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     

Critical and Compensation Temperatures of the Ising Bilayer System Consisting of Spin-1/2 and Spin-1 Atoms

The critical and compensation temperatures of the bilayer Bethe lattices with one of the layers having only spin-1/2 atoms and the other having only spin-1 atoms placed symmetrically are studied by using exact recursion relations in a pairwise approach. The Hamiltonian of the model consist of the bilinear intralayer coupling constants of the two layers J ₁ and J ₂ for the interactions of the atoms in layers with spin-1/2 and spin-1, respectively, and the bilinear interlayer coupling constant J ₃ between the adjacent atoms with spin-1/2 and spin-1 of the layers. After obtaining the ground state phase diagram with J ₁ > 0, the variations of the order-parameters and the free energy are investigated to obtain the phase diagram of the model by considering only the ferromagnetic ordering of the layers, i.e. J ₁ > 0 and J ₂ > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent spins of the layers, J ₃ > 0 or J ₃ < 0, respectively. It was found that the system presents both second- and first-order phase transitions and, tricritical points. The compensation temperatures was also observed for the appropriate values of the system parameters. PACS: 05.50.+q 05.70.Fh 64.60.Cn 75.10.Hk     

Phase transition of an antiferromagnetic system of triplet ions with uniaxial anisotropy in a parallel magnetic field

Using a molecular field approximation we study the metamagnetic behavior in a magnetic field parallel to the anisotropy axis, of an assembly of pseudo spins (S = 1) with a single ion uniaxial anisotropy (D) of the same order of magnitude as the magnetic exchange couplings. The ions are divided in two sublattices with an intrasublattice ferromagnetic coupling (J₁) and an antiferromagnetic coupling (J₂) between distinct sublattices. We have taken a particular interest in the evolution of the phase diagram with parameters D, J₁ and J₂ and we have developed the study of the nature of the point separating first and second order transition lines. A comparison with experimental situations concerning FeCl₂ and FeBr₂ is given.     

Spin glass and antiferromagnetism in Kondo-lattice disordered system

The competition between spin glass (SG), antiferromagnetism (AF) and Kondo effect is studied here in a model which consists of two Kondo sublattices with a Gaussian random interaction between spins in different sublattices with an antiferromagnetic mean J ₀ and standard deviation J. In the present approach there is no hopping of the conduction electrons between the sublattices and only spins in different sublattices can interact. The problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields which can be solved at mean field level within the static approximation and the replica symmetry ansatz. The obtained phase diagram shows the sequence of phases SG, AF and Kondo state for increasing Kondo coupling. This sequence agrees qualitatively with experimental data of the Ce₂Au_1-x Co _x Si₃ compound.Received: 9 April 2003, Published online: 9 September 2003PACS: 05.50.+q Lattice theory and statistics; Ising problems - 64.60.Cn Order disorder transformations; statistical mechanics of model systems     

Magnetization curves of a spin- bilayer system (A2) (ApB1−p)1 (B)2 with disordered interfaces

A calculation is presented for the component magnetizations of an infinite multilayer Ising system, consisting periodically of two layers of spin- A ions, two layers of spin- B ions, and a disordered layer interface in between that is characterized by a random arrangement of A and B ions like a two-dimensional A_pB_1−p alloy. The system is a simple cubic Ising-type structure with a coordination number z = 6. The model is general for ferro- and for antiferromagnetic A-B exchange couplings. The A-A and B-B exchange couplings are regarded as ferromagnetic. An effective field theory that goes beyond mean field, is employed to calculate the bulk-like transition temperature, the different component magnetizations as well as the total bulk-like magnetization. The component magnetizations are calculated for different realistic model values of ferro- and antiferromagnetic A-B exchange constants, as a function of temperature and of the concentration parameter p that characterizes the disorder in the interface. We show that the presence of a disordered interface may significantly affect the component and total magnetizations. In particular, for the case of antiferromagnetic exchange couplings, it is shown that the system can acquire a compensation temperature for certain domains of values of the concentration parameter p in the disordered interface.     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

On the random antiphase state in the ± J spin glass model in two dimensions

Numerical calculations of a ground state and the rigidity have been made for samples of 50 × 50 Ising spins interacting via ± J bonds on a square lattice using Edmond's algorithm, a method well established in optimization theory. For some value of the concentration (0.1<x<0.2) of antiferromagnetic bonds (-J), an ordered (rigid) state occurs with zero magnetization due to magnetic wall separating domains of opposite spins. This new phase, here named a random antiphase state, could be an intermediate phase between ferromagnetism and paramagnetism.     

