Cluster spin glass ordering in diluted spinel Zn0.5Co0.5FeCrO4

The disordered spinel system, Zn_0.5Co_0.5FeCrO₄ has been investigated using the low field magnetization and ac susceptibility measurements. From the present results it appears that this system orders into a cluster spin glass state with the magnetic moments of the ferrimagnetic clusters randomly frozen. Compared to the Ni and Co zinc ferrites with the same magnetic dilution, introduction of Cr into the B sites appears to increase the frustration and disorder dramatically. The predicted phase diagrams for the ordering in diluted magnetic spinels do not describe the magnetic behaviour of this system, presumably due to the disorder in the B sublattice in addition to the dilution in the A sublattice.     

Chiral-glass transition in a diluted dipolar-interaction Heisenberg system

Recently, numerical simulations reveal that a spin-glass transition can occur in the three-dimensional diluted dipolar system. By defining the chirality of triple spins in a diluted dipolar Heisenberg spin glass, we study the chiral ordering in the system using parallel tempering algorithm and heat bath method. The finite-size scaling analysis reveals that the system undergoes a chiral-glass transition at finite temperature.     

Spin-glass transition of the three-dimensional Heisenberg spin glass

It is shown, by means of Monte Carlo simulation and finite size scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass ordering develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes it possible to thermalize lattices of size L = 32, larger than in any previous spin-glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allows us to consider scaling corrections.     

Vibrational entropy of dislocations in Al

The region nearest to a lattice defect must be described by an atomistic model, while a continuum model suffices further away from the defect. We study such a separation into two regions for an edge dislocation. In particular we focus on the excess defect energy and vibrational entropy, when the dislocation core is described by a cluster of about 500–100?atoms, embedded in a large discrete and relaxed, but static, lattice. The interaction between the atoms is given by a potential of the embedded-atom model type referring to Al. The dynamic matrix of the vibrations in the cluster is fully diagonalized. The excess entropy ΔS near the core has positive and negative contributions, depending on the sign of the local strain. Typically, ΔS/k _B ≈ 2 per atomic repeat length along the dislocation core in fcc Al. In the elastic continuum region far from the dislocation core the excess entropy shows the same logarithmic divergence as the elastic energy. Although the work refers to a specific material and defect type, the results are of a generic nature.     

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.     

Orbital ordering and Jahn-Teller distortion in Perovskite ruthenate SrRuO3

Local density approximation plus on-site Coulomb interaction U band structure calculations reveal that SrRuO3 exhibits a half-metallic ground state with an integer spin moment of 2.0 microB/SrRuO3. An associated tilting 4dt2g orbital ordering on a Ru sublattice is observed under the on-site Coulomb interaction U in the presence of lattice distortion. This finding unravels the on-site Coulomb correlation as the driving force of the 4d orbital ordering and Jahn-Teller distortion as well as of the half-metallic ground state.     

Spin glass ordering of Zn0.75Co0.25Fe0.5Cr1.5O4 cubic spinel

The linear and nonlinear low field AC susceptibilities of Zn_0.75Co_0.25Fe_0.5Cr_1.5O₄ show peaks due to non-critical contributions, which mask the peak due to spin glass ordering. They extend into the region of temperatures in which Mössbauer spectra do not show any magnetic component. When a DC field of 200 Oe suppresses the non-critical contributions, peak due to spin glass ordering is clearly visible. The spin glass ordering is thus shown to be a thermodynamic transition. The critical exponent is found to fall within the range found using other spin glasses. Mössbauer spectra in zero fields provide T_SG, which agrees with the peak temperature of AC susceptibilities in the absence of non-critical contributions. 〈S_Z〉 determined using Mössbauer spectra does not show any anomaly. In the presence of a field of 5 T, the spectra show SG ordering at 4.2 K, which converts into ferrimagnetic ordering at higher temperatures.     

The resistivity maximum in the ternary spin glass system Au-Cu-Mn

The temperature of the resistivity maximum, T_m, in the ternary spin glass system Au-Cu-Mn has been analysed in terms of Larsen's theory in order to highlight the contribution from the Kondo effect and the RKKY interaction energy to the resistivity maximum in spin glasses. The competition between these two contributions has been effectively illustrated and a good agreement with theory is obtained for samples with varying magnetic and nonmagnetic atom concentration. A comparison of the dependence of T_m and the RKKY interaction energy on the lattice pressure generated due to addition of Au with reported pressure studies on Mn alloys shows that there is a close relation between the lattice pressure and the externally applied pressure.     

Dynamical and static spin conductivities in the Heisenberg model on honeycomb lattice: The effects of magnetic long range ordering

We have studied both dynamical and static spin conductivities of Heisenberg antiferromagnet on honeycomb lattice in the presence of a magnetic long range ordering. The effects of spatial anisotropy as weak Dzyaloshinskii–Moriya interaction and next nearest neighbor exchange coupling on the behaviors of conductivities are discussed. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. Using Holstein–Primakoff bosonic transformations, the behaviors of spin transport properties have been studied by means of excitation spectrum of mapped bosonic gas. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various Dzyaloshinskii–Moriya interaction strengths. Furthermore we have studied the frequency dependence of dynamical spin conductivity for various Dzyaloshinskii–Moriya interaction strengths and different next nearest neighbor coupling constants. We find that the height of peak in the temperature dependence of static spin conductivity increases upon increasing the anisotropy parameter. The static spin conductivity is found to be monotonically increasing with anisotropy parameter due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different next nearest neighbor coupling constants.     

Magnetic structure factors Heisenberg model for magnetic ordered graphene like structure

We have theoretically studied the magnetic structure factors of Heisenberg model on honeycomb lattice in the presence of anisotropic Dzyaloshinskii–Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the frequency dependence of both longitudinal and transverse dynamical spin susceptibilities has been investigated for various physical parameters in the model Hamiltonian. Using Holstein–Primakoff bosonic transformations, the behavior of magnetic susceptibilities properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of static spin susceptibilities on Dzyaloshinskii–Moriya interaction strength for various next nearest neighbor interaction strengths. We have found the dependence of static longitudinal spin structure factor on Dzyaloshinskii–Moriya interaction strength shows a divergence behavior at phase transition point for various next nearest neighbor exchange constants. Also our results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to lower frequency with next nearest neighbor coupling constant.     

Disordered magnets

The physics of strongly-disordered magnets and especially that of spin glass is an example of a scientific problem whose ideas and results are widely used in different and sometimes rather distant areas (up to biology, for example). This is the consequence of the paradoxical nature of the main question of this problem: how does ordering occur in systems which do not possess any apparent order at all? In other words, how can one find genuine (but hidden) internal variables which determine dynamics (and thermodynamics) of the system having no macroscopic order parameter. From the theoretical point of view the “generic model” for such a system is the well-studied model of spin glass with infinite-range interaction. The next necessary step is to understand the degree of applicability of the results of infinite-range models to real systems. Further there are a number of phenomena which are completely beyond the frame of this model and are governed by fluctuation effects. The theory of fluctuation phenomena in strongly disordered magnets is at the very beginning of its development. In this report we discuss some relevant problems which have been well studied. In the case of genuine spin glasses the problems are as follows: whether there exists a thermodynamic phase transition to the spin glass phase and how does it occur? What is the physics of non-exponential relaxation far above the transition point? Further there are a number of systems belonging to the spin glass universality class (in the sense of phase-transition theory) but possessing the same sort of short-range order. We consider the following spin glasses with local helical order (for example, the diluted yttriumbased alloys YEr, YDy); amorphous magnets with strong random-axis anisotropy; disordered magnets with strong dipolar interaction. We discuss mainly the structures of low-temperature phases in these systems.     

On the connection between spin glasses and gauge field theories

A simple connection between Ising spin glasses and the Z₂ lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

An Entropy Functional for Riemann-Cartan Space-Times

By viewing space-time as a continuum elastic medium and introducing an entropy functional for its elastic deformations, T. Padmanabhan has shown that general relativity emerges from varying the functional and that the latter suggests holography for gravity and yields the Bekenstein-Hawking entropy formula. In this paper we extend this idea to Riemann-Cartan space-times by constructing an entropy functional for the elastic deformations of space-times with torsion. We show that varying this generalized entropy functional permits to recover the full set of field equations of the Cartan-Sciama-Kibble theory. Our generalized functional shows that the contributions to the on-shell entropy of a bulk region in Riemann-Cartan space-times come from the boundary as well as the bulk and hence does not suggest that holography would also apply for gravity with spin in space-times with torsion. It is nevertheless shown that for the specific cases of Dirac fields and spin fluids the system does become holographic. The entropy of a black hole with spin is evaluated and found to be in agreement with Bekenstein-Hawking formula.     

