Diluted Spin Systems Research Articles

Itinerant ferromagnetism in a spin-fermion model for diluted spin systems

Itinerant ferromagnetism in a spin-fermion model for diluted spin systems

Computer Simulation of the Phase Transitions in Three-Dimensional Weakly Diluted Spin Systems

Computer Simulation of the Phase Transitions in Three-Dimensional Weakly Diluted Spin Systems

Optimized two-dimensional networks with edge-crossing cost: Frustrated antiferromagnetic spin system.

We consider a quasi-two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute antiferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean-field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

Singular self-energy for itinerant electrons in a dilute Ising spin bath

We consider itinerant spinless electrons moving as defects in a dilute two-dimensional Ising spin system, leading to an effective interaction mediated by spin fluctuations. Coupled self-consistent equations are analyzed after expressing the spin and fermion operators in terms of Grassmann variables. The effective mass, density of states, and specific heat are evaluated. We found that at low temperature and low electron density the effective mass is reduced, whereas in the critical region it sharply diverges. At higher temperature, the fermions behave like a Fermi liquid with a small enhanced mass.

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz, Leone and Toninelli proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution [5] and a general distribution [6]. Panchenko and Talagrand [16] simplified the proof and generalized the result of [5] for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks [21] and allows to bypass the arguments in [6] based on the study of the Sherrington-Kirkpatrick (SK) model.

Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices

The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components are described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different 29Si concentrations in magnetic fields directed along three crystallographic axes is considered.

Copper(II) complex of new non-innocent O-aminophenol-based ligand as biomimetic model for galactose oxidase enzyme in aerobic oxidation of alcohols

Mononuclear copper(II) complex of tetra-dentate o-aminophenol-based ligand (H2LBAPP) has been synthesized and characterized. The three dentate precursor (HLBAP) of the final ligand was synthesized first, while the title four-dentate copper bound ligand was synthesized in situ, isolated only in the final copper species [CuLBAPP]. This copper coordination complex reveals a distorted square-planar geometry around the copper(II) centre by one oxygen and three nitrogen atoms from the coordinating ligand. The ligand is thus twice deprotonated via hydroxy and amine groups. The complex is red, non-typical for copper(II), but the effective magnetic moment of 1.86 B M. and a single isotropic symmetry EPR signal with g 2.059 confirm a S = 1/2 diluted spin system, without copper-copper magnetic coupling. Electrochemical oxidation of this complex yields the corresponding Cu(II)–phenyl radical species. Finally, the title complex CuLBAPP has shown good and selective catalytic activity towards alcohol to aldehyde oxidation, at aerobic room temperature conditions, for a set of different alcohols.

Variational Problems with Percolation: Dilute Spin Systems at Zero Temperature

We study the asymptotic behavior of dilute spin lattice energies by exhibiting a continuous interfacial limit energy computed using the notion of Γ-convergence and techniques mixing Geometric Measure Theory and Percolation while scaling to zero the lattice spacing. The limit is not trivial above a percolation threshold. Since the lattice energies are not equi-coercive, a suitable notion of limit magnetization must be defined, which can be characterized by two phases separated by an interface. The macroscopic surface tension at this interface is characterized through a first-passage percolation formula, which highlights interesting connections between variational problems and percolation issues. A companion result on the asymptotic description on energies defined on paths in a dilute environment is also given.

Field-Theory Description of Nonequilibrium Critical Dynamics for Spin Systems

Renormalization-group approach is applied to investigate the short-time nonequilibriumcritical behavior of pure and diluted spin systems with nonmagnetic point-like impurities.The dissipative relaxation dynamics with non-conserved order parameter is considered. For thefirst time the description of the order parameter growth induced by the initial nonequilibriumstate of system is carried out at fixed dimension d = 3 without use of ε-expansion.

