Pseudospin Hamiltonian Research Articles

Monte Carlo simulations of strain pseudospins: Athermal martensites, incubation times, and entropy barriers

We study martensitic transition kinetics through temperature-quench Monte Carlo simulations for a square/rectangle ferroelastic transition, described by a Hamiltonian of three-state pseudospins $S$, without extrinsic disorder. Here $S=0$ for high-temperature austenite, and $S=\ifmmode\pm\else\textpm\fi{}1$ for the two martensite variants. The temperature-dependent pseudospin Hamiltonian comes from the total scaled free energy functional, evaluated at the three minima of Landau polynomials in order-parameter strains. It includes power-law anisotropic interactions from the St. Venant compatibility constraint, which orient the elastic domain walls in a symmetry-breaking diagonal direction. We find that temperature-time-transformation (TTT) plots for domain-wall phase evolution have phase crossover temperatures, which are understood through an effective-droplet energy parametrization. For temperature cycling through the phases, there are hysteretic peaks in physical quantities. For temperature quenches, a ``vapor'' of martensitic droplets converts at a time ${t}_{m}(T)$ to a vibrating ``liquid'' of bidiagonal domain walls, which then orient at a time ${t}_{C}(T)$ to a static ``crystal'' of single-diagonal martensitic twins, which can have bound residual austenite. Focusing on the conversion time ${t}_{m}$, we find a material-parameter phase diagram, which has regions of nonactivated ``athermal'' and activated ``isothermal'' martensites. In an athermal, nonactivated regime, there are explosive austenite-martensite conversions at temperatures below a residual-austenite spinodal in the TTT diagram, while above it, there are conversion tails, as in experiment. We find ${t}_{m}(T)$ has a quasi-universal Vogel-Fulcher divergence at transition, with a log-normal conversion-rate distribution. The incubation times ${t}_{m},\phantom{\rule{0.28em}{0ex}}{t}_{C}$ are attributed to entropy barriers, with signatures of flat energies, during pathway searches for finite-scale transition textures, which are explicitly identified through textural and internal-stress snapshots. In a glasslike energy landscape picture, these entropic pathways to many locked-twin states dominate those to a single-variant martensite state, of almost the same energy density. Other transitions in 2D and 3D can be similarly studied. More generally, the models could be used to explore conceptual issues of how systems equilibrate after a deep quench.

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local meanfield approximation of their pseudospin hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their $N_{OP}$-component order parameters, with Landau free energies that have a single zero-strain 'austenite' minimum at high temperatures, and spontaneous-strain 'martensite' minima of $N_V$ structural variants at low temperatures. In a reduced description, the strains at Landau minima induce temperature-dependent, clock-like $\mathbb{Z}_{N_V +1}$ hamiltonians, with $N_{OP}$-component strain-pseudospin vectors ${\vec S}$ pointing to $N_V + 1$ discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local meanfield approximation of their pseudospin hamiltonians, that include the powerlaw interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in a generalized Blume-Capel model. We then consider transitions with two-component ($N_{OP} = 2$) pseudospins: the equilateral to centred-rectangle ($N_V =3$); the square to oblique polygon ($N_V =4$); the triangle to oblique ($N_V =6$) transitions; and finally the 3D cubic to tetragonal transition ($ N_V =3$). The local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related hamiltonians illustrate that structural-transitions in materials science can be the source of interesting spin models in statistical mechanics.

Phase transitions in crystals with a BCC structure

A theory of bcc-hcp and bcc-fcc structural phase transformations in metals with a high-temperature bcc lattice has been constructed on the basis of a pseudo-spin Ising Hamiltonian, which describes cooperative oscillations of atomic planes in a two-well potential with allowance for interactions between nearest neighbors. The picture of diffuse scattering and of the combined rearrangement of original Bragg reflections and diffuse scattering into Bragg reflections upon transitions into low-temperature phases has been calculated at all temperatures. It is shown that the bcc-hcp and bcc-fcc phase transformations occur in a temperature interval rather than at a point. In the case of the bcc-hcp transformation, as the temperature decreases, the bcc structure first transforms jumpwise into an orthorhombic structure close to the hcp structure and then, with a further decrease in temperature, this structure smoothly changes into the strictly close-packed hexagonal structure at T → 0. In the case of the bcc-fcc transition, there occurs an analogous transformation into a strictly close-packed face-centered cubic structure at T → 0, but now through a monoclinic structure.