Temperature dependence of the lattice parameters and magnetic properties of Er3Ir single crystals

Er₃Ir single crystals were grown by the Czochralski method from a levitated melt. The electrical resistivity thermal dependence exhibits ordering temperature of the erbium sublattice at 40 K and a spin reorientation process at 22 K. The DC and AC magnetic susceptibility show antiferromagnetic ordering in the form of an asymmetric peak. The magnetization in strong magnetic fields up to 140 kOe exhibits anisotropy. The lattice parameters’ thermal dependence of Er₃Ir and Er₃Ni show anisotropy and anomalous behaviour.     

Is Pauling’s Hypothesis Violated in the Hexagonal Modification of Ice?

The effect of long-range dipole interaction on the fulfilment of Pauling’s hypothesis concerning the degeneracy of proton configurations satisfying the ice rules is studied for the case of hexagonal ice. It is shown that the ice rules imply a significant reduction of the contributions to the ground state energy from the next-nearest neighbors. The ground state energy of proton subsystem as a function of quasimomentum ceases to change if more than a hundred primitive unit cells in each direction are taken into account. The final amplitude of the energy changes are about 70 K. The analysis reveals the proton ordering in hexagonal ice with the simple unit cell of the oxygen sublattice is impossible. However, that does not exclude proton ordering with a more complex cell caused by distortion of the hexagonal oxygen lattice.     

Theory of orientational glasses models,concepts, simulations

This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former models have been treated both in the Sherrington-Kirkpatrick-Parisi infinite-range limit, and in the short-range case. Among the surprising findings of these treatments we emphasize the first-order glass transition (though lacking a latent heat) of the infinite-range Potts glass, the suggestion that the short-range Potts glass in d = 3 is at its lower critical dimension, and the fact that Potts glasses at zero temperature have a non-zero entropy even for continuous distribution of the interactions. Combining the theoretical results with pertinent experimental findings, it is shown that no definite conclusions on what is the best model for orientational glasses can as yet be drawn, and probably the different classes of models should rather be considered as simple limiting cases of a very complex behaviour.     

Nonmonotonic zero-point entropy in diluted spin ice

Water ice and spin ice are important model systems in which theory can directly account for "zero-point" entropy associated with quenched configurational disorder. Spin ice differs from water ice in the important respect that its fundamental constituents, the spins of the magnetic ions, can be removed through replacement with nonmagnetic ions while keeping the lattice structure intact. In order to investigate the interplay of frustrated interactions and quenched disorder, we have performed systematic heat capacity measurements on spin ice materials which have been thus diluted up to 90%. Investigations of both Ho and Dy spin ices reveal that the zero-point entropy depends nonmonotonically on dilution and approaches the value of Rln2 in the limit of high dilution. The data are in good agreement with a generalization of Pauling's theory for the entropy of ice.     

Magnetocaloric Effect in Anisotropic Mixed Spin ½—1 System: Pair Approximation Method

We use the Pair Approximation method to analyze the magnetic and magnetocaloric behaviors of diluted mixed spin ${\rm S_A}$=1 and spin ${\rm S_B}$=1/2 with the anisotropic Heisenberg model, on a cubic lattice with coordination number $z$=6. Our system is described in presence of an external magnetic field; the phase diagram and thermodynamic properties related to the concentration of magnetic atom (A or B) and the single ion anisotropy are constructed and discussed. Special attention is paid to magnetocaloric properties provided by isothermal entropy change as well as the cooling capacity. These cooling power keys are plotted and discussed as a function of interaction anisotropy and magnetic component concentration of two sublattices ions A and B. Numerical results show a double peak structure in the entropy change curve and the inverse magnetocaloric effect related to the presence of the negative single-ion anisotropy.     

Magnetocaloric Effect in Anisotropic Mixed Spin1/2–1 System: Pair Approximation Method

We use the Pair Approximation method to analyze the magnetic and magnetocaloric behaviors of diluted mixed spin S_A=1 and spin S_B=1/2 with the anisotropic Heisenberg model, on a cubic lattice with coordination number z=6. Our system is described in presence of an external magnetic field; the phase diagram and thermodynamic properties related to the concentration of magnetic atom(A or B) and the single ion anisotropy are constructed and discussed.Special attention is paid to magnetocaloric properties provided by isothermal entropy change as well as the cooling capacity. These cooling power keys are plotted and discussed as a function of interaction anisotropy and magnetic component concentration of two sublattices ions A and B. Numerical results show a double peak structure in the entropy change curve and the inverse magnetocaloric effect related to the presence of the negative single-ion anisotropy.