Dynamical mean-field theory of a simplified double-exchange model

Simplified double-exchange model including transfer of the itinerant electrons with spin parallel to the localized spin in the same site and the indirect interaction J of kinetic type between localized spins is comprihensively investigated. The model is exactly solved in infinite dimensions. The exact equations describing the main ordered phases (ferromagnetic and antiferromagnetic) are obtained for the Bethe lattice with (z is the coordination number) in analytical form. The exact expression for the generalized paramagnetic susceptibility of the localized-spin subsystem is also obtained in analytical form. It is shown that temperature dependence of the uniform and the staggered susceptibilities has deviation from Curie-Weiss law. Dependence of Curie and Néel temperatures on itinerant-electron concentration is discussed to study instability conditions of the paramagnetic phase. Anomalous temperature behaviour of the chemical potential, the thermopower and the specific heat is investigated near the Curie point. It is found for J=0 that the system is unstable towards temperature phase separation between ferromagnetic and paramagnetic states. A phase separation connected with antiferromagnetic and the paramagnetic phases can occur only at . Zero-temperature phase diagram including the phase separation between ferromagnetic and antiferromagnetic states is given. Received 28 May 1999 and Received in final form 14 July 1999     

Observation of exchange bias and spin-glass-like ordering in ɛ-Fe2.8Cr0.2N nanoparticles

Nanoparticles of ɛ-Fe_2.8Cr_0.2N system exhibit the exchange bias phenomenon due to the exchange coupling of the spins of the antiferromagnetic (AF) oxide/oxynitride surface layer and the ferromagnetic (FM) nitride core. Exchange bias is observed at 10 K both in the absence and presence of cooling field. Due to the interface disorder, a mixture of parallel and anti-parallel/perpendicular coupling of the AF and FM spins is observed. The roughness of AF-FM interface induces disorder due to the random exchange anisotropy. The saturation magnetization is also found to be drastically lowered as compared to parent ɛ-Fe₃N. Below 58 K, the broad peak (T _E ≅ T _f ) in zero-field cooled (ZFC) magnetization curves indicates the presence of unidirectional anisotropy and spinglass-like ordering, that arises from the freezing of localized frustrated spins.      

Quantum fluctuations and ground state of weakly interacting helix spin chains in a magnetic field

Ferromagnetic spin chains of a hexagonal lattice coupled by a weak antiferromagnetic interaction J₁ develop a helix arrangement if the intrachain antiferromagnetic NNN exchange J₂ is sufficiently large. We show that the classical minimum energy spin configuration is an umbrella when an external magnetic field is applied. The scenario is dramatically changed by quantum fluctuations. Indeed we find that the zero point motion forces the spins in a plane containing the magnetic field so that classical expectation is deceptive for our model. Our result is obtained by controlled expansion in the low field-long wavelength modulation limit. Received: 9 September 1997 / Revised: 15 October 1997 / Accepted: 17 November 1997     

Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest- and next-nearest neighbour interactions (the J ₁-J ₂ model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb₂VO(PO₄)₂ seems to have mixed ferro- and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the J ₁-J ₂ model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of J ₁ and J ₂ from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic J ₁ is also briefly discussed.Received: 19 March 2004, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.-w Theory and models of many-electron systems - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

P.E.HSQC: a simple experiment for simultaneous and sign-sensitive measurement of (1JCH+DCH) and (2JHH+DHH) couplings

The angular information content of residual dipolar couplings between nuclei of fixed distance makes the accurate and sign-sensitive measurement of (¹J_CH + D_CH) and (²J_HH + D_HH) couplings highly desirable. Experiments published so far are typically highly specialized for the effective measurement of a subset of couplings. The P.E.HSQC presented here, is an E.COSY based experiment which allows the simultaneous measurement of all heteronuclear and homonuclear couplings within CH, CH₂, and CH₃ groups in a single spectrum with the necessary precision and sign information. The simplicity of the approach and the absence of artefacts like phase distortions due to antiphase evolution make it ideally suited for coupling determination of organic molecules at natural abundance.     