Compressed H-bonds in solids. Pressure-dependent ferroelectric behavior of KDP/DKDP

Hydrostatic pressure effect on ferroelectric structural phase transition (SPT) in KDP (KH 2PO 4) and DKDP (KD 2PO 4) as typical examples of H-bonded solids is considered in the frames of pseudospin Hamiltonian, its parameters Ω(H/D) and J ij (H/D) describe the quantum motion of proton/deuteron along the H/D-bond and pair interaction between these nuclei at different bonds, respectively. These parameters are determined by means of the cluster non-empirical calculations (SCF, MP2-MP4, B3LYP) for the characteristic structural fragments of the compounds of interest. The clusters geometry was taken from the neutron-diffraction data, obtained for pressure values P = 0 and P = 16.5 kbar. The molecular field approximation (MFA) together with more refined Bethe cluster approach (BCA) were applied to study the T c of SPT on the base of the calculated values of Ω(H/D) and J ij (H/D). In agreement with the experiments for both techniques T c decreases with the growth of P due to the proton/deuteron transfer barrier width and height reduction as well as owing to the diminution of the protons/deuterons effective interaction. The related BCA results for KDP and DKDP are discussed in more details.

Highly Anisotropic Exchange Interactions in a Trigonal Bipyramidal Cyanide-Bridged NiII3OsIII2 Cluster

This article is a part of our efforts to control the magnetic anisotropy in cyanide-based exchange-coupled systems with the eventual goal to obtain single-molecule magnets with higher blocking temperatures. We give the theoretical interpretation of the magnetic properties of the new pentanuclear complex {[Ni(II)(tmphen)(2)](3)[Os(III)(CN)(6)](2)} x 6 CH(3)CN (Ni(II)(3)Os(III)(2) cluster). Because the system contains the heavy Os(III) ions, spin-orbit coupling considerably exceeds the contributions from the low-symmetry crystal field and exchange coupling. The magnetic properties of the Ni(II)(3)Os(III)(2) cluster are described in the framework of a highly anisotropic pseudo-spin Hamiltonian that corresponds to the limit of strong spin-orbital coupling and takes into account the complex molecular structure. The model provides a good fit to the experimental data and allows the conclusion that the trigonal axis of the bipyramidal Ni(II)(3)Os(III)(2) cluster is a hard axis of magnetization. This explains the fact that in contrast with the isostructural trigonal bipyramidal Mn(III)(2)Mn(II)(3) cluster, the Ni(II)(3)Os(III)(2) system does not exhibit the single-molecule magnetic behavior.

Chiral decomposition in the electronic structure of graphene multilayers

and byhopes that these elegantly tunable systems might be usefulelectronic materials. In this paper, we demonstrate an unan-ticipated low-energy property of graphene multilayers, whichfollows from an interplay between interlayer tunneling andthe chiral properties of low-energy quasiparticles in an iso-lated graphene sheet. Our conclusions apply in the strongestform to models with only nearest-neighbor interlayer tunnel-ing, but are valid over a broad field range as we explainbelow. We find that the low-energy band structure of anygraphene multilayer consists of a set of independent pseu-dospin doublets. Within each doublet, the bands are de-scribed by a pseudospin Hamiltonian of the form

Spin density matrix of a two-electron system. II. Application to a system of two quantum dots

This work is a sequel to our preceding work [Phys. Rev. B 77, 045319 (2008)]. Here we compare pure-spin and pseudospin dynamics using as an example a system of two quantum dots, a pair of localized conduction-band electrons in an $n$-doped GaAs semiconductor. Pure-spin dynamics is obtained by tracing out the orbital degrees of freedom, whereas pseudospin dynamics retains (as is conventional) an implicit coordinate dependence. We show that magnetic field inhomogeneity and spin-orbit interaction result in a nonunitary evolution in pure-spin dynamics, whereas these interactions contribute to the effective pseudospin Hamiltonian via terms that are asymmetric in spin permutations, in particular, the Dzyaloshinskii-Moriya (DM) spin-orbit interaction. We numerically investigate the nonunitary effects in the dynamics of the triplet-state population, purity, and Lamb energy shift as a function of interdot distance and magnetic field difference $\ensuremath{\Delta}\stackrel{P\vec}{B}$. The spin-orbit interaction is found to produce effects of roughly 4 orders of magnitude smaller than those due to $\ensuremath{\Delta}\stackrel{P\vec}{B}$ in the pure-spin model. We estimate the spin-orbit interaction magnitude in the DM-interaction term. Our estimate gives a smaller value than that recently obtained by Kavokin [Phys. Rev. B 64, 075305 (2001)], who did not include double-occupancy effects. We show that a necessary and sufficient condition for obtaining a universal set of quantum logic gates, involving only two spins, in both pure-spin and pseudospin models is that the magnetic field inhomogeneity $\ensuremath{\Delta}\stackrel{P\vec}{B}$ and the Heisenberg interaction are both nonvanishing. We also briefly analyze pure-spin dynamics in the electron on liquid helium system recently proposed by Lyon [Phys. Rev. A 74, 052338 (2006)].

