Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.     

Generalized transformation for decorated spin models

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.     

Magnetic phase transitions and phase diagrams of DyMn2Ge2

The experimental studies of magnetic phase transitions in the layered tetragonal intermetallic compound DyMn₂Ge₂ are continued. The existence of spontaneous phase transitions is confirmed by the results of measurements of the temperature dependences of lattice parameters and the initial magnetic susceptibility. The measurements in strong (up to 50 T) and ultrastrong (up to 150 T) fields revealed two new field-induced magnetic transitions. The inclusion of the exchange interaction between next-to-nearest layers of manganese and the crystal field effects for the rare-earth subsystem along with the antiferromagnetic exchange interaction of nearest Mn layers has made it possible to describe the magnetic properties of DyMn₂Ge₂ in a wide range of magnetic fields. The parameters of these interactions are determined from a comparison of the experimental and theoretical magnetization curves and H-T phase diagrams.     

Magnetic properties of MnxMg1-xS solid solutions

The static magnetic properties of the polycrystalline solid solutions Mn_xMg_1-xS(0<x?1) are reported. The experimental data reveal the appearance of a critical concentration x_c=0.13±0.01 for long-range magnetic ordering, which is in good agreement with the result of a series expansion of the mean cluster size for a face-centered cubic lattice with exchange interactions up to 12 nearest neighbours and 6 next-nearest neighbours. At concentrations far below x_c the existence of long-range exchange interactions is demonstrated.     

Ferroquadrupolar Order in the Spin-1 Bilinear-Biquadratic Model up to the Second Nearest Neighbor

We have studied some ferroquadrupolar phases of the S = 1 Heisenberg model with bilinear and biquadratic exchange interactions on the square lattice up to the second nearest neighbor, using the SU(3) Schwinger bosons formalism in a mean field approximation. This technique is very convenient to treat nematic order. This technique has the advantage of using the fundamental representation of the SU(N) group instead of SU(2), designed to capture spin-quadrupolar order in addition to the dipolar magnetic order. We also present quadrupole structure factors that can be measured in future experiments. Our calculations can have implications in the study of iron-based superconductors.     

Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

We perform Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, z_c = 1.0588 ± 0.0003. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.     

Vortex deconfinement in the XY model with a magnetic field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.     

Universality of the ratio of the critical amplitudes of the magnetic susceptibility in a two-dimensional ising model with nonmagnetic impurities

The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q _c = 0.407254). The behavior of the effective critical exponent γ(q) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.     

The range of transferred hyperfine interactions in EuS

We report on a Mössbauer study of the transferred hyperfine fields at the ¹⁵¹Eu nuclei in the Eu_1?xSr_x series of mixed compounds. The totally transferred hyperfine field amount ?(5.3 ± 0.3) T corresponding to saturation values for the hyperfine field of ?(33.4 ± 0.2) T for x = 0 and ?(28.1 ± 0.2) T extrapolated for x = 1. Our results strongly support fairly long range magnetic interactions instead of the generally accepted model covering only nearest and next nearest neighbour interactions.     

A Monte Carlo study of the first-order transition in a Heisenberg FCC antiferromagnet

A nearest neighbor Heisenberg antiferromagnet on a face-centered cubic lattice is studied by extensive Monte Carlo simulations in zero magnetic field. The parallel tempering algorithm is utilized, which allows one to overcome a slow relaxation of the magnetic order parameter and to fully equilibrate moderately sized clusters with up to N ? 7 × 10³ spins. By collecting energy and order parameter histograms on clusters with up to N ? 2 × 10⁴ sites, we accurately locate the first-order transition point at T _c = 0.4459(1)J.     

High pressure-high field Mössbauer spectroscopy on pure and magnetically diluted europium-monochalcogenides

By simultaneously applying pressures up to 19.6 kbar and magnetic fields up to 13 T, the magnetic hyperfine (hf) fields of the Eu-monochalcogenides Eu X (X = S, Se, Te) and of the magnetic dilution system Eu_xSr_1-xS were studied using the ¹⁵¹Eu Mössbauer effect. Expected relations between the magnetic exchange interactions and the transferred hyperfine (thf) fields have been confirmed. The pressure dependence of the total hf field in the ferromagnetically saturated state of EuS, EuSe and EuTe has been shown to be due mainly to the pressure response of the thf field of the nearest Eu-neighbours. Except with EuO the thf fields of the next nearest Eu-neighbours and the Eu-core polarization field are nearly insensitive to pressure. The results are discussed in terms of the exchange model proposed by T. Kasuya.     

