Sequence Of Ground States Research Articles

Investigating patterns in aluminum distribution and stability in mordenite zeolite structure: Analysis and theoretical conclusions from existing experimental data

Building upon our prior theoretical study, this work focuses on determining the position of the seventh, eighth, and ninth aluminum atoms, along with their respective exchange ▪ cations, within the unit cell of mordenite zeolite. The main objective was to identify the positions of these atoms and cations that correspond to the minimum energy state. As a result, the ground state sequence that describes the order in which aluminum atoms enter in the framework as their number increases was completed. Through our investigation, we were able to derive an analytical expression, based on the Madelung energy, which describes the stability of mordenite zeolite as a function of its Si/Al ratio. This expression provides valuable insights, revealing that as the aluminum content within the framework increases, the stability of the zeolite exhibits an asymptotic decrease. It was found that for the mordenite zeolite, Löwenstein's rule is valid for the full range of Si/Al ratios. Interestingly, the restriction that only one aluminum atom can be accommodated per ζ-cage justifies the nature of the aluminum saturation limit (Si/Al=5) in the mordenite zeolite framework. Furthermore, we conducted an evaluation of the aluminum distribution across various configurations and compared it to different experimental observations. This analysis allowed us to make a comprehensive comparison and draw meaningful insights regarding the distribution patterns of aluminum in the mordenite zeolite.

First-principles based atomistic modeling of phase stability in PMN–xPT

We have performed molecular dynamics simulations using a shell model potential developed by fitting first-principles results to describe the behavior of the relaxor–ferroelectric (1 − x)PbMg1/3Nb2/3O3–xPbTiO3 (PMN–xPT) as a function of concentration and temperature, using site occupancies within the random site model. In our simulations, PMN is cubic at all temperatures and behaves as a polar glass. As a small amount of Ti is added, a weak polar state develops, but structural disorder dominates, and the symmetry is rhombohedral. As more Ti is added the ground state is clearly polar and the system is ferroelectric, but with easy rotation of the polarization direction. In the high Ti content region, the solid solution adopts ferroelectric behavior similar to PT, with tetragonal symmetry. The ground state sequence with increasing Ti content is R–MB–O–MC–T. The high-temperature phase is cubic at all compositions. Our simulations give the slopes of the morphotropic phase boundaries, crucial for high-temperature applications. We find that the phase diagram of PMN–xPT can be understood within the random site model.

Random field Ising model: statistical properties of low-energy excitations and equilibriumavalanches

With respect to the usual thermal ferromagnetic transitions, thezero-temperature finite-disorder critical point of the random field Isingmodel (RFIM) has the peculiarity of involving some ‘droplet’ exponentθ that enters the generalized hyperscaling relation2 − α = ν(d − θ). In the present paper, to better understand the meaning of this droplet exponentθ beyond its role in the thermodynamics, we discuss the statistics of low-energyexcitations generated by an imposed single spin-flip with respect to the groundstate, as well as the statistics of equilibrium avalanches, i.e. the magnetizationjumps that occur in the sequence of ground states as a function of the externalmagnetic field. The droplet scaling theory predicts that the distributiondl/l1 + θ of thelinear size l of low-energy excitations transforms into the distributionds/s1 + θ/df for thesize s (number of spins) of excitations of fractal dimensiondf (s ∼ ldf). In the non-mean-field regiond < dc, droplets are compactdf = d, whereas in the mean-fieldregion d > dc, droplets havea fractal dimension df = 2θ leading to the well-known mean-field resultds/s3/2. Zero-field equilibrium avalanches are expected to display the same distributionds/s1 + θ/df. We also discuss the statistics of equilibrium avalanches integrated over the externalfield and finite-size behaviors. These expectations are checked numericallyfor the Dyson hierarchical version of the RFIM, where the droplet exponentθ(σ) can be varied as a function of the effective long-range interactionJ(r) ∼ 1/rd + σ ind = 1.

Skyrmion lattice in a two-dimensional chiral magnet

We develop a theory of the magnetic field-induced formation of Skyrmion crystal state in chiral magnets in two spatial dimensions, motivated by the recent discovery of the Skyrmionic phase of magnetization in thin film of ${\text{Fe}}_{0.5}{\text{Co}}_{0.5}\text{Si}$ and in the A phase of MnSi. Ginzburg-Landau functional of the chiral magnet rewritten in the ${\text{CP}}^{1}$ representation is shown to be a convenient framework for the analysis of the Skyrmion states. Phase diagram of the model at zero temperature gives a sequence of ground states, helical $\text{spin}\ensuremath{\rightarrow}\text{Skyrme}$ $\text{crystal}\ensuremath{\rightarrow}\text{ferromagnet}$, as the external field $B$ increases, in good accord with the thin-film experiment. In close analogy with Abrikosov's derivation of the vortex lattice solution in type-II superconductor, the ${\text{CP}}^{1}$ mean-field equation is solved and shown to reproduce the Skyrmion crystal state.

Time-dependent local Green’s operator and its applications to manganites

An algorithm is presented to calculate the electronic local time-dependent Green's operator for manganites-related hamiltonians. This algorithm is proved to scale with the number of states $N$ in the Hilbert-space to the 1.55 power, is able of parallel implementation, and outperforms computationally the Exact Diagonalization (ED) method for clusters larger than 64 sites (using parallelization). This method together with the Monte Carlo (MC) technique is used to derive new results for the manganites phase diagram for the spatial dimension D=3 and half-filling on a 12x12x12 cluster (3456 orbitals). We obtain as a function of an insulating parameter, the sequence of ground states given by: ferromagnetic (FM), antiferromagnetic AF-type A, AF-type CE, dimer and AF-type G, which are in remarkable agreement with experimental results.

Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the Thomas-Fermi limit. The sequence of ground states (within these single-ring configurations) is determined as a function of the external rotation frequency by comparing the free energy of the various states. For each ground state, the Tkachenko-like excitations and the associated dynamical stability are analyzed.

A simple model for the prediction of ground states of interacting 2D electron droplets and quantum dots

A simple model is presented for predicting the numerically "observed" sequence of ground states (GSS) of 2D electron droplets and quantum dots in strong magnetic fields. The model is based on the assumption that exchange and correlation in the 2D electron gas induce gaps in the lowest Landau level, producing a sub-Landau level (SLL) structure. The sequence of GSS results from filling the SLLs as the total angular momentum L is increased. Using the numerically "known" energies (for a few L) for N<or=6 we present a fit formula to predict, to within 2% accuracy, the GSs for higher N and L for which exact diagonalization results are unavailable. Typical results for N=6, 7 and 10 droplets are presented.

Spin-orientation phase transitions in itinerant multiple spin-density-wave systems

Using a simple Landau model the authors have found six different magnetic phases: one cubic (TSDW), three tetragonal (SSDW, DSDW, ASDW) and two orthorhombic (OSDW and GSDW) phases. The above phases may be categorised by the number of order parameters and the number of non-zero magnetic moments. It is found that second-order transitions between states with different numbers of magnetic components have discontinuities in the elastic constants, whereas those maintaining the number of components have vanishing shear components. For a specific parametrisation of the authors' model they find a sequence of ground states that have identical symmetries to those found in the Mn-Ni system. The authors predict the vanishing of a shear elastic constant at one of the tetragonal-to-orthorhombic phase transitions but not the other. They also discuss an alternative microscopic model for determining the onset of the various phases. This involves the calculation of the n-point static Green functions in the long-wavelength limit for a simple one-band model.

The convergence of the one-dimensional ground states to an infinite lattice

For one-dimensional systems interacting via a two-body potential, the sequence of ground states is proved to converge to an infinite lattice, for a large open class of interactions, containing in particular the Lennard-Jones potential.

High-spin positive-parity states in 179Hf studied by the 180Hf(τ, α) 179Hf reaction AT 32 MeV

Full angular distributions are presented for states populated in the reaction 180Hf(τ, α) 179Hf at 32 MeV beam energy. Positive-parity states associated with the i 13 2 unique parity intruder orbital are given special attention. Thus, angular distributions for the five first members of the [624 9 2 ] groundstate sequence are given, as well as for a number of more highly excited states, some being new assignments. The distribution of l = 6 transfer strength is quite characteristic, two 13 2 + states being substantially more populated than the rest. The characteristic features of the data are explained by a quasiparticle-rotor calculation employing deformed Woods-Saxon orbitals, but only if the hexadecapole shape parameter of the nuclear potential is β 4 ∼ −0.08. The often anomalous differential cross sections for I π ≠ 13 2 + band members are well accounted for by a rotor model CCBA calculation employing transfer form factors extracted from the orbitals of the deformed Woods-Saxon field, and including non-adiabatic Coriolis mixing effects.

High spin states in 67Ga

The nucleus 67Ga has been studied through the reaction 57Fe( 12C, pnγ) 67Ga at E 12 c = 40 MeV. New levels above 4 MeV excitation energy have been found and nuclear properties of these states are proposed from investigations of prompt γ-rays using in-beam γ-spectroscopic techniques. Comparison between the ground state sequence in 66Zn and the favoured states of positive parity up to J π = 25 2 + in 67Ga suggests that the latter can be explained in terms of coupling a g 9 2 proton to the 66Zn core. A second collective band of positive parity is proposed to be based on a configuration [( f 5 2 ) J≠O 2π g 9 2 ] 15 2 + . Results on magnetic substate populations of nuclear states formed in different heavy-ion induced reactions compiled. The α 2, α 4 combinations are consistent with the assumption of Gaussian distributed substate populations within the experimental errors.

Gamma-ray spectroscopy of 66Zn and 67Zn and the role of the [formula omitted] orbital

Measurements of γ-ray yield functions, γ-γ coincidence spectra and y-ray angular distributions following the 64Ni(α, n) and (α, 2n) reactions have been made. Beam energies of 17 to 25 MeV were used. Among the new levels observed, with their proposed spin-parity assignments, are: in 66Zn, 3708 keV, (5) +; 3896 keV, 5 −; 4812 keV, (7 −); 5110 keV, (8 −); 6417 keV; (10 −); 7516 keV, (12 +); and in 67Zn, 2937 keV, 13 2 + ; 3491 keV, 17 2 or 19 2 ; 3492 keV, ( 13 2 (si+)); 4221 keV, ( 19 2 −); 4631 keV, ( 21 2 + ); 4685 keV, ( 21 2 −). Comparison between the ground-state sequence, 0 + to 6 +, in 66Zn and the first 9 2 + to 21 2 + levels in 67Zn strongly suggests that the latter be described as a g 9 1 neutron orbital weakly coupled to the 66Zn core. Other sequences of high-spin 66Zn states are proposed to be formed from two-quasiparticle states containing the g 9 2 excitation, coupled to the same ground-state sequence.