Nuclear quadrupole double resonance spectrometer with magnetic property measurement system direct current superconducting quantum interference device detector and automatic tuning

A new nuclear quadrupole double resonance spectrometer based on a commercial superconducting quantum interference device (SQUID) setup (a Magnetic Property Measurement System (MPMS) from Quantum Design) is described. The experiment involves the indirect detection of pure quadrupole resonances (PQR) of a dilute spin system via the direct SQUID detected NMR of an abundant spin system. The experiment is conducted at low (3-20 K) temperatures and the magnetic field is cycled between a high (5.5 T) polarizing field, to an intermediate (0.1 T) detection field, to zero field where the sample is irradiated with a modulated search RF and back to the detection field. Loss of the NMR signal indicates the detection of a PQR. The RF circuit used for both the NMR and zero field irradiation is digitally controlled. Use of the External Device Control allows for the complete automation of the system. Test measurements on diphenyl ether are in good agreement with previously reported results. Pure (17)O quadrupole resonances were detected for spin systems with concentrations as low as 120 μM.

Overview of Spin Temperature, Thermal Mixing and Dynamic Nuclear Polarization

The aim of this short article is to give a very schematic account of the main concepts associated with the spin temperature theory, in nuclear and in dilute electronic spin systems, and their applications to electron–nuclear thermal mixing as a mechanism of dynamic nuclear polarization. The body of existing theoretical and experimental material on these subjects is much too large to be described in any detail, and a selection can be found in the general references and in references therein.

Effects of dilution and disorder on magnetism in diluted spin systems

AbstractThe influence of configurational disorder on the magnetic properties of diluted Heisenberg spin systems is studied with regard to the ferromagnetic stability of diluted magnetic semiconductors. The equation of motion of the magnon Green's function is decoupled by Tyablikov approximation. With supercell approach, the concentrations of magnetic ions are determined by the size of the supercell in which there is only one magnetic ion per supercell in our method. In order to distinguish the influence of dilution and disorder, there are two kinds of supercells being used: the diluted and ordered case and the diluted and disordered case. The configurational averaging of magnon Green function due to disorder is treated in the augmented space formalism. The random exchange integrals between two supercells are treated as a matrix. The obtained magnon spectral densities are used to calculate the temperature dependence of magnetization and Curie temperature. The results are shown as following: (i) dilution leads to increasing the averaged distance of two magnetic ions, further decreases the effective exchange integrals and is main reason to reduce Curie temperature; (ii) spatial position disorder of magnetic ions results in the dispersions of the exchange integrals between two supercells and slightly changes ferromagnetic transition temperature; (iii) the exponential damping of distance dependence obviously reduces Curie temperature and should be set carefully in any phenomenological model. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Accurate heteronuclear J-coupling measurements in dilute spin systems using the multiple-quantum filtered J-resolved experiment

A new solid-state MAS NMR experiment is proposed to accurately measure heteronuclear (19)F-(207)Pb J-coupling constants, even though these couplings are not visible on high speed (19)F 1D MAS spectra; in particular, we demonstrate that the J-resolved experiment combined with scalar multiple-quantum filtering considerably improves the resolution of J-multiplet patterns for dilute spin systems.

Random Multi-Overlap Structures and Cavity Fields in Diluted Spin Glasses

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by Aizenman, Sims and Starr for non-diluted spin glasses. We use such concept to find generalized bounds for the free energy of the Viana-Bray model of diluted spin glasses and to formulate and prove the Extended Variational Principle that implicitly provides the free energy of the model. Then we exhibit a theorem for the limiting RaMOSt, analogous to the one found by F. Guerra for the Sherrington–Kirkpatrick model, that describes some stability properties of the model. Last, we show how our technique can be used to prove the existence of thermodynamic limit of the free energy. The present work paves the way to a revisited Parisi theory for diluted spin systems.

Disorder in diluted spin systems

The influence of substitutional disorder on the magnetic properties of diluted Heisenberg spin systems is studied with regard to the magnetic stability of ferromagnetic diluted semiconductors (DMS). The equation of motion for the magnon Green's function within Tyablikov approximation is solved numerically for finite systems. The resulting spectral density is then used to estimate the magnetization and Curie temperature of an infinite system. This method is suitable for any form of a ferromagnetic exchange interaction. Besides different lattices and spin magnitude $S$, exchange interactions of different range are examined. The results show that, for short-range interaction, no magnetic order exists below the critical percolation concentration, whereas a linear dependence of the Curie temperature on the concentration of spins is found for ferromagnetic long-range interaction.