Elektronen-Kern-Doppelresonanz-Untersuchung vonU 2-Zentren in Kaliumchlorid

U ₂-centers in alkali halides are neutral hydrogen atoms in interstitial lattice sites, as has been shown by EPR measurements. The hyperfine interactions with the proton and with the four nearest halogen nuclei are resolved in the EPR spectrum. In order to resolve hyperfine interactions with further nuclei of the surrounding lattice ENDOR measurements have been performed onU ₂-centers in KCl at 77 °K. The analysis of the ENDOR spectra gave precise values for the hyperfine and quadrupole interaction constants of the nearest neighbour chlorine and potassium nuclei. The isotropic hyperfine constant of the chlorine neighbours is 24 times larger than that of the potassium neighbours although both nuclei are on equivalent first shell lattice positions. The hyperfine interactions of second shell potassium nuclei [(1/2, 1/2, 3/2)-position] show an unexpectedly large isotropic hyperfine constant. One expects a pure magnetic dipole-dipole interaction for the outer shell nuclei because of the concentrated hydrogen wave function. Two further chlorine shells could be approximately analysed. A theoretical estimate of the hyperfine and quadrupole interaction constants was made by orthogonalizing the 1s hydrogen wave function to the cores of the surrounding ions. If one takes into account the mutual overlap of neighbouring potassium and chlorine ions, one gets the right order of magnitude of the measured constants and a value of 10.4∶1 for the ratio of the isotropic hyperfine constants of the first shell chlorine and potassium nuclei. The relatively large isotropic constant of the second shell potassium nuclei can also be explained on this basis.     

Pressure-Induced Decrease in the Curie Temperature of Gd<Subscript>2</Subscript>Fe<Subscript>17</Subscript>: LSDA+U Calculations

To explain the magnetic properties of advanced ferromagnetic intermetallic compounds of the R₂Fe₁₇ (R is a rare-earth element) class, experimentalists often use the hypothesis of competition between ferromagnetic exchange and antiferromagnetic exchange between four types of the nearest iron atoms in nonequivalent lattice sites. For the rhombohedral Gd₂Fe₁₇ ferromagnet, we calculate the magnetic moments of iron and gadolinium ions, the parameters of exchange between Fe atoms, and Curie temperature T_C at a zero pressure and during hydrostatic lattice compression. The magnetic moment of the unit cell of Gd₂Fe₁₇ is shown to decrease under pressure, and this decrease is almost completely associated with a decrease in the magnetic moments of Fe rather than Gd ions, the pressure dependence of the magnetic moments of which is weaker by an order of magnitude. In contrast to the hypothesis regarding the competition of exchange interactions between different kinds of Fe atoms, the parameters of exchange between the nearest iron atoms in different crystallographic sites are found to be positive ferromagnetic (at a zero pressure and during compression), and a ferromagnetic character of interaction is shown to remain unchanged under pressure even for Fe atoms in the so-called dumbbell sites with the nearest interatomic distances. The Curie temperature T_C of Gd₂Fe₁₇ is shown to decrease with increasing pressure. The changes in the exchange parameters and the magnetic moments of Gd₂Fe₁₇ during compression are found to be mainly related to a change in the position of energy spectrum branches with respect to each other and the Fermi level ?_F rather than to a change in the overlapping of wavefunctions, which play a minor role.     

Mössbauer effect in α-Fe2O3 following the reaction56Fe(d,p)57Fe

Mössbauer spectra in α-Fe₂O₃ were measured below and above the Morin temperature following the reaction⁵⁶Fe(d, p)⁵⁷Fe. Within high accuracy, shift, quadrupole splitting, and Debye-Waller-factor are found to be the same as corresponding radioactive source data, whereas the magnetic field is lower by 10 kG. It follows that 10^?7 s after the nuclear reaction essentially all excited recoils are at normal lattice sites with nearest neighbors being undisturbed. The deviation in magnetic field cannot be explained by a rise in temperature.     