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

Spin resonance of conduction electrons and EPR of localized moments in a low-dimensional organic conductor [Pd(dddt)2]Ag1.5Br3.5

The EPR spectra of a quasi-two-dimensional organic metal [Pd(dddt)₂]Ag_1.5Br_3.5 contain signals due to the spin resonance of conduction electrons (CESR) and signals due to the localized magnetic moments of Ag²⁺. The system of Ag²⁺ ions exhibits a strong indirect antiferromagnetic exchange interaction characterized by the Weiss constant Θ=−280(25) K, which leads to magnetic ordering at a temperature of T ₀=70(10) K. The same temperature T ₀ corresponds to a strong anomaly in the CESR linewidth. The observed anomaly in the CESR linewidth, as well as some features of the temperature dependence of conductivity in the system studied, are explained by the interaction between conduction electrons and Ag²⁺ ions localized in the anion layers (π-d interaction) and by antiferromagnetic ordering of the spins of Ag²⁺ magnetic ions.     

Magnetoelastic instability in the XXZ rings with next-nearest neighbour coupling

This paper numerically investigates the magnetoelastic instability in the S = 1/2 {XXZ} rings containing finite spins N with antiferromagnetic nearest-neighbour ({NN}) and next-nearest neighbour ({NNN}) coupling. It finds that, as the {NN} anisotropy Δ₁ equals the {NNN} anisotropy \varDelta₂, there exists a critical {NNN} coupling strength J₂^c(≈0.5), at which the systems always locate in dimerized phase for arbitrary large spring constant. As Δ₁ \ne Δ₂, the values of J₂^{\rm c} are dependent on N and the difference of (Δ₁-\varDelta₂).     

Studies of the exactly dimerized bilayer Heisenberg model via strong coupling expansions

The one-triplet excitation spectra and thermodynamic properties for the dimerized phase of the frustrated bilayer Heisenberg model are studied using strong-coupling expansion theory. The model has an exact dimerized ground state as well as exact one-triplet excitations in a special case that the frustration J₂ is equal to the in-plane coupling J₁. We demonstrate that the models with and without frustrations have distinct excitation spectra, so their thermodynamic properties exhibit quite different behaviors. Especially, the low-temperature behaviors of the frustrated model with J ₁=J ₂ are independent of the inter-dimer couplings, due to the exact one-triplet excitations. Received 16 March 2000 and Received in final form 2 July 2000     

A frustrated quantum spin-s model on the Union Jack lattice with spins s > 1/2

The zero-temperature phase diagrams of a two-dimensional (2D) frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number s = 1 and s = \frac32\frac{3}{2}. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength J ₁ > 0, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength J ₂ ≡ κ J ₁ > 0. The bonds are arranged such that on the 2×2 unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with J ₂ = 0) produce an antiferromagnetic Néel-ordered phase, but as the relative strength κ of the frustrating NNN bonds is increased a phase transition occurs in the classical case (s→ ∞) at κ _c ^cl = 0.5 to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a Néel-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling κ _c1 = 0.580 ± 0.015 for s = 1 and κ _c1 = 0.545 ± 0.015 for s = \frac32\frac{3}{2}. In both cases the ground-state energy E and its first derivative dE/dκ seem continuous, thus providing a typical scenario of a second-order phase transition at κ = κ _c1. However, the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. Thus, the phase transition at κ = κ _c1 between the Néel antiferromagnetic phase and the canted ferrimagnetic phase for both the s = 1 and s = \frac32\frac{3}{2} Union Jack models is similar in nature to that found previously for the s = \frac12\frac{1}{2} Union Jack model. It is thus also completely comparable to the transition in the s = \frac12\frac{1}{2} XXZ model on the 2D square lattice between two Néel antiferromagnetic phases, one aligned along the z-axis and the other along some perpendicular direction in the xy-plane.     

Relaxation to Equilibrium for Two Dimensional Disordered Ising Systems in the Griffiths Phase

We consider Glauber–type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder–averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder–average C(t) of time–autocorrelation function satisfies (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J ₀>0, our results apply even if the active bonds percolate and J ₀ is larger than the critical value J _c of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper bound is optimal. This implies the existence of a dynamical phase transition which occurs when J crosses J _c . Received: