Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis

We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.     

Magnetic properties of BiFeO3 micro-cubes synthesized by microwave agitation

In this article, we present results of field cooled (FC) and zero field cooled (ZFC) magnetization measurements and investigation of aging and memory effect in bismuth ferrite (BFO) multiferroic micro-cubes obtained by means of simple microwave synthesis procedure. It is found that difference between FC and ZFC magnetizations appear at the temperature of freezing of ferromagnetic domain walls. The decay of the magnetic moment versus time described by power-law relation and the absence of memory effect are caused by domain growth mechanism rather than by the spin-glass phase. The negligible value of remnant magnetic moment indicates that BFO compound exhibits low concentration of ferromagnetic domains and can be close to ferromagnetic to spin-glass transition.     

Vitrification in a 2D Ising model with mobile bonds

A bond-disordered two-dimensional Ising model is used to simulate Kauzmann's mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to nearest neighbors at the same rate as the spins flip. For slow cooling, the theoretical minimum energy configuration is approached, characterized by an amorphous distribution of locally optimally arranged impurity bonds. Rapid cooling to low temperatures regularly finds bond configurations of higher energy, which are both a priori rare and severely restrictive to spin movement, providing a simple realization of kinetic vitrification. A supercooled liquid regime is also found, and characterized by a change in sign of the field derivative of the spin-glass susceptibility at a finite temperature. Received 3 August 2000 and Received in final form 9 March 2001     

Dynamic spin-glass behavior in a disorder-free,two-component model of quantum frustrated magnets

Motivated by the observation of a spin-glass transition in almost disorder-free Kagome antiferromagnets, and by the specific form of the effective low-energy model of the S = 1/2, trimerized Kagome antiferromagnet, we investigate the possibility to obtain a spin-glass behavior in two-component, disorder-free models. We concentrate on a toy-model, a modified Ashkin-Teller model in a magnetic field that couples only to one species of spins, for which we prove that a dynamic spin-glass behavior occurs. The dynamics of the magnetization is closely related to that of the underlying Ising model in zero field in which spins and pseudo-spins are intimately coupled. The spin-glass like history dependence of the magnetization is a consequence of the ageing of the underlying Ising model. Received 21 September 2001 and Received in final form 16 January 2002     

Exchange bias effect in partially oxidized amorphous Fe-Ni-B based metallic glass nanostructures

The magnetic properties of amorphous Fe-Ni-B based metallic glass nanostructures were investigated. The nanostructures underwent a spin-glass transition at temperatures below 100 K and revealed an irreversible temperature following the linear de Almeida-Thouless dependence. When the nanostructures were cooled below 25 K in a magnetic field, they exhibited an exchange bias effect with enhanced coercivity. The observed onset of exchange bias is associated with the coexistence of the spin-glass phase along with the appearance of another spin-glass phase formed by oxidation of the structurally disordered surface layer, displaying a distinct training effect and cooling field dependence. The latter showed a maximum in exchange bias field and coercivity, which is probably due to competing multiple equivalent spin configurations at the boundary between the two spin-glass phases.     

Freezing Temperature in Dilute Ising Spin Glasses with Long-Range Interactions

The onset of spin-glass freezing in dilute Ising systems with long-range interactions is investigated with the use of numerical simulations. We show that taking pair correlations explicitly into account results in the renormalization of the interaction matrix and suppression of the density of localized states compared with conventional mean field theory. Application of the theory to the RKKY interaction in the dilute limit raises the question of the appropriate boundary eigenvalue of the effective interaction matrix that separates localized and extended states. We identify the onset of spin-glass freezing with the temperature T _g at which this boundary eigenvalue is equal to one. Numerical simulations reproduces the linear concentration dependence of T _g in the very dilute limit, in agreement with scaling relations, and show a significant improvement over the conventional mean-field theory in the value obtained for the freezing temperature.     

Reentrant phases in the ± J spin glass

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic interacions, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterized by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.     