Magnetic properties and concurrence for fluid 3He on kagome lattice

We present the results of magnetic properties and entanglement for kagome lattice using Heisenberg model with two- and three-site exchange interactions in strong magnetic field. Kagome lattice correspond to the third layer of fluid ³He absorbed on the surface of graphite. The magnetic properties and concurrence as a measure of pairwise thermal entanglement are studied by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. The system exhibits different magnetic behaviors depending on the values of the exchange parameters (J ₂, J ₃). We have obtained the magnetization plateaus at low temperatures. The central theme of the paper is comparing the entanglement and magnetic behavior for kagome lattice. We have found that in the antiferromagnetic region behavior of the concurrence coincides with the magnetic susceptibility one.     

Absorption of light by exchange-coupled ions in a 2D antiferromagnet

The optical absorption spectra of Rb₂Mn_xCd_1?xCl₄ crystals are experimentally studied in the vicinity of a magnon sideband of the exciton band at a manganese content x ranging from 1.0 to 0.4. Additional absorption bands are observed with an increase in the magnetic structural disorder upon replacement of manganese ions by cadmium ions. An analysis of the evolution of the additional absorption bands in a magnetic field during the spin-flop phase transition and the change in the intensity with variations in the manganese content x demonstrates that these bands are associated with the excitation of the exchange-coupled pairs of manganese ions located in different environments in a plane square lattice. The phase boundary between the antiferromagnetic and spin-flop phases is constructed using the results of optical measurements. The manganese content corresponding to the magnetic percolation point is evaluated.     

Simulation of magnetic properties of the two-dimensional magnetic with anisotropic antiferromagnetic interactions and cluster ordering by quantum Monte Carlo

Magnetic with anisotropic antiferromagnetic exchange interactions and special topology of coupling in the square lattice with spins pairs ordering is studied by quantum Monte Carlo method. The antiferromagnetic order is found to be more stable as compared to spin liquid state. Exchange interactions and wave vector of structure modulation for Cu₃B₂O₆ is estimated. Neel temperature versus strength of exchange in spin pair is calculated. Plateau and modulation of magnetic structure in field magnetization dependence is revealed.     

Ising model with competing interactions on a Cayley tree

An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK _r and effective field per siteK _r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J < 0 values whereX _r, and K_r iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.     

Magnetic properties of ferromagnetic diluted Zn x Cd1–x Cr2Se4 spinels are studied by Green's functions,mean field theory and high temperature series expansions theories

The field induced reorientation of the magnetization of ferromagnetic (or antiferromagnetic) structure is treated within the framework of many-body Green's function theory by considering all components of the magnetization. The mean field theory is used to calculate the nearest neighbour and the next-neighbour super-exchange J₁(Cr–Cr) and J₂(Cr–(Zn(Cd)–Se)–Cr), respectively, for the Zn_1–x Cd _x Cr₂Se₄ in the range 0 < x < 1. The intraplanar and the interplanar interactions are deduced. The high temperature series expansions (HTSEs) are derived for the magnetic susceptibility and the two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation (RPA). The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The obtained results are comparable with those obtained by magnetic measurements. 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.     

Magnetic properties of 2D nano-islands II: Ising spin model with out-of-plane magnetic field

An Ising effective field theory model is presented to calculate the magnetic properties of 2D nano-islands on a nonmagnetic substrate, subject to an externally out-of-plane applied magnetic field. The system Hamiltonian contains nearest neighbor exchange interactions, single-atom magnetic anisotropies, and the Zeeman term. The calculations yield, in particular, the single site spin correlations, the magnetizations, and the isothermal susceptibilities, for the core and periphery domains of the nano-island. The choice of a spin S=1 for the atoms of the system permits the analysis of local spin fluctuations via the single site spin correlations. We investigate in this respect the effects due to the different magnetocrystalline anisotropies and reduced dimensionalities, for the core and periphery domains, and in particular the critical influence of the applied magnetic field. Detailed theoretical results are presented for the square and hexagonal lattice symmetries, with numerical applications for the 2D monolayer Co nano-islands on a Pt substrate. It is shown that the remarkable differences between the magnetic properties of the core and periphery domains in zero field are washed out when an out-of-plane field is applied. The applied field also provokes critical discontinuities for the spin correlations and magnetization reversals, for the core and periphery domains, which are especially evident for the hexagonal lattice nano-island in the range of fields of interest. The discontinuities and magnetization reversals occur over elementary temperature widths, and shift to lower temperatures with increasing field. The field-dependant isothermal susceptibilities show new features very different from those for the susceptibilities in zero field. The present Ising model does not show any blocking temperature transition to superparamagnetism.