Orbital ordering and spin-singlet formation in a pyroxene compound NaTiSi 2O 6

We analyse the ground state of the one-dimensional Ti–O network of NaTiSi 2O 6. First, we make the Hartree–Fock calculation of the original d–p model and obtain the ground-state phase diagram. We find that the orbital ferro and spin antiferro state is realized when the effect of lattice distortion is taken into account. We derive the effective spin–pseudospin Hamiltonian by the perturbation theory up to the fourth order of hoppings and its ground state is calculated by the density matrix renormalization (DMRG) method. We find that without the effect of distortion the orbital ordering occurs and the system is in the state of spin singlet, which indicates that the spin fluctuation plays an essential role in this phase transition.

Quantum chemistry application to H‐bonded ferroelectrics via mean field theory involving proton correlation

AbstractA problem of entirely theoretical evaluation of ferroelectric characteristics of H‐bonded crystals is considered based on the quantum chemical calculations of different levels. This consideration employs the Ising‐type pseudospin formalism and treats the “zero‐dimensional” TKHS family crystals M3(H/D)(AO4)2 as convenient examples. Ab initio and post‐Hartree–Fock schemes are applied to calculate the parameters of pseudospin Hamiltonians. The simple mean (molecular) field approximation (MFA) and Bethe clusters approach (BCA), which partly takes into account proton–proton (deuteron–deuteron) correlations, are compared. It is found that both mean field approximations describe the unusual low‐temperature ferroelectric behavior of the TKHS‐like materials qualitatively well. MFA overestimates significantly the critical temperature Tc of the structural phase transition paraelectric phase—antiferroelectric phase. The use of BCA provides the Tc value much closer to the experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Anomalous spin excitations in a coupled spin?pseudospin model for anisotropic Hubbard ladders at quarter filling

By using the quantum Monte-Carlo and density-matrix renormalization group methods, we study the coupled spin–pseudospin Hamiltonian in one-dimension (1D) that models the charge-ordering instability of the anisotropic Hubbard ladder at quarter filling in a strong coupling limit. We here present the temperature dependence of the specific heat of the system to clarify consequences of the interplay between its spin and charge degrees of freedom. We show that there is a parameter and temperature region where the spin degrees of freedom are separated from the charge degrees of freedom and behave like a 1D antiferromagnetic Heisenberg model.

Pseudospin Hamiltonian Parameters from Quantum Chemical Treatment: K 3 H(SO 4 ) 2 (TKHS) Family

A problem of pure theoretical evaluation of Ising ( J ij ) and tunneling ( z H/D ) parameters in pseudospin Hamiltonians is considered for H-bonded ferroelectrics. The TKHS family is examined as a example. Two methods of J ij evaluation are applied. Various quantum-chemical approaches are probed. The z H/D determination using proton potential energy profiles is also discussed. The obtained parameters allow to explain qualitatively the quantum paraelectric behavior of H-members and the antiferroelectric behavior of D-members of this family even by molecular field approximation. The latter overestimates T c values. The cluster approximation allows to substantially approach the estimated T c to experimental ones.

Origin of G-type Antiferromagnetism and Orbital-Spin Structures in LaTiO3

The possibility of the $D_{3d}$ distortion of ${\rm TiO}_6$ octahedra is examined theoretically in order to understand the origin of the G-type antiferromagnetism (AFM(G)) and experimentally observed puzzling properties of ${\rm LaTiO}_3$. By utilizing an effective spin and pseudospin Hamiltonian with the strong Coulomb repulsion, it is shown that AFM(G) state is stabilized through the lift of the $t_{2g}$-orbital degeneracy accompanied by a tiny $D_{3d}$-distortion . The estimated spin-exchange interaction is in agreement with that obtained by the neutron scattering. Moreover, the level-splitting energy due to the distortion can be considerably larger than the spin-orbit interaction even when the distortion becomes smaller than the detectable limit under the available experimental resolution. This suggests that the orbital momentum is fully quenched and the relativistic spin-orbit interaction is not effective in this system, in agreement with recent neutron-scattering experiment.