Thermomagnetic hysteresis and electrical transport in amorphous films

We report resistivity and magnetization measurements on an amorphous Ni₇₄Mn₂₄Pt₂ thin film in the temperature range of 3–300 K. Two significant features are apparent in both the magnetic susceptibility and electrical resistivity. A low-temperature (low-T) anomaly is observed at about 40 K, where a cusp appears in the resistivity, while a concomitant step-like increase in zero-field-cooled (ZFC) magnetization (M) appears with increasing temperature. The low-T anomaly is attributed to a crossover from a pure re-entrant spin-glass within individual domains to a mixed ferro-spin-glass regime at lower temperatures. By contrast, the high-temperature (high-T) anomaly, signaled by the appearance of hysteresis below 250 K, corresponds to the freezing of transverse spins in individual domains acting independently. Between the low-T and high-T anomalies a small but discernable magnetic hysteresis is observed for warming vs. cooling in the field-cooled (FC) case. This behavior clearly indicates the presence of domain structure in the sample, while the disappearance of this hysteresis at lower temperatures indicates the complete freezing of the spin orientation of these domains. According to these results, we have divided the magnetic state of this sample into three regions: at temperatures above 250 K, the sample behaves like a soft ferromagnet, exhibiting M vs. H loops with very small hysteresis (less than 5 Oe). As the temperature is lowered into the intermediate region (the range 40–250 K), spins become frozen randomly and progressively within the individual domains. These domains behave independently, rather than as a cooperative behavior of the sample. Weak irreversibility sets in, indicating the onset of transverse spin freezing within the domains. At temperatures below 40 K, the M vs. H loops exhibit larger hysteresis, for both the ZFC and FC cases, as in a pure spin-glass. We have also demonstrated giant noise in the resistivity at temperatures just below 250 K. Such noise can originate from fluctuations of the domains near the film surface because of competing effective bulk and surface anisotropy fields. The large observed amplitude may be explained by means of a large ferromagnetic anisotropy in the resistivity due to the large spin–orbit effect seen in NiMn systems. Finally, the low-T peak in the resistivity has been analyzed using Fisher and Langer's expression based on the Friedel Model proposed for critical transitions in transition metals (s–d systems). The fitted results are in satisfactory agreement with the predictions of this model.     

Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives

Phase transitions in spin-glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the “community detection” problem when cast in terms of a general Potts spin-glass type problem. As such, our results apply to rather broad Potts spin-glass type systems. Community detection describes the general problem of partitioning a complex system involving many elements into optimally decoupled “communities” of such elements. We report on phase transitions between solvable and unsolvable regimes. A solvable region may further split into “easy” and “hard” phases. Spin-glass type phase transitions appear at both low and high temperatures (or noise). Low-temperature transitions correspond to an “order by disorder” type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered (or an unsolvable) phase. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard computational problems and spin glasses. The correspondence between the two types of transitions (spin glass and dynamic) is likely to extend across a larger spectrum of spin-glass type systems and hard computational problems. We briefly discuss potential implications of these transitions in complex many-body physical systems.     

EHF–Resonance Studies of Energy Gap in Reentrant Magnets

An EHF-resonance technique of millimeter wavelength band was used for the study of reentrant magnetic systems (Fe _p Ni _1–p ) ₇₇ B ₁₃ Si ₁₀ (p=0.09; 0.10) at low temperatures (down to 0.3K) and high applied magnetic fields. The linear dependence of magnetization on the temperature that characterizes the spin-glass state in such reentrant systems in strong magnetic field was discovered. The energy of localized excitations characterizing spin-glass state was estimated.     

Boltzmann distribution of free energies in a finite-connectivity spin-glass system and the cavity approach

At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of the same macroscopic state, while it can not spontaneously jump between two different macroscopic states. Ergodicity of the whole configurational phase space of the system, however, can be recovered if a temperature-annealing process is repeated an infinite number of times. In a heating-annealing cycle, the environmental temperature is first elevated to a high level and then decreased extremely slowly until a final low temperature T is reached. Different macroscopic states may be reached in different rounds of the annealing experiment; while the probability of finding the system in macroscopic state α decreases exponentially with the free energy F _α (T) of this state. For finite-connectivity spin glass systems, we use this free energy Boltzmann distribution to formulate the cavity approach of Mézard and Parisi [Eur. Phys. J. B, 2001, 20: 217] in a slightly different form. For the ±J spin-glass model on a random regular graph of degree K = 6, the predictions of the present work agree with earlier simulational and theoretical results.      