Crossover behavior in three-dimensional dilute spin systems.

We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.

Replica bounds for optimization problems and diluted spin systems

In this paper we generalize to the case of diluted spin models and random combinatorial optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to prove that the replica method generates variational bounds for disordered systems. We analyze a family of models that includes the Viana–Bray model, the diluted p-spin model or random XOR-SAT problem, and the random K-SAT problem, showing that the replica/cavity method, at the various levels of approximation, provides systematic schemes to obtain lower bounds of the free-energy at all temperatures and of the ground state energy. In the case of K-SAT and XOR-SAT it thus gives upper bounds of the satisfiability threshold. Our analysis underlines deep connections with the cavity method which are not evident in the long range case.

Scaling Hysteresis of Dynamical Transition in Dilute Heisenberg Spin Systems

The Monte Carlo method was employed to perform a numerical simulation for a classical discrete diluted Heisenberg spin system driven by an oscillating external magnetic field. To form the diluted spin system based on the isotropic Heisenberg model, we introduced in the Hamiltonian of the typical Heisenberg model both a random uniaxial anisotropy energy term characterizing an amorphous state with a proportion X and a deterministic uniaxial or triaxial anisotropy energy term representing a crystalline state with a proportion 1—X as balance. The dynamical transitional behavior of the diluted spin system mentioned above, i.e. the hysteresis loop scaled against parameter X and random uniaxial as well as deterministic uniaxial/triaxial anisotropy constants D and A, respectively, was studied in detail. For the first time, a scaling formula correlating the hysteresis loop area Aarea with the parameters X, A, and D has been put forward by us as Aarea ∼ AδDηXσ. The main conclusions are summarized in the following: (i) At a specific value X (defined as Xmin), the investigated spin system gains the minimal hysteresis, which has been supported experimentally in another part of our investigation. (ii) The scaling exponents δ, η, and σ of the diluted spin system are constants independent of the lattice size, the frequency, the amplitude of the driving field, and the temperature of system. The sum of exponents δ + η (≈0.9) of the diluted spin system equals the exponents δ, η of a single either deterministic uniaxial/triaxial or random uniaxial anisotropy spin system. (iii) The specific value Xmin versus the logarithm of the ratio A/D shows a peculiar sigmoidal trend.

SCALING HYSTERESIS OF DYNAMICAL TRANSITION OF DILUTED HEISENBERG SPIN SYSTEM 

The Monte Carlo method was employed to perform the numerical simulation for classical discrete diluted Heisenberg spin system driven by an oscillating external magnetic field. To form the diluted spin system based on isotropic Heisenberg model, we introduced in the Hamiltonian of a typical Heisenberg model both random anisotropy energy term characterizing amorphous state with a proportion X and uniaxial anisotropy energy term representing crystalline state with a proportion 1-X. The dynamical transition behavior of the Spin system mentioned above, hysteresis loop scaled with parameter X and random as well as uniaxial anisotropy constant D and A, respectively, was studied in detail. It has been put forward a scaling relationship between hysteresis loop area and parameter X, A and D as below: Aarea-AδDηXσ . The main conclusions can be summarized below:(1)At a specific value X(defined as Xmin), the investigated system gains minimal hysteresis which has been proved experimentally in our another investigation. (2) The exponents δ,η and σ of the diluted spin system are universal constants, and the sum of δ+η(～0.9) equals the exponent δ,η of single either uniaxial or random anisotropy spin system. (3)The specific value Xmin versus logarithm of the ratio of A/D shows a peculiar sigmoidal trend.

Study of universality class for site-bond correlated diluted spin systems in the n-vector model

Using the mean-field renormalization group approximation, the n-vector model is used to study the critical properties of the site-bond correlated diluted model on d-dimensional hypercubic lattices, by employing two different exchange interactions. The critical temperature and percolation concentrations are obtained. The phase diagram in the T– p plane on a simple cubic lattice for the classical Heisenberg ( n=3) model is presented. The values for the critical magnetic and thermal exponents for classical XY and the Heisenberg models, respectively, are obtained and the results, when compared with the other methods, are an improvement, even for small size clusters. In addition, the relation between the initial slopes for correlated and uncorrelated models is universal.