti ferromagnetic bonds. The system is equivalent to an annealed mixture system of the n-vector Potts model. It is found that the additional phase of Mattis' type appears for n > 1 replicated system. The n-dependence of the phase diagram (concentration vs temperature) is investigated for this system. 6 ) applied the n-replica method introduced by Edwards and Anderson ll to an Ising model with random bonds and pointed out the existence of the spin glass phase of Mattis' type?) for integer n > 2 in the case of the symmetric distribution of ferromagnetic and antiferromagentic bonds. He emphasized that the n-replica method even for n greater than 1 is also important because the spin glass phase appearing in the system for n > 2 is considered to be similar to that proposed by Edwards and Anderson in the quenched system, and called this method the real replica method_ AharonyS) also investigated a random Ising model with ferromagnetic and anti ferromagnetic bonds, generalizing the n-replica method given by Stephen and Grese) for the dilute system. He predicted that the Mattis phase for n< 1 exists between the ferromagnetic and anti ferromagnetic critical phases at the ground state_ In this paper, extending the Syozi modeFO) with ferromagnetic and antiferromagnetic bonds to the n-replicated system,!lI we investigate the n-replicated system in detail. It is noted that the system is always an annealed one except for n = 0 limit and the original Syozi model corresponds to n = 1 system. In § 2, we formulate the real n-replica method and show a schematic phase diagram for n = 2 on the square and triangular lattices in § 3_ In § 4, we discuss the aspect of the phase diagram for general n_ The summary and discussion are given in § 5_

Frustrated magnets offer a unique playground for exploring emergent quantum phenomena. We report the synthesis, structural details, and magnetic properties ofS= 1 frustrated system Ni12(HPO4)6(PO4)2(OH)6through magnetization and specific heat measurements along with the density functional theory (DFT) calculations. The titled compound hosts a three-dimensional frustrated spin-lattice wherein Ni2+(S= 1) magnetic moments constitute hexagonal rings. The DFT electronic structure calculation reveals that Ni2+moments in the hexagonal rings have alternate ferromagnetic (FM) and antiferromagnetic (AFM) interactions with considerable inter-hexagonal ring magnetic interactions. The magnetic susceptibilityχ(T) data follow Curie-Weiss (CW) behavior at high temperatures with a large CW temperature of about -250 K, implying the strong AFM interactions between the Ni2+(S= 1) magnetic moments. Theχ(T) and specific heat data show an anomaly at 61 K, indicating the presence of magnetic order. Alternative FM and AFM bonds in the hexagonal ring induce magnetic frustration, and the non-negligible inter-hexagonal ring interactions lead to the long-range magnetic order in the titled compound.

A number of experimental studies have evaluated the potential of hydrophobic high-silica zeolites for the adsorptive removal of emerging organic contaminants, such as pharmaceuticals and personal care products, from water. Despite the widespread use of molecular modelling techniques in various other fields of zeolite science, the adsorption of pharmaceuticals and related pollutants has hardly been studied computationally. In this work, inexpensive molecular simulations using a literature force field (DREIDING) were performed to study the interaction of 21 emerging contaminants with two all-silica zeolites, mordenite (MOR topology) and zeolite Y (FAU topology). The selection of adsorbents and adsorbates was based on a previous experimental investigation of organic contaminant removal using high-silica zeolites (Rossner et al., Water Res. 2009, 43, 3787–3796). An analysis of the lowest-energy configurations revealed a good correspondence between calculated interaction energies and experimentally measured removal efficiencies (strong interaction – high removal), despite a number of inherent simplifications. This indicates that such simulations could be used as a screening tool to identify promising zeolites for adsorption-based pollutant removal prior to experimental investigations. To illustrate the predictive capabilities of the method, additional calculations were performed for acetaminophen adsorption in 11 other zeolite frameworks, as neither mordenite nor zeolite Y remove this pharmaceutical efficiently. Furthermore, the lowest-energy configurations were analysed for selected adsorbent-adsorbate combinations in order to explain the observed differences in affinity.

A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca3Co2O6. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.

Field history analysis of spin configurations in the random-field Ising model

In 1977, Gérard Toulouse has proposed a new concept termed as “frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention the Villain’s model, the fully frustrated simple cubic lattice, the antiferromagnetic triangular lattice. The former models are systems with mixed ferromagnetic and antiferromagnetic bonds, while in the latter containing only an antiferromagnetic interaction, the frustration is caused by the lattice geometry. These frustrated spin systems have novel properties that we will review in this paper. One of the striking aspects is the fact that well-established methods such as the renormalization group fail to deal with the nature of the phase transition in frustrated systems. Investigations of properties of frustrated spin systems have been intensive since the 80’s. I myself got involved in several investigations of frustrated spin systems soon after my PhD. I have learned a lot from numerous discussions with Gérard Toulouse. Until today, I am still working on frustrated systems such as skyrmions. In this review, I trace back a number of my works over the years on frustrated spin systems going from exactly solved 2D Ising frustrated models, to XY and Heisenberg 2D and 3D frustrated lattices. At the end I present my latest results on skyrmions resulting from the frustration caused by the competition between the exchange interaction and the Dzyaloshinskii–Moriya interaction under an applied magnetic field. A quantum spin-wave theory using the Green’s function method is shown and discussed.

The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO). The interaction between the pulses is realized by means of measurement-based optoelectronic feedforward, which enhances the gain for lower-energy spin configurations. We present an efficient method of simulating the CIM on a classical computer that outperforms the CIM itself, as well as the noisy mean-field annealer in terms of both the quality of the samples and the computational speed. It is furthermore advantageous with respect to the CIM in that it can handle Ising Hamiltonians with arbitrary real-valued node coupling strengths. These results illuminate the nature of the faster performance exhibited by the CIM and may give rise to a new class of quantum-inspired algorithms of classical annealing that can successfully compete with existing methods.

The thermodynamics at low temperatures of an Ising spin system with random ferromagnetic and antiferromagnetic bonds is considered. It is shown that the replica method leads to expansions for the free energy and correlation functions in terms of the amount of frustration. At low temperatures in two dimensions the Toulouse sum over minimal strings is obtained. An estimate for the entropy at zero temperature and equally probable ferromagnetic and antiferromagnetic bonds is obtained.