Magnetic properties for the Mn2GeTe4 compound

Measurements of magnetic susceptibility χ, in the temperature range from 2 to 300 K, and of magnetization M vs. applied magnetic field B, up to 5 T, at various temperatures were made on polycrystalline samples of the Mn₂GeTe₄ compound. It was found that Mn₂GeTe₄ has a Néel temperature T_N of about 135 K, shows mainly antiferromagnetic behavior with a very weak superimposed ferromagnetic component that is attributed to spin canting. Also, the magnetic results suggest that a possible spin-glass transition takes place at T_f≈45 K. The spin-glass order parameter q(T), determined from the susceptibility data, was found to be in agreement with the prediction of conventional spin-glass theory. The M vs. B results indicated that bound magnetic polarons (BMPs) occur in the compound, and that the effects from BMPs disappear at approximately 80 K. The M vs. B curves were well fitted by a Langevin type of equation, and the variation of the fitting parameters determined as a function of temperature. Using a simple spherical model, the radius of the BMP in the material was found to be about 27 Å; this value is similar to the effective Bohr radius for an acceptor in the II-IV-V₂ and I-III-VI₂ ternary semiconductor compounds.     

The magnetic and superconducting phase diagram of Gd-doped lanthanumsulfides

The system La_3-x( )_xS₄ [where ( ) denotes a vacancy] containing up to 25 at.% Gd is shown to be a model system in which magnetic interactions in metals can be studied. By measuring the temperature dependence of the low field a.c. susceptibility, the superconducting, spin-glass and ferromagnetic transitions can be determined as a function of the Gd concentration. The depression of the superconducting transition temperature mainly follows the theory of Abrikosov and Gor'kov, with a possibility for coexistence of superconductivity and spin-glass magnetic order near a critical concentration of 3 at.% Gd. The transition from spin-glass to ferromagnet is well-defined with the percolation limit for the long range ferromagnetic order at 14 at.% Gd.     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Vacancy-induced spin-glass behavior of Prussian blue analogue Fe1.1Crx[Cr (CN)6]0.6−x·nH2O nanowires

Prussian blue analogue Fe^II_1.1Cr^II_x[Cr^III(CN)₆]_0.6−x·nH₂O nanowires were synthesized by electrodeposition. The magnetic properties investigation indicates that the nanowires exhibit cluster spin-glass behavior, which undergoes a magnetic transition to a frozen state below about 62 K. Spin disorder arising from reduced coordination and broken exchange bonds between spin centers due to the structural defects may be the reason that causes the spin-glass freezing behavior. The negative magnetization observed at temperature lower than the compensation temperature (T_comp∼43 K) at a field of 10 Oe may be due to the different temperature dependences of the ferromagnetic site Fe-Cr and antiferromagnetic site Cr-Cr.     

Spin-glass-like behaviour and long-range order in dilute YTb alloys

Using neutron diffraction, we have examined the magnetic ordering of two YTb alloys whose magnetic properties are characteristic of spin-glass materials. For YTb_{5 at %} we have determined that a spiral state appears below the susceptibility cusp at 26.6 K, despite differences between field coolled and zero field cooled magnetization. No evidence for long-range order was found for YTb_{3 at %} below its cusp at 15.5 K. We conclude that irreversibility alone can not be used to characterize the spin-glass state.     

Spin glasses on thin graphs

In a recent paper [C. Baillie, D.A. Johnston and J.-P. Kownacki, Nucl. Phys. B 432 (1994) 551] we found strong evidence from simulations that the Ising antiferromagnet on “thin” random graphs — Feynman diagrams — displayed a mean-field spin-glass transition. The intrinsic interest of considering such random graphs is that they give mean-field theory results without long-range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle-point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin-glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.

We then investigate numerically spin glasses with a ±J bond distribution for the Ising and Q = 3, 4, 10, 50 state Potts models, paying particular attention to the independence of the spin-glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution P(q) for all of the models. The parallels with infinite-range spin-glass models in both the analytical calculations and simulations are pointed out.     

Magnetism in FeNiW disordered alloys: Experiment and theory

We report here an experimental study of magnetization of FeNiW alloys at different compositions. We have studied variation of magnetization with temperature (at low external fields) and magnetic field (at low temperatures). The alloy shows para to ferromagnetic transitions across the composition range. We do not find any indication of the spin-glass phase. We have supplemented the experimental work with theoretical analysis using the first-principles tight-binding linear muffin-tin orbitals based augmented space recursion method. Our theoretical estimates of magnetic moment and Curie temperatures agree well with experiment. Our mean-field phase analysis also does not indicate the possibility of a spin-glass phase.