Dynamical Susceptibility in KH2PO4-type Crystals above and belowTc

The time dependent cluster approximation called the path probability method (PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KH2PO4-type hydrogen-bonded ferroelectrics in order to calculate the homogeneous dynamical susceptibility above and below the ferroelectric transition temperature. Above the transition temperature all the calculations are carried out analytically in the cactus approximation of the PPM. Below the transition temperature the dynamical susceptibility is also calculated accurately since the analytical solution of spontaneous polarization in the ferroelectric phase can be utilized. When the temperature is approached from both sides of the transition temperature, only one of relaxation times shows a critical slowing down and makes a main contribution to the dynamical susceptibility. The discrepancy from Slater model (ice-rule limit) is discussed in comparison with some experimental data.

Magnetic and Orbital States and Their Phase Transition of the Perovskite-Type Ti Oxides: Strong Coupling Approach

The properties and mechanism of the magnetic phase transition of the perovskite-type Ti oxides, which is driven by the Ti-O-Ti bond angle distortion, are studied theoretically by using the effective spin and pseudospin Hamiltonian with strong Coulomb repulsion. It is shown that the A-type antiferromagnetic (AFM(A)) to ferromagnetic (FM) phase transition occurs as the Ti-O-Ti bond angle is decreased. Through this phase transition, the orbital state changes only little whereas the spin-exchange coupling along the c-axis is expected to change from positive to negative nearly continuously and approaches zero at the phase boundary. The resultant strong two-dimensionality in the spin coupling causes rapid suppression of the critical temperature, as observed experimentally. It may induce large quantum fluctuations in this region.

Application of the path probability method to dynamical susceptibility in KH2PO4-type crystals

The time dependent cluster approximation called the path probability method (PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KH2PO4-type hydrogen-bonded ferroelectrics to calculate the dynamical electric susceptibility above and below the transition temperature.

Application of the Cluster Variation Method to Anisotropic Polarization Fluctuations in KD2PO4-Type Crystals above and below the Transition Temperature

The cluster variation method (CVM) in the cactus approximation is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KD 2 PO 4 -type hydrogen-bonded ferroelectrics to calcula...

Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model.

A strong-coupling expansion is applied to the anharmonic Holstein model and to the Holstein-Hubbard model through fourth order in the hopping matrix element. Mean-field theory is then employed to determine transition temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic effects are not easily mimicked by an on-site Coulomb repulsion, and that anharmonicity strongly favors superconductivity relative to charge-density-wave order. Surprisingly, the phase diagram is strongly modified by relatively small values of the anharmonicity.

Hydrodynamics of superfluid 4He in a pseudospin model.

A microscopic theory of nonlinear dynamics in superfluid $^{4}\mathrm{He}$ is formulated using a model in which a system of bosons with hard cores plus attractive nearest-neighbor interactions is described by a pseudospin Hamiltonian on a lattice. In this framework, the superfluid order parameter is the expectation value of the spin-flip operator. Using the spin-coherent-state representation, a nonlinear evolution equation is derived for the order parameter in the lattice model, and calculations are carried out with its continuum version, as is appropriate for the description of a liquid phase. The well-known Gross-Pitaevskii equation for the order parameter (valid for T\ensuremath{\sim}${T}_{\ensuremath{\lambda}}$) is recovered in the leading small-amplitude approximation of our equation. Further, a microscopic basis is provided for the nonlinear effects discussed in phenomenological treatments of superfluid $^{4}\mathrm{He}$ films. In bulk $^{4}\mathrm{He}$, considering a cylindrically symmetric vortex solution, a vortex core of finite thickness and a nonsingular vorticity is obtained. The finiteness of the vortex energy is shown to arise as a natural consequence of the formalism. Unidirectional traveling-wave solutions for the superfluid density with velocity-dependent amplitudes are shown to exist. Finally, for a specific choice of parameters, a static-domain-wall solution is also possible.

Quasispin seniority and the variational description of the nuclear free energy

The concept of quasispin seniority is discussed within the framework of an approximate treatment for obtaining free energies in the case of nuclear systems described by pseudospin Hamiltonians.

Observations of phase transitions in the mixed crystal system Dy pGd 1-pVO 4

The low temperature crystallographic and magnetic phase transitions in the mixed crystal system Dy p Gd 1- p VO 4 (0 ⩽ p ⩽ 1) have been studied using thermal expansion measurements and Mössbauer spectroscopy. The introduction of magnetic Gd 3+ ions into the DyVO 4 host causes an anomalous dip in the Néel temperature T N ( p), and a rapid reduction of the distortion temperature T D ( p) which differs from results on similar mixed systems. A number of pseudo-spin Hamiltonians that model these observations